Department of Physics

The phonon laser realized in a trapped ion, i.e., a self-sustained mechanical oscillator, has demonstrated the unique characteristics in practically detecting externally applied electric signals without the prerequisite of sideband cooling. Entering the quantum regime via sideband cooling is expected to further improve its sensing performance. Here we report the first experimental realization of a quantum-regime single-ion phonon laser ($\bar{n}<10$) using a trapped $^{40}\mathrm{Ca}^+$ ion and demonstrate electrometry based on its phase-space symmetry-breaking response to weak resonant electric fields. By tuning the phonon-laser parameters, we reveal that the sensing performance is fundamentally governed by the finite-time relaxation dynamics of the underlying open quantum system. We find that a slow Liouvillian relaxation, correlated with the finite experimental interaction window, effectively enhances the dynamic susceptibility while maintaining the structural robustness of the limit cycle. This regime, when applied to the detection of electric fields, produces a shot-noise-limited peak sensitivity of $14.15 \pm 0.77~μ\mathrm{V/m}/\sqrt{\mathrm{Hz}}$ and a minimum detectable field variation of $δE_{\mathrm{min}} \approx 1.83~μ\mathrm{V/m}$. Our results establish quantum phonon lasers as a practical platform for advanced sensing and highlight the central role of Liouvillian dynamics in non-equilibrium electrometry.

Electron transfer through chiral structures can exhibit spin asymmetry, known as the chiral-induced spin selectivity effect, whose microscopic origin remains an open question. While path-interference within the chiral moiety has been proposed as a key mechanism, its experimental validation requires precise and versatile tunability of system parameters. Here we implement a programmable quantum simulation of spin-dependent electron transfer in a donor--chiral-bridge--acceptor model using a trapped ion. The bridge is encoded in internal states of the ion with tunable nearest- and next-nearest-neighbor couplings, while donor and acceptor states are coupled via a spectator bosonic motional mode. We observe spin-dependent interference within the bridge, and further reveal spin-dependence in donor-to-acceptor transfer dynamics, controlled by amplitude and phase of the coupling parameter. Our results identify interference among spin-dependent pathways as a microscopic origin of spin-dependent transfer, and open a route toward quantum simulations of complex chiral lattices with multi-level and bosonic degrees of freedom.

We present an approach based on tensor networks for distributed quantum computing simulation of chemical wavepacket dynamics in a continuous variable representation. The central idea is that the tensor-network representation of the multidimensional time-evolution operator naturally induces an elevated Hilbert space where the dynamics decomposes into a set of independent lower-dimensional propagations. This transformation converts an entangled quantum evolution into a set of parallel computational tasks that can be executed asynchronously across heterogeneous quantum and classical computing architectures. The resulting formalism establishes a direct connection between tensor-network decompositions, uniformly controlled quantum circuits, and asynchronous distributed quantum computing. The approach is developed with a goal towards hybrid quantum/classical implementation, and is appropriate for a general heterogeneous mixture of quantum hardware systems. The experimental realization of the asynchronously distributed quantum processes that arise from the tensor-network decomposition are carried out on the Sandia National Laboratories' trapped-ion quantum computer, where the circuits are compiled using native partial-entangling $XX(θ)$ gates, reducing the expected two-qubit gate infidelity by more than 30\% relative to conventional fully entangling decompositions. We demonstrate the methodology by quantum computing the vibrational spectra of a small protonated water cluster that shows critical quantum nuclear behavior. Such water cluster systems have been found to be challenging for experimental action spectroscopy and for theory, and here, for the first time, we provide results for vibrational spectroscopy that are in agreement with the respective classical results to within 4cm$^{-1}$, thus allowing for the potential for spectroscopic accuracy from quantum computations.

The Th-229 nuclear isomeric state has the lowest energy of all known nuclear excited states, placing it within the reach of current table-top laser technology. This extraordinary property has made this nuclear isomer an attractive candidate for a nuclear optical clock of incredibly high precision and accuracy, both as isolated trapped Th-229 ions and embedded into solid-state platforms. Activity around Th-229 has surged in recent years, driven by breakthroughs in its direct laser excitation. The underlying nuclear physics that gives rise to this unique isomer will be elucidated, as well as the nearly half-century of efforts that led to its direct excitation. The design and systematics of a Th-229 nuclear clock will be discussed, both in ion traps and in the solid-state. These systematics, such as frequency shifts and quenching channels, can be leveraged both to probe the local chemical environment, and as a control knob during clock operation. Finally, the nuclear clock's high sensitivity to the variations of fundamental constants will be discussed.

An ultimate theory of a phase of matter should describe all its universal properties via quantities that are measurable numerically and experimentally. In this work, we present a microscopic universal theory of symmetry-enriched topological quantum spin liquids (TQSLs) in two spatial dimensions, which directly utilizes microscopically measurable quantities to describe the universal properties. This theory applies to generic TQSLs, which can be Abelian or non-Abelian, chiral or non-chiral. The symmetries are also general, which can include both internal and lattice symmetries, unitary and anti-unitary symmetries, and discrete and continuous symmetries. There can be spin-orbit coupling, the microscopic degrees of freedom may transform linearly or projectively under the symmetries, and the symmetries can permute anyons. The input of the theory is some microscopic states with anyons, operators that control the dynamics of anyons, and symmetry actions in the TQSL, and its output is a set of data characterizing the universal properties, whose underlying mathematical structure is a generalization of category theory. Based on this theory, we find an explicit bijective map between the universal data characterizing a TQSL with a symmetry described by a group $G$, where the symmetry actions may include both lattice and internal symmetries, and the corresponding universal data for a TQSL with only an internal symmetry group $G$, and thus establish a precise crystalline equivalence principle. We demonstrate our theory in symmetry-enriched TQSLs realized on quantum processors based on superconducting qubits, trapped ions, and Rydberg atoms, and in each example we verify the Lieb-Schultz-Mattis anomaly matching condition. Our theory provides a solid basis for identifying and manipulating symmetry-enriched TQSLs, which further paves the way for fault-tolerant quantum computation based on these systems.

Gottesman-Kitaev-Preskill (GKP) states are essential non-Gaussian resources for fault-tolerant photonic quantum computing, enabling logical qubit encoding with intrinsic robustness against errors. Several approaches to GKP state preparation have been explored, including measurement-based protocols in circuit QED and trapped-ion systems, cat-state breeding, and photon-subtraction schemes. However, these methods are either restricted to specific platforms or require deep non-Gaussian resource chains with exponentially low success probabilities. Gaussian Boson Sampling (GBS) offers a compelling all-photonic alternative by generating non-Gaussian states through measurement-induced nonlinearity, without the need for matter-based ancilla or active feedforward. Nevertheless, its practical implementation is limited by the exponential computational cost of evaluating matrix hafnians-#P-complete functions that govern photon-number probabilities. To address this challenge, we introduce a two-stage Histogram Gradient Boosting surrogate pipeline that predicts, without any hafnian computation, the optimal heralding pattern, circuit fidelity, and post-selection probability for candidate GBS circuits, while reserving exact quantum simulation exclusively for surrogate-selected candidates. Trained on circuit configurations across 3-5 optical modes, the surrogate achieves 90.0% GKP-detection accuracy on a held-out set, representing a 23.7 percentage-point improvement over the baseline, with a fidelity mean absolute error of 0.032 and a log-scale post-selection probability $R^2 = 0.837$, reducing the total simulation burden by approximately 90%.

Quantum hardware platforms are getting increasingly sophisticated in their ability to simulate condensed matter, including but not limited to strongly-correlated, topological, and non-equilibrium phenomena. This review surveys recent progress in quantum-hardware-based simulations of condensed matter, primarily emphasizing gate-based digital quantum computer simulation, with analog experiments discussed as complementary benchmarks. We first review major hardware platforms, including superconducting qubits, trapped-ions, ultracold atoms, Rydberg arrays, photonic systems, and moire quantum materials. We then introduce the basic ingredients of digital quantum simulation. Building on this foundation, we discuss representative applications to condensed-matter physics, spanning ground-state problems, strongly correlated matter, topological phases, non-equilibrium dynamics, open-system physics, and high-energy-physics-inspired simulations. Finally, we summarize key methodological tools used in state-of-the-art quantum-simulation workflows. We emphasize that present noisy quantum simulations serve not only as near-term demonstrations, but also as prototypes for the encodings, diagnostic protocols and error-control strategies required for future fault-tolerant quantum simulation.

In the presence of a magnetic field, hyperfine clock qubits can acquire a vector differential light shift that can be tuned via polarization to suppress the total differential light shift of high-power, off-resonant laser light. We experimentally measure this "magic" polarization condition, suppressing differential light shifts in both the ${}^2\mathrm{S}_{1/2}$ ground and ${}^2\mathrm{F}_{7/2}^o$ metastable clock qubits of $^{171}\mathrm{Yb}^+$. We present calculations of the minimum bias magnetic fields required to suppress differential light shifts in the ground state clock qubits of commonly trapped ion species, finding that they are below the strengths of fields already typically present in experiments. We further present methods for metastable clock-qubit control in $^{171}\mathrm{Yb}^+$, demonstrating a state preparation and measurement infidelity of $2.9^{+3.0}_{-1.5}\times10^{-4}$ ($-35 \pm 4 \, \mathrm{dB}$).

Large ion crystals in Penning traps provide a platform for quantum simulation and sensing with hundreds of spins, but their continuous rigid-body rotation has so far limited flexible local qubit control. Here we demonstrate programmable site-selective spin control across large rotating ${}^{9}\mathrm{Be}^{+}$ crystals in a Penning trap. A tightly focused off-resonant laser beam drives local $R_z$ phase rotations via differential AC Stark shifts. Beam steering synchronised with crystal rotation enables addressing of arbitrary ions throughout the crystal. Ramsey-based characterisation shows $R_z(π)$ gate fidelity of 94.6% and nearest-neighbour crosstalk of 1.2%. We use this capability to prepare spatially structured spin patterns, generating a biskyrmion spin texture in a single-layer crystal, then extending the method to bilayer crystals we perform layer-selective addressing operations. We further demonstrate dual-quadrature Ramsey sensing by imprinting a relative $π/2$ phase shift between spatial sub-ensembles, enabling simultaneous measurement of orthogonal spin components within a single experimental realisation. These results establish programmable local control in large rotating ion crystals, opening new routes for engineering spatially structured quantum states in multidimensional trapped-ion systems.

The exponential growth of many-body Hilbert space presents a fundamental barrier to quantum technology, obscuring the search for physically significant states within an astronomically vast landscape. Consequently, resources for quantum-enhanced metrology have been largely confined to the symmetric subspace whose dimensionality scales only polynomially with the particle number-leaving the vast majority of the Hilbert space largely unexplored and poorly understood. Here we challenge this paradigm by demonstrating that metrological advantage can arise as a ubiquitous feature across exponential-dimensional manifolds. By tailoring the first-moment structure of random unitaries, we uncover dense manifolds of engineered random states (ERSs) where Heisenberg-limited scaling emerges as a statistically generic property. This ubiquity endows these resource states with inherent resilience against parameter disorder. We experimentally validate this framework on a trapped-ion processor, achieving a metrological enhancement of $6.98 \pm 0.38$ dB beyond the standard quantum limit. Potential applications extend to diverse platforms, ranging from superconducting circuits and waveguide QED to solid-state spins and polar molecules. Our results establish a powerful paradigm where quantum-enhanced precision can be harvested from the exponential vastness of the Hilbert space.

Excitation of trapped-ion hyperfine qubits with fast optical Raman pulses enables faster-than-trap-period entangling gates with qubits of long coherence time for practical quantum computation. Achieving high-fidelity fast two-qubit gates requires high-quality spin-dependent kicks (SDKs), which form their fundamental building blocks. Here, we characterize the control parameters (including Raman frequency difference, pulse arrival times, Lamb--Dicke parameter, temperature, pulse width, and SDK time) that maximize the performance of single-ion SDKs for protocols compatible with performed experiments involving a small number of fast pulses. We demonstrate through analytical methods and numerical simulations that, within the model commonly used for infidelity optimization, finite pulse duration is the dominant source of error, exceeding the contribution of secular motion by orders of magnitude for nanosecond-scale SDKs. Low infidelities -- below $10^{-3}$ for schemes with $\gtrsim10$ fixed-amplitude, equispaced, picosecond pulses -- are achievable in SDK times on the order of nanoseconds. These results provide quantitative design rules for achieving competitive SDK fidelities with current pulsed-laser technology, laying the foundation for sub-microsecond trapped-ion quantum entangling operations.

AC mains power line-synchronous disturbances are a common source of coherent, time-dependent error in precision quantum-control experiments. We show that when these disturbances are reproducible with respect to the mains phase, their effect can be measured in a line-triggered frame and compensated through software updates to control sequences. In our system, the disturbances manifest as magnetic-field-induced shifts in the energy level structure of a trapped $^{137}\text{Ba}^+$ ion, resulting in time-dependent detunings between the ion transitions and a local oscillator, as well as additional phases accumulated on superpositions of energy levels. We demonstrate a compensation protocol that corrects for the instantaneous oscillator detuning during control pulses, and for the phase accumulated by the energy levels between pulses. The calibrated AC line contribution to the detuning is reduced by $21(9)\times$, while the fitted AC phase amplitude is reduced below the measurement uncertainty. We then study gate performance on a magnetic-field-sensitive qubit and find that uncompensated mains-synchronous errors produce time-dependent fluctuations that make the usual randomized-benchmarking decay model unreliable. With compensation enabled, these fluctuations are suppressed sufficiently to recover a standard benchmarking decay and extract an average gate fidelity of $99.93(1)\%$. Finally, we extend the framework to multilevel qudit control and apply it to a single-qudit Bernstein-Vazirani algorithm, where AC compensation increases the success probability on a 16-level qudit from $10(7)\%$ to $70(9)\%$. These results show that reproducible line-synchronous noise can be treated as a calibrated control-frame error and corrected without additional hardware.

Quantum phase estimation (QPE) is an underlying technology for extracting the excitation spectra of many-electron systems, yet its practical use on current hardware is hindered by low grid resolution and environmental noises. Here we propose QPE averaged over variable grids (QAVG), a vernier-type approach that combines low-resolution QPE with multiple origin shifts and physically motivated continuous parametrization to reconstruct the spectra accurately. We introduce this approach into an end-to-end workflow for the {\it ab initio}-based model system for a CO molecule adsorbed onto the $χ$-Fe$_5$C$_2$ surface. We perform experiments on Quantinuum H2-2 using both physical QPE circuits and logical QPE circuits encoded in the Steane code with offline bit-flip correction. We demonstrate that QAVG accurately reconstructs the spectra with deviations much smaller than the nominal QPE resolution, even when the noisy histograms are used. The cost landscapes averaged over the shifted grids substantially suppress the local minima arising from the spectral leakage, thereby stabilizing the optimization of trial parameters. These results indicate that QAVG provides a robust route to quantum simulations of correlated spectra toward the era of early-fault-tolerant quantum computers.

Microwave dressing of Rydberg ions creates tunable eigenstates with controllable polarizability and interaction strength, but coherent navigation between these states has remained elusive. Here, we report on the first demonstration of coherent population transfer between different Rydberg states of a trapped ion. We investigate both microwave-mediated Rabi oscillations between Rydberg S and P states and adiabatic transfer between microwave-dressed Rydberg states. Between Rydberg S and P states we achieve a population transfer efficiency of 91.5(5)% in a single microwave $π$-pulse. Microwave dressing hybridizes the S and P Rydberg states into new eigenstates with tunable polarizability, enabling both noise-resilient zero-polarizability states and maximally interacting states. We demonstrate adiabatic transfer between these zero-polarizability and maximally dressed states, enabling experiments that combine noise-resilient excitation with strong dipole-dipole interactions and Förster resonance control within a single measurement sequence.

We run a numerical linked-cluster expansion with a quantum algorithm (NLCE+QA), computing ground-state energies and one quasi-particle dispersions in the thermodynamic limit using a 20-qubit trapped-ion quantum processing unit (QPU). The NLCE+QA framework extracts thermodynamic-limit properties from small-cluster calculations, making it naturally suited for near-term quantum devices. Projector-based block-diagonalization schemes such as projective cluster-additive transformation (PCAT) are essential to NLCE+QA, and they involve matrix inversion and square root operations that amplify measurement noise. A central question is therefore whether current hardware can provide expectation values that are accurate enough to withstand non-linear classical post-processing. We explore this challenge for the transverse-field Ising model (TFIM) in one dimension, on a ladder geometry, as well as in a longitudinal field in one dimension. For the quantum algorithm, we consider adiabatic state preparation (ASP), as well as a variational quantum eigensolver (VQE) trained on a classical device. The final expectation values are obtained from the QPU, using a novel alternative to the Hadamard test that we name the CX-test. We explore the regimes currently attainable on quantum devices and comment on the improvements needed for quantum computers to achieve results beyond classical reach.

We construct a detailed microscopic noise model for multi-qubit (MQ) gate operations in the context of trapped ion architecture with all-to-all connectivity. We find that phonon heating and motional dephasing are well captured by effective single- and two-qubit error channels that can, in principle, act between arbitrary pairs of qubits. Nevertheless, the median magnitude of two-qubit errors between uncoupled qubits is substantially smaller than that of errors between gate-coupled qubits. Errors associated with photon scattering are shown to solely propagate to qubits participating in gate operations. Lastly, we combine all noise sources, assigned with experimentally relevant parameters, and explore the scalability of a quantum error correction (QEC) scheme based on the rotated surface code, as a function of error rates and code size. Our analysis bridges device-level physics and QEC performance for MQ gates in trapped-ion architectures.

Quantum simulations are traditionally confined to exploring dynamics starting from unentangled or low-entanglement states due to severe bottlenecks in protocol design, hardware performance, and classical verification. Here, we report the first experimental observation of non-equilibrium dynamics initiated directly from a many-body critical state. Using a fully-connected trapped-ion processor, we prepare the critical ground state of a transverse-field Ising model via a hardware-tailored, logarithmic-depth quantum circuit based on multi-scale entanglement renormalization. Following this initialization, we apply a deep Floquet drive that maintains emergent conformal symmetry, enabling us to benchmark the lattice dynamics against analytical results from continuum theory. In the resulting conformal heating phase, we extract a central charge consistent with the Ising universality class ($c=1/2$) from the universal decay of the Loschmidt echo and observe spatial energy localization predicted by field theory. Conversely, the non-heating phase exhibits global finite-time revivals. This work establishes a scalable and versatile framework for exploring critical quantum dynamics.

Quantum-enhanced multiparameter sensing is often associated with distributed architectures or 2-anticoherent states, whereas squeezing in a single collective ensemble is typically limited to single-parameter metrology. Here, we show that a single ensemble can support simultaneous multiparameter squeezing when each sensor is promoted from a qubit to a qudit (i.e., spin with $d$ energy levels). We develop a general framework in which the optimal product probe state, the corresponding global readout observables, and the associated squeezing parameters are all determined from the single-site quantum Fisher information matrix. We then present a minimal qudit construction for two-parameter vector magnetic field sensing with local dimension $d=3$. We further identify a collective twisting-like interacting Hamiltonian that generates such multiparameter-squeezed states and numerically demonstrate scalable metrological gain. In particular, for a trapped-ion qutrit chain with power-law interactions, we obtain up to 12 dB enhancement in two-parameter sensing for $N=256$ sensors. Our results establish qudit-enabled multiparameter squeezing in a single ensemble as a distinct route to multiparameter quantum metrology with global readout, and highlight its potential advantage over distributed multi-ensemble strategies in the fixed-sensor-budget regime.

Electron and ion-cyclotron waves are well known to exist in solar system plasmas but their existence and importance in galaxy clusters is an open question. Guided by numerical simulations, (Ley et al. (2024)) argued that whistlers (electron-cyclotron) and ion-cyclotron (IC) waves are generated by trapped particles in mirror modes in the nonlinear stages of the mirror instability under ICM conditions. Building on this work, we construct a novel particle propagation simulation of the ICM plasma based on the static electromagnetic field configuration from the fully kinetic particle-in-cell (PIC) simulation of the nonlinear mirror instability by (Ley et al. (2024)). We study how the trapping rate of particles is related to the secondary waves driven by mirror modes. We observe that secondary whistlers and IC waves enhance trapped particle escape from mirror modes. We measure the particle-wave scattering rate by whistlers and IC waves, demonstrate that the scattering rates and wave amplitudes follow the proportionality relation expected from quasilinear theory, and show the existence of a significant correlation between scattering rates and the excitation of secondary instabilities.

With coupled detuned oscillators, either individual or collective oscillations are observable. The latter is used in quantum information processing in linear Paul traps. Here, we study the transition from collective radial modes at stronger axial confinements into individual radial oscillations at low axial confinements in a tapered Paul trap. The eigenmodes are experimentally studied in detail in the transition regime and compared with theoretical predictions. The features studied will enable investigation of modified heat transport phenomena and defect formation in trapped ions.

We develop a complete theoretical framework for open quantum systems coupled to scale-invariant environments. We show that such environments are universally described by unparticle baths characterized by a single scaling dimension $d_{\mathcal{U}}$. This work provides the proof of the uniqueness theorem, the formalism of the resulting non-Markovian dynamics, and applications to several physical systems. From the uniqueness theorem, we derive the non-Markovian memory kernels, the exact noise kernel including vacuum and thermal contributions, and a fractional generalization of the Caldeira-Leggett master equation for arbitrary $d_{\mathcal{U}}$. The scaling dimension governs a rich phase structure, including a thermalization transition at $d_{\mathcal{U}}=3/2$, the Ohmic boundary at $d_{\mathcal{U}}=2$, and a decoherence transition at $d_{\mathcal{U}}=5/2$ in the thermal regime, beyond which long-time quantum coherence is protected. Three realizations are studied. For the quantum Ising model at criticality, coupling to the energy operator in $(1+1)$ dimensions gives $d_{\mathcal{U}}=3/2$, producing $1/f$ noise, while the $(2+1)$D case yields $d_{\mathcal{U}}\approx1.413$ from the conformal bootstrap. In inflationary cosmology, massless scalar and graviton baths in de Sitter spacetime give $d_{\mathcal{U}}=2$, predicting linear decoherence growth consistent with the quantum-to-classical transition. For high-energy astrophysical neutrinos, the decoherence rate $Γ_{\mathrm{decoh}}\propto \mathcal{B}(E,T_{\mathcal{U}})L^{5-2d_{\mathcal{U}}}$ provides an observable signature of the scaling dimension. We also compare the framework with Caldeira-Leggett and Lindblad approaches, analyze the validity regimes, and discuss experimental implications for trapped-ion simulators, neutrino telescopes, and superconducting qubits.

We present measurements of K-shell x-ray emission following charge exchange of fully ionized argon with various neutral gaseous targets at small collision energies inside an electron beam ion trap. We also resolve the principal quantum number of electron capture in extreme-ultraviolet spectra from initially bare and hydrogen-like oxygen ions held in the same trap. We analyze discrepancies between these as well as previous measurements with theoretical models based on the multichannel Landau-Zener approach.

Stochastic resonance (SR) could amplify weak electric-field signals in nonlinear systems by means of the externally injected noises. Here we propose and experimentally demonstrate a modified SR method, termed squeezing-induced SR, implemented in the system involving a trapped ion behaving as a Duffing oscillator. We find that squeezing the phase noise of the oscillator results in amplified fluctuation of the corresponding amplitude, which helps achieve the SR. Since no auxiliary noise source is needed, the squeezing-induced SR may enhance the signal-to-noise ratio by 4.28 $\pm$ 0.39 dB compared to the conventional noise-induced SR under identical conditions of the electric-field detection. This technique offers a promising approach for developing atomic ion sensors for detecting weak electric-field signals.

The Jaynes-Cummings (JC) interaction-the coherent exchange of excitations between a two-level system and a harmonic oscillator-is one of the fundamental interactions of quantum optics, realized across platforms such as cavity quantum electrodynamics, trapped ions, mechanical resonators, and superconducting circuits. Although JC interactions and qubit rotations form a universal gate set for oscillator control, practical implementations have not been demonstrated. Here we develop and experimentally demonstrate universal JC-based oscillator control by compiling arbitrary unitary gates into sequences of JC interactions and qubit rotations. In our experiment, the oscillator is realized using a mode of a high quality factor microwave cavity and the ancilla qubit using a superconducting transmon circuit, with the JC interaction implemented by a sideband interaction enabled by the Josephson nonlinearity. The native gates are constructed to be closed below a chosen cutoff photon number, encoding a qudit with suppressed leakage errors, while ancilla relaxation errors are detectable. We further find that the dispersive shift serves as a compilation resource that reduces circuit depths. We demonstrate universal qudit control and implement a single-qutrit gate set with a mean post-selected process fidelity of 96%, as well as ququart and ququint shift gates. These results establish Jaynes-Cummings control as a practical route to universal oscillator control, enabling programmable bosonic processors across a variety of quantum platforms.

Variational compression can significantly lower implementation overheads for encoding the time evolution of Hamiltonians into quantum circuits. However, they usually lack global convergence guarantees and well-established scaling behavior. In this work, we provide a recipe for choosing the initial point of such variational optimizations that guarantees convergence to a quantum circuit with near-optimal gate complexity $\mathcal{O}\left( N \, t \, \text{polylog}(N \, t/ε) \right)$ for all local and translationally invariant Hamiltonians. We demonstrate our method by encoding the globally controlled time evolution of a Heisenberg antiferromagnet on a Kagome lattice. For $N = 48$ sites, evolution time $t=0.1$ and infidelity $ε\approx1\%$, the controlled time-evolution circuit requires 960 two-qubit B gates, for which we propose a straightforward implementation scheme for ion-trap setups. Thereby, our recipe extends digital quantum simulators toward system sizes and geometries that are challenging for classical computation.

Building on the demonstrated sensitivity of the Heavy Ion Monitor on a Chip (HIMoC) presented in Part I of this work, we performed additional irradiation exposures using 24.8 MeV/u beams of $^{14}$N, $^{22}$Ne, and $^{40}$Ar at the Texas A&M University Cyclotron Institute. A novel simulation workflow was developed that couples the particle-transport toolkit Geant4 with the open-source TCAD simulator DEVSIM to model the heavy-ion-induced signal in HIMoC devices. The model represents energy deposition by primary heavy ions and secondary electrons as Gaussian charge-loss profiles that produce measurable threshold-voltage shifts in the device. Good agreement between simulated and experimental $ΔV_{\mathrm{th}}$ distributions was obtained. HIMoC was also shown to generate a signal that scales approximately linearly with a dose-like quantity proportional to ion fluence, LET, and active detector area. These results support HIMoC as a passive heavy-ion dosimeter and provide a framework for modeling the effects of radiation-induced charge loss in charge-trapping non-volatile memory devices.

Microfabricated ion trap chips are at the core of some of the most advanced quantum computers. How a large number of ions is arranged and controlled on an ion trap chip depends on the chosen trap architecture. One such architecture is the quantum spring array (QSA). In the QSA architecture, ion chains are arranged in a two-dimensional lattice and interact with ion chains in neighboring sites in the radial and axial directions of the respective chain. This interaction, or coupling, is mediated by the Coulomb force while keeping ions in separate trapping sites, and scales inversely with the third power of the separation. The capability to control the distance between ions in the lattice is thus essential. In previous works, the radial separation between ions was tuned by controlling the rf pseudo-potential, which revealed to be experimentally challenging to realize while maintaining low heating rates. In this work, we present an ion trap chip design that allows tuning of the radial distance between ions using only dc voltages. The radial transport is executed between different interaction zones, designated for quantum operations, through specifically designed transition zones. A prototype of this type of ion trap chip was microfabricated on fused silica substrate. Its functionality is characterized by demonstrating dc-controlled radial transport of a single ion through a transition zone and measuring stray fields and ion heating rates in the center of the trap. Moreover, the fabrication of a multi-metal layer version of such a trap is presented as a scaling path for the presented chip design.

How much energy does a quantum computer consume? Are they more efficient than their classical counterparts? In this work, we make a step towards answering these questions. We define the energy efficiency of a quantum computer as the ratio of the number of algorithms it can perform during a given time over the energy consumed by the hardware during this time. We analyze the most representative physical platforms currently envisioned to be used as building blocks of quantum computers: superconducting qubits, silicon spin qubits, trapped ions, neutral atoms and photonic qubits. Including insights from experts in all these technologies and taking into account algorithm compilation constraints, we discuss the advantages and inconveniences of each platform from an energy standpoint. Beyond providing concrete values of the energy consumption of current quantum computers, we lay the foundation of a framework to benchmark the energy efficiency of any future quantum computing architecture.

Nitrogen-bearing polycyclic aromatic hydrocarbons (N-PAHs) are key precursors to complex organic molecules in both the interstellar medium and the nitrogen-rich planetary atmospheres. Despite the recent detections of nitrogen-functionalized astromolecules, their formation pathways remain an open question. The discrepancies between their predicted and observed abundances point to unknown mechanism that govern their evolution in the astrophysical environments. Employing an ion trap technique and electronic structure calculations, we unravel multiple barrier-less reactions between gas-phase pyrimidine cations (C$_4$H$_4$N$_2^+$) and acetylene (C$_2$H$_2$) which form an hitherto unreported endocyclic- N-PAHs (C$_8$H$_7$N$_2^+$). The present measurements on reactions involving a double-nitrogen subsituted aromatic heterocycle have implications to the astrochemistry of both the Titan's atmosphere and interstellar medium.

Recent work has identified a dynamical squeezing phase transition in power-law interacting bilayer XXZ spin models, separating a fully collective phase with Heisenberg-limited squeezing from a partially-collective phase with universal critical scaling. Here we test and establish the universality of this transition along two qualitatively different microscopic axes: lattice geometry, by studying square, triangular, and honeycomb $2\mathrm{D}$ bilayers as well as $1\mathrm{D}$ ladders, and a symmetry-preserving rescaling $λ$ of the interlayer couplings relative to the intralayer ones. Combining a Bogoliubov instability analysis with discrete truncated Wigner simulations, we find that the transition persists across all four lattice geometries and over a wide range of $λ$ with critical exponents consistent within error, providing strong evidence for a genuine non-equilibrium universality class. The Bogoliubov theory recovers the previously identified scaling $a_Z^* \propto L$ in the long-range interacting regime $α< d+2$, and yields an analytical scaling $a_Z^* \propto L^{2/(α-d)}$ for the critical aspect ratio with system size for $α>d+2$, with $α$ the power-law exponent in dimension $d$. This uncovers a previously unrecognized sub-linear regime for short-range interactions. By tuning $λ$ we vary the interlayer coupling strength at fixed layer spacing, demonstrating that the dynamical transition can be driven purely through interaction engineering without modifying the underlying geometry. These findings provide a versatile route toward controlling entanglement generation in Rydberg-array, polar molecule, and trapped-ion platforms with applications in quantum sensing and simulation.

For a single trapped ion, the excitation spectrum of a narrow optical transition consists of a Doppler- and recoil-free carrier accompanied by motional sidebands, which are equally spaced by the trap secular frequency and lie under a Doppler-broadened envelope that is shifted by the photon recoil. Outside the Lamb-Dicke regime, the large photon recoil distributes the line strength across many sidebands and suppresses excitation of the carrier. With multiple ions, the motional spectrum becomes dense, and the carrier is further weakened. Here, we predict a counterintuitive revival effect: increasing the number of ions in a linear chain can restore strong carrier excitation even under trapping conditions far from the single-ion Lamb-Dicke regime. Using a quantum-mechanical model of the excitation dynamics in linear ion chains, we find that sufficiently long chains concentrate the spectrum into the carrier. This effect enables efficient excitation of light ions at short wavelengths. It may also benefit multi-ion optical clocks and mixed-species quantum-logic spectroscopy.

We leverage recent advances in 3D-printing technology to design and fabricate a micro-ion trap with a spatially distinct loading zone for more efficient loading of ions from effusive thermal ovens. The design reduces the Mathieu-$q$ parameter in the loading zone by increasing the ion-electrode separation $r_0$, thereby potentially facilitating more effective laser cooling of hot ions. This circumvents the temporary thermal instability that arises when the rf potential is reduced during ion loading, a common practice to enable efficient laser cooling of hot ions. Simulations predict that expanding $r_0$ maintains a high trapped ion fraction from a simulated thermal source across a wide range of Mathieu-$q$ parameters. We demonstrate the manufacturability of this design by 3D-printing the rf rails of a four-rod ion trap and discuss the limitations imposed by state-of-the-art additive manufacturing techniques. We briefly compare hot-ion capture in the three-dimensional design presented here with that in a representative planar trap, illustrating one instance in which the former may be better for loading. The article concludes with an outlook for how this design may be incorporated into a quantum-CCD architecture to enhance ion loading and reduce associated experimental overheads.

The accurate estimation of observables is a crucial task in quantum computing. Recent advances have highlighted the need for (a) specialized protocols for qudit-based devices, that include (b) error-aware strategies. Here, we present AQUIRE, the first protocol that can (a) accurately estimate both the mean and the error of an observable on qudit-based quantum computers. AQUIRE achieves this by constructing a Bayesian model to accommodate generalized Pauli operators. It is designed to continuously monitor the estimated average and the associated error of the observable, adjusting the subsequent measurements in real-time. Additionally, AQUIRE is (b) device- and experiment-specific error-aware, and accounts for hardware imperfections and experimental noise during the estimation process. We demonstrate AQUIRE's advantage via numerical simulations and showcase its ability to quantify the noise affecting the estimation by implementing it on a trapped-ion qudit quantum processor. By exploiting general commutation relations and overlap grouping measurements, our protocol is state-of-the-art when restricted to qubit-based quantum computers and extends this advantage to the qudit case.

Establishing the precise computational boundary between classically tractable fermionic systems and those capable of genuine quantum advantage is a central challenge in quantum simulation. While injecting non-Gaussian ``magic" inputs into free-fermion circuits is widely expected to generate intractable complexity, we identify a physically motivated intermediate regime. We prove that for block-product paired non-Gaussian fermionic states, essential quantum simulation primitives -- transition amplitudes, overlaps, and arbitrary-weight number correlators -- can be efficiently approximated to additive error under free-fermionic dynamics. This tractability stems from an algebraic reduction that compresses exponentially large multiparticle interference into a single coefficient of a multivariate Pfaffian polynomial. Because these classical estimators match the intrinsic $O(1/\sqrt{K})$ statistical uncertainty of quantum hardware utilizing $K$ measurement shots, they constitute a practical benchmark. Building on this foundation, we construct an additive-error estimator for high-weight Wilson observables in the noninteracting quench of recent trapped-ion experiments, providing a rigorous classical benchmark. Extending this to quantum chemistry, we demonstrate that core overlap-based subroutines for antisymmetrized products of strongly orthogonal geminals admit efficient additive-error Pfaffian-kernel estimators. Ultimately, these results sharpen the boundary of quantum advantage, establishing that the paired-electron scaffold is dequantized and clarifying where quantum resources are indispensable.

Penning traps, renowned for their unparalleled precision in determining fundamental properties such as mass and magnetic moments, are cornerstone instruments in modern physics. Their applications span from nuclear structure studies to stringent tests of quantum electrodynamics and CPT invariance. Although Penning traps have been demonstrated for fundamental studies, often employing superconducting magnets, their high cost and operational complexity remain challenges. In this work, we report the development of a compact cryogenic Penning trap that utilizes a permanent magnet to provide a confining magnetic field, offering a more economical and flexible alternative. We have successfully demonstrated all core functionalities of this system, including ion generation, transport, confinement, manipulation, and signal detection. This compact trap not only serves as a vital technical testbed for the development of the Shanghai Penning Trap, but also establishes a cryogenic Penning-trap experiment platform for ion trapping and cooling applications as well as envisaged spectroscopic studies applications.

As hybrid qubit-oscillator algorithm development and trapped-ion hardware demonstrations advance in parallel, there is a lack of a compilation layer connecting the two at the pulse level in the vertical software stack. While qubit gate control and pulse synthesis are well-established, the translation of hybrid qubit-oscillator primitives to the pulse level has not been systematically addressed. This gap is further compounded by the inherently continuous parametric nature of such gates. Each distinct parameter value defines a physically unique operation requiring independent pulse optimization, making static pre-compilation strategies inapplicable. To fill this gap, we present HyPulse, a hardware-aware pulse synthesis and generation framework, which contributes a two-phase architecture decoupling pulse discovery from circuit assembly. An offline optimization engine populates a content-addressed cache of high-fidelity primitives: If a pulse for a given gate, parameter, and device specification already exists in the library, it is retrieved instantly; otherwise the optimizer synthesizes, hashes, and caches it automatically. An online assembler then constructs circuit-specific pulse programs ready to drive trapped-ion hardware control systems via DAX/ARTIQ (Duke) and JaqalPaw/QSCOUT (Sandia), trapped-ion pulse execution backends.

Parallel processing of information plays a critical role in accelerating computation. This includes quantum computers, where parallel processing of quantum information will play a critical role in practical quantum advantage. Here, we demonstrate a new type of parallel entangling gates in a trapped-ion quantum computer, that simultaneously provides efficient gate-pulse synthesis and calibration, as well as graph-pattern-agnostic implementation. We demonstrate the resulting reduced execution time in three well-known algorithms, exhibiting disjoint gates, a star graph and a ring graph respectively. For disjoint qubit pairs the execution time of our parallel gates is comparable to that of a single-pair entangling gate resulting in an approximately linear speed up. For all graph patterns our parallel gate fidelities are comparable to the fidelity of a single-pair entangling gate. These advantages motivate architectures featuring multiple medium length ion chains in future quantum computing devices.

We propose a quantum-enhanced sensing scheme for the detection of wave-like dark matter and high-frequency gravitational waves using two-dimensional ion crystals in a Penning trap. The protocol employs spin-motion squeezed states to improve the signal-to-noise ratio and enable a super-Heisenberg scaling with respect to the number of ions over a broad parameter range. We analyze the sensitivity of the protocol to representative wave-like dark matter candidates, including the axion-like particle and the dark photon, as well as to high-frequency gravitational waves, taking into account the decoherence and dephasing of the ion spins. Our results indicate that two-dimensional ion crystals and this new protocol provide a promising platform for probing previously unexplored parameter space in searches for light dark matter and high-frequency gravitational waves.

The quantum Mpemba effect (ME) in Markovian systems is conventionally explained by a smaller overlap between the initial state and the slowest decay mode (SDM). Such state, initially farther away from equilibrium or steady state, relaxes faster than closer ones, resulting to a crossing of their trajectories. This picture, by neglecting the transient dynamics, holds in the long-time limit. Here we experimentally observe multiple trajectory crossings (multi-ME) in the relaxation dynamics of a trapped ion. Such novel dynamics takes place in a unusual scenario where the initial state instead has a larger overlap with the SDM. We develop a theoretical framework based on relaxation speed to understand the multi-ME. We show that the initial relaxation speed is governed by the fastest decay mode, which together with the SDM overlap gives a phase diagram that reveals both the occurrence and the types of quantum ME observed in our experiment. Our study goes beyond the simple picture based on the long-time limit, tracks continuously the quantum ME dynamics, and establishes a comprehensive framework to describe the transient quantum relaxation.

The fragility of quantum metrological advantages under loss remains a major barrier to practical quantum sensing. For a two-photon-driven (TPD) Kerr resonator (TPD-Kerr model) subject to unavoidable single-photon loss (SPL), both the quantum Fisher information gain and squeezing level exhibit hard-to-track long-lived damped oscillations, restricting useful sensing and squeezing to extremely short time windows. We show that adding engineered two-photon loss (ETPL) -- forming a TPD-Kerr-ETPL hybrid model -- significantly mitigates these oscillations and converts the decay into a smooth, monotonic drop. This extends the high-sensitivity windows by over an order of magnitude. Moreover, we reveal a temporal hierarchy of quantum resources: the initial boost in metrological sensitivity arises from Gaussian squeezing, while sustained high-precision sensing stems from dissipatively stabilized non-Gaussian even-parity cat states. Crucially, only in models that include ETPL -- such as the TPD-Kerr-ETPL and TPD-ETPL systems -- does the dynamics actively mitigate SPL's detrimental effects, transforming damped oscillation into a smooth, easily trackable trajectory and enabling a prolonged, usable metrological window. Our approach transcends encoding-based or feedback-controlled schemes, offering a fully autonomous route to high-precision measurement without real-time feedback control. This establishes a general design principle: engineered loss, combined with appropriate driving, can actively preserve metrologically useful non-Gaussian quantum resources even in the presence of SPL -- paving the way toward robust, scalable quantum sensors in superconducting circuits, optomechanics, and trapped-ion platforms.

Ion trap quantum computers often store qubits on field-sensitive S_1/2 ground state Zeeman levels of the valence electron, such as in 40Ca+, 88Sr+, and 138Ba+ atomic systems. We experimentally synthesize magnetically insensitive qubit states in multiple metastable electronic D_3/2 Zeeman levels in such an atomic system. We demonstrate coherent operations within the D_3/2 manifold of 138Ba+, including coherent flopping between the synthesized qubit states, and our results agree with theory. Such an encoding may allow for more flexible use of atomic levels for photonic interfaces, and with a measured improvement in the qubit coherence time T2* by a factor of 3, this lays the foundation for further improvement for quantum computing and network applications.

Engineering large-scale quantum computers which simultaneously provide high-fidelity quantum operations, low memory errors, low crosstalk, and reasonable resource usage remains an outstanding challenge across quantum computing platforms. In trapped ions, progress has largely focused on alkaline-earth and ytterbium ions, whose simple electronic structures facilitate control over their internal state. Here we investigate singly-ionized yttrium ($^{89}\mathrm{Y}^+$), a two-valence-electron ion whose ground-state manifold hosts a nuclear-spin qubit and which also features a variety of low-lying metastable manifolds, for applications in quantum information processing. Because experimental data are limited, we perform high-resolution laser-induced fluorescence spectroscopy to measure the hyperfine structure of several low-lying levels, and carry out comprehensive electronic structure calculations to determine lifetimes, transition matrix elements, and hyperfine coefficients for manifolds addressable with visible, near-visible, or infrared wavelengths. Using these results, we analyze schemes for qubit storage, initialization, readout, leakage mitigation, and single- and two-qubit gates. These results position $^{89}\mathrm{Y}^+$ as a uniquely capable next-generation trapped-ion qubit, combining field-insensitive nuclear-spin or clock-qubit storage with spectrally isolated transitions for operations.

The strong dipole-dipole interaction of trapped Rydberg ions offers the possibility of sub-microsecond entanglement gates. For example a two-qubit Control-Phase gate in 88 Sr + ions can be realized, by simultaneous excitation to the Rydberg states via stimulated Raman adiabatic passage (STIRAP) with simultaneous microwave induced dipole-dipole interaction. We show that this excitation protocol distorts the dark-state of the STIRAP stage and is prone to decay from the intermediate state. Here, we propose a novel pulse ordering, in which the STIRAP and the microwave dressing of the Rydberg states occurs in separate stages, preventing mutual interference effects that are detrimental to the gate fidelity. We show that, for experimentally feasible parameters, the proposed excitation scheme can achieve a fidelity of 99.93%, surpassing the experimentally demonstrated gate. In addition, we demonstrate a non-adiabatic speed-up to 400 ns by employing asymmetric pulse shapes in the STIRAP stage. The entangling phase is then controlled solely through the interaction strength by nonresonant asymmetric chirping of the microwave field.

Quantum simulation with controllable many-body platforms offers a powerful route to exploring complex phases and dynamics that are difficult to access in natural materials. Among these, topological spin textures such as skyrmions are central to modern condensed-matter physics and play a key role in chiral quantum many-body systems. Their controlled realisation in large, programmable quantum platforms, however, remains an outstanding challenge. Here, we report deterministic generation and site-resolved reconstruction of topological spin textures in a two-dimensional crystal of more than 150 trapped ions. Using globally applied spin-dependent forces, we generate skyrmion configurations and reconstruct the full vector spin field with single-ion resolution, obtaining a winding number of 0.99$\pm$0.02 and a mean local fidelity of 0.87$\pm$0.04. In addition, we implement single-ion-resolved control to deterministically prepare domain-wall states, extending our approach to a broader class of non-uniform spin textures. These results establish trapped-ion crystals as a platform for engineering complex spin textures and open the door to exploring topology-dependent nonequilibrium dynamics in long-range interacting quantum systems.

One of the promising applications of digital quantum processors is the simulation of many-body quantum systems. They have been already used to investigate several ergodicity violating mechanisms, which were initially discovered in synthetic quantum matter, such as many-body localisation, Hilbert space fragmentation and quantum many-body scars (QMBS). In addition to conventional QMBS, a recently discovered mechanism for ergodicity violation are the so-called asymptotic quantum many-body scars (AQMBS). These become more stable as system size is increased, leading to progressively longer thermalisation timescales. In this work, we show a connection between gapless excitations and AQMBS in certain qudit-based models. We then consider a 2-local model, hosting both conventional and asymptotic scars, in which the AQMBS states are gapless excitations of a ground state localisation transition. By exploiting the structure of the found AQMBS states and the all-to-all connectivity of the Quantinuum H1-1 quantum processor, we prepare these states in logarithmic circuit depth, and probe their thermalisation behaviour under Floquet dynamics. Performing simulations on up to N = 20 qubits and up to 418 entangling ZZ gates, we find slower thermalisation times as the system size is increased, providing the first experimental signatures of asymptotic scars.

We propose a novel measurement-free scheme for stabilizing a spin-oscillator hybrid qubit via autonomous quantum error correction. The engineered Lindbladian renders the code space into an attractive steady-state subspace, realized by coupling the storage mode to a rapidly cooled bath through a controlled beam-splitter and spin-dependent displacement interactions. The continuous variable-discrete variable hybrid approach to autonomous quantum error correction preserves the hardware efficiency of conventional dissipation engineering while simplifying the required system-bath coupling. The construction is compatible with simple logical gates and leverages primitives already demonstrated in experimental platforms, such as trapped-ion systems, suggesting a practical route to hardware-efficient, noise-biased logical qubits without repeated syndrome measurements and feedforward.

Stacking order in bilayers of transition metal dichalcogenides (TMDs) controls structural symmetry and layer-to-layer interactions, offering a direct route to tune their electronic properties and enable optoelectronic applications. The work function is a key parameter that determines the electronic and optoelectronic device performance. However, a comprehensive understanding of the influence of stacking order on work function of TMDs remains limited. Herein, we employ Kelvin Probe Force Microscopy (KPFM) to probe spatial variations in surface potential and thereby determine the work function of AA'- and AB-stacked MoS2 bilayers grown using NaCl-assisted chemical vapor deposition (CVD) technique. The work function increases with layer number in both AA'- and AB-stacked MoS2, with a larger work function difference in AB-stacked layers, reflecting their stronger interlayer coupling. KPFM measurements clearly resolve local electronic heterogeneities arising from carrier trapping at residual surface particulates from CVD growth. Photoinduced surface potential variations imply n-type doping in MoS2 due to enhanced photogating from trapped holes and Na+ ions at the MoS2/SiO2 interface. Our study demonstrates the competing effects of interlayer coupling, substrate-induced photogating, and carrier trapping by surface particulates in determining the localized optoelectronic response of MoS2 bilayers. Correlative atomic force microscopy measurements in lateral force microscopy and force modulation microscopy modes probe the nanomechanical response to electronic variations. These findings provide new insights into the localized optoelectronic response of CVD-grown AA'- and AB-stacked MoS2, with significant implications for the design and reliability of optoelectronic devices.

Quantum simulations of high-energy physics in $2+1$D can probe dynamical phenomena nonexistent in one spatial dimension and access regimes that are challenging for existing classical simulation methods. For string dynamics -- relevant to hadronization -- a plaquette term is required to realize genuine $2+1$D behavior, as it endows the gauge field with dynamics and enables the propagation of photon-like excitations. Here, we realize a U$(1)$ quantum link model of quantum electrodynamics in two spatial dimensions with a tunable plaquette term on a \texttt{Quantinuum System Model H2} quantum computer. We implement, to our knowledge, the largest quantum simulation of string-breaking dynamics reported to date, on a $5 \times 4$ matter-site square lattice using $51$ qubits. The simulation uses a shallow circuit design with a two-qubit gate depth of $28$ per Trotter step and up to $1540$ entangling gates. Starting from far-from-equilibrium string configurations, we measure the probability for the string to propagate within the lattice plane and find signatures of genuine $2+1$D dynamics only when the plaquette term is present. In a resonant regime, we observe the annihilation of string segments accompanied by the production of electron--positron pairs that screen them. We further find that, only with a nonzero plaquette term, matter creation extends across the lattice plane rather than remaining confined to the initial string path. These results experimentally realize string breaking and demonstrate the emergence of dynamical gauge fields in two spatial dimensions, establishing a route to photon-like propagation in programmable quantum simulators of gauge theories.

A major goal of the quantum simulation of high-energy physics (HEP) is to probe real-time nonperturbative far-from-equilibrium quantum processes underlying phenomena such as hadronization in quantum chromodynamics (QCD). The quantum simulation of the dynamics of confining strings and glueballs, both essential aspects of quark confinement, in a controllable first-principles way is an important step towards this goal. Here, we realize a $\mathbb{Z}_2$ lattice gauge theory in $2+1$D with a tunable plaquette term on a \texttt{Quantinuum System Model H2} trapped-ion quantum computer. We implement a shallow depth-6 Trotter circuit on a $6 \times 5$ matter-site square lattice utilizing all $56$ available qubits to execute over $1000$ entangling gates. We prepare far-from-equilibrium initial string configurations that we quench across a range of parameters to observe rich dynamical phenomena, such as the formation of gauge-invariant closed-loop excitations reminiscent of glueballs in QCD and multi-order string breaking accompanied by spontaneous matter creation. We further demonstrate experimentally that the system displays genuine $2+1$D dynamics, as evidenced by string snapshots over time that cannot be trivially mapped to $1+1$D physics. Our results demonstrate digital quantum simulations of nonequilibrium dynamics in a higher-dimensional lattice gauge theory and provide an experimentally accessible setting for phenomena related to confinement physics.

Optical atomic clocks have been rapidly developing in recent decades, resulting in major improvements in both precision and accuracy. As a result, they have become instrumental in multiple areas of applied and fundamental research. Despite all atomic frequency references having more than two energy-levels, the commonly used model for evaluating their ultimate limits assumes a two-level atom. This leads to frequency interrogation protocols and theoretical stability bounds that are suboptimal for a true multi-level atom. The most fundamental stability bound assumes two noise sources - quantum projection noise and spontaneous decay from the excited state. In this work, we analyze a model that includes these noise types and is generalized beyond the two-level assumption, where spontaneous decay can branch to more than a single ground state. This model allows for detection and exclusion of atomic frequency interrogations in which the atom decayed, leading to a frequency stability improvement of up to $\approx 4.5 \text{ dB}$ compared with the two-level model. Furthermore, we identify an even greater stability enhancement of $\approx 5.4 \text{ dB}$ for frequency comparisons between atoms in an odd parity Bell state. These enhancements are particularly relevant for the numerous trapped-ion optical clock species that operate close to lifetime-limited stability. We calculate new stability limits for those cases and provide a detailed experimental protocol for frequency interrogation with an $^{27}\text{Al}^{+}$ optical ion clock.

We propose an adiabatic Ramsey interferometry technique for detecting weak nonlinearities with trapped ions. The method relies on using the quantum Rabi model as a probe, which is sensitive to nonlinear symmetry-breaking perturbations. We show that the couplings which arise either from anharmonic terms of the trapping potential or due to higher order terms in the Coulomb interaction expansion can be efficiently estimated by measuring the spin state probabilities alone. We show that the spin signal is amplified by the mean-phonon excitations, which results in the estimation precision reaching the super-Heisenberg limit. Notably, achieving such high-precision estimation does not require specific entangled state preparation and can be reached even for initial thermal motion state. Furthermore, we show that the super-Heisenberg scaling can be observed even in the presence of weak spin-dephasing.

High-fidelity quantum gates require precise classical control signals, yet the analog hardware delivering these signals introduces nonlinear distortions that degrade gate performance. We demonstrate digital predistortion of an acousto-optic modulator used to generate multi-tone entangling-gate waveforms in a trapped-ion processor based on $^{88}$Sr$^+$. By measuring and inverting the static nonlinear amplitude response of the modulator, we apply a feed-forward correction that extends its linear operating range and suppresses spurious intermodulation products. Spectral analysis of the gate beam shows 3--5 dB suppression of the dominant intermodulation tones, approximately doubling the usable diffraction efficiency at a $10^{-3}$ estimated gate-error threshold. Direct two-qubit Bell-state fidelity measurements confirm that predistortion consistently improves entangling-gate performance. The calibrate-and-invert methodology is device and platform agnostic, applicable to any nonlinear element in the classical control chain of a quantum processor.

We study the spin-$1$ Babujian-Takhtajan chain deformed by its third conserved charge $Q_3$. We derive $Q_3$ and show that it is a dimensionless energy current and that its local density is a dressed scalar-chirality operator rather than bare chirality alone, as is the case for the spin-$1/2$ Heisenberg chain. The deformation $H_α=H+αQ_3$ therefore provides a local, exactly solvable current bias: it leaves the eigenstates of the original Hamiltonian unchanged, but reorders them so that selected high-energy current-carrying states become ground states of the tilted problem. Using the thermodynamic Bethe ansatz and confirming the analytical calculations with DMRG, we find a quantum phase transition at $α_c={J}/(8π)$. For $α<α_c$, the ground-state remains the undeformed Babujian-Takhtajan phase whose low-energy effective field theory is described by the $SU(2)$ Wess-Zumino-Witten (WZW) model at level $k=2$ representing a critical phase characterized by a central charge $c=3/2$ and $\langle Q_3\rangle=0$. For $α>α_c$, a finite rapidity interval forms, and the system enters a gapless chiral current-carrying sector described by a $c=3/2$ CFT. Near the threshold, the free energy starts quadratically as a function of $α-α_c$, while the energy current turn on linearly. The scalar chirality turns on at the same threshold, showing that the postcritical sector is simultaneously current-carrying and chiral. The most immediate experimental routes are composite spin-1 bosons in optical lattices, and programmable qutrit simulators based on trapped ions or superconducting circuits.

We present a measurement-based quantum thermal machine that extracts work from the back-action of generalized quantum measurements whose working medium is a coupled two-level quantum system. Specifically, we derive universal optimization criteria for a three-stroke measurement-based engine cycle with coupled two-level system of Ising-like interaction as a working medium. Furthermore, we present two numerical algorithms to optimize the engine work extraction and enhance its performance. Our numerical results demonstrate: (i) efficiency peaks in the projective-measurement limit; (ii) symmetry breaking (detuning or weak coupling) enlarges the exploitable energy gap; and (iii) performance remains robust ($>50\%$ of optimum) under $\sim\!10^\circ$ feedback-pulse errors. The framework is platform-agnostic and directly implementable with current superconducting, trapped-ion, or NMR technologies, providing a concrete route to scalable, measurement-powered quantum thermal machines.

Trapped atomic ion qubits exhibit long coherence times and high fidelity qubit state preparation, manipulation and detection, making them well-suited for scalable quantum computing applications. Among several atomic species used in quantum computing and other application, singly-charged ions of barium stand out due to their long wavelength transitions and the presence of very long-lived metastable internal states. However, elemental barium is a highly reactive metal making it experimentally difficult to work with when making atomic beam sources. In this paper, we demonstrate a method of using resistively heated ovens loaded with a barium magnesium alloy (BaMg) as a source of barium for ion traps. This alloy is not very chemically reactive and does not oxidize in air. We found that a sample of BaMg in a resistively heated oven produced barium vapor pressures on the same order as a metallic barium sample prepared the same way. Two separate ovens, one with a sample of BaMg and one with metallic barium, were used as source for an ion trap. We observed reliable trapping of 138Ba+ ions both with the elemental barium source, and the BaMg source.

Precision measurements of $β$ decay transitions offer a promising channel through which the Standard Model (SM) can be probed. There is currently an ongoing effort to increase the precision on measurements of $\mathcal{F}t$-values for superallowed $β$ decay transitions between mirror nuclides. These allow for a determination of $V_{ud}$ which is complementary to that obtained from pure Fermi $0^+ \rightarrow 0^+$ transitions. The Superallowed Transition BEta-NEutrino Decay Ion Coincidence Trap (St. Benedict), under construction at the Nuclear Science Laboratory (NSL) at the University of Notre Dame, seeks to measure the Fermi-to-Gamow-Teller mixing ratio for transitions between mirror nuclei in order to expand the list of nuclides from which $V_{ud}$ can be extracted. Production and selection of the species of interest will be done in-flight, using the \textit{TwinSol} magnetic separator system. The first element of St. Benedict will be a large volume gas catcher which will thermalize radioactive ion beams for low energy delivery to the rest of the system. Offline commissioning of this gas catcher has been completed using an internal potassium source, and the device demonstrated a transport efficiency upwards of 95\% for pressures of 66 mbar and lower.

Quantum computing experiments and testbeds with large qubit counts have until recently been a privilege afforded only to large companies or quantum technologies where scaling to hundreds or thousands of qubits does not require a substantial increase in quantum control hardware (neutral atoms, trapped ions, or spin defects). Superconducting and spin qubit testbeds critically depend on scaling their control systems beyond what a single electronics board can provide. Multi-board control systems combining RF, fast DC control, bias, and readout require precise synchronization and communication across many hardware and firmware components. To address this, we present XCOM, a network that synchronizes QICK boards and the absolute clocks governing quantum program execution to within 100 ps, free of drift and loss of lock. XCOM also provides deterministic, all-to-all simultaneous data communication with latency below 185 ns. Like QICK itself, XCOM is compatible with a broad range of qubit technologies and is designed to scale to large systems.

Nonlocal games provide application-level benchmarks for quantum hardware whose classical performance bounds are information-theoretic, holding against all classical strategies regardless of computational resources. We implement a 14-vertex graph coloring game, the smallest graph exhibiting a quantum-classical separation for this game type, on four trapped-ion quantum processors across three institutions. One system achieved a win rate that surpasses the classical bound with statistical significance, marking the first violation of a classical bound in a graph coloring nonlocal game on quantum hardware. The remaining systems achieved win rates comparable to the best superconducting processors evaluated on the same game, further illustrating the potential of nonlocal games as cross-architecture quantum benchmarks.

Monolithic three-dimensional (3D) Paul traps combine the high-precision microfabrication of two-dimensional (2D) chip traps with the deep trapping potentials and low heating rates characteristic of macroscopic 3D Paul traps, which are typically machined by traditional means and mechanically assembled. However, achieving low motional heating rates and optical access with a high numerical aperture (NA) while maintaining the high radio-frequency (RF) voltages required for trapping heavy ionic species, such as Yb$^{+}$ and Ba$^{+}$, remains a significant technical challenge. In this work, we present a fused-silica, monolithic segmented 3D Paul trap with an ion-electrode distance of 250 $μ$m, and stable operation at high RF voltages. We benchmark the performance of the trap using Yb$^{+}$ ions, demonstrating axially homogeneous trapping potentials spanning over 200 $μ$m about the axial center of the trap, high multi-directional optical access (up to 0.7 NA), and radial motional heating as low as $\dot{\bar n}=1.1 \pm 0.1 $ quanta/s at radial trap frequencies about 3 MHz near room temperature. Furthermore, we observe a motional Ramsey coherence time, ${T}_{2}$, of about 95 ms for the radial center-of-mass mode. We demonstrate the generation of a two-qubit Bell state with a parity contrast of ${99.3}^{+0.7} _{-1.5}$% with state preparation and measurement correction. These results establish fused-silica monolithic 3D Paul traps as a scalable, modular platform for quantum simulation, computation, metrology, and networking with heavy ionic species.

One-axis twisting (OAT) interaction is a pivotal resource for manipulating quantum states of atomic ensembles, enabling spin squeezing, atomic-cat-state generation, and weak-phase amplification. Current implementations of OAT dynamics predominantly rely on the Tavis-Cummings model of light-atoms coupling; however, this approach inevitably introduces an additional Stark term that entangles the light with the atoms, which compromises the unitarity of OAT evolution and thereby degrades the OAT-based control precision. Here we propose a scheme based on a driven Tavis-Cummings model to achieve near-unitary OAT evolution. We demonstrate that both constant and time-varying driving of an atoms-cavity hybrid system can realize near-unitary OAT evolution, albeit with distinct coupling strength. Furthermore, when atomic dissipation is taken into account, we find that the time-varying-driving scheme exhibits superior resistance to decoherence. Our approach is broadly applicable to a variety of atomic platforms, including cold atoms, trapped ions, and nitrogen-vacancy centers.

The Superallowed Transition Beta-Neutrino Decay Ion Coincidence Trap (St. Benedict) is currently under construction at the Nuclear Science Laboratory (NSL) of the University of Notre Dame. It aims to measure the beta-neutrino angular correlation parameter for superallowed mixed mirror beta decay transitions. Measurements of this kind offer unique insight into the electroweak part of the Standard Model through tests of unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix. St. Benedict is comprised of several beam-manipulating components including a radio frequency quadrupole (RFQ) ion guide. This ion guide features an off-line source at $90^\circ$ to the beam path for testing and calibration of downstream components once St. Benedict is online. Off-line commissioning of the ion guide demonstrated a transport efficiency greater than 95% for ions coming from the upstream RF carpet chamber. When taking ions from the $90^\circ$ off-line source a lower efficiency of 60% was obtained.

The astrophysical rapid neutron capture nucleosynthesis process (r-process) remains an active area of research due to the fact that it occurs in extreme conditions and involves reactions with exotic nuclei that are difficult to study experimentally. For the first time using the Phase-Imaging Ion Cyclotron Resonance (PI-ICR) technique, we measured the mass excesses of \textsuperscript{130}Te, \textsuperscript{130}Sn, and \textsuperscript{130}Sn\textsuperscript{m} with the Canadian Penning Trap (CPT). Our results show good agreement with previous Penning trap values obtained using the Time-of-Flight Ion Cyclotron Resonance (TOF-ICR) and the Fourier Transform Ion Cyclotron Resonance (FT-ICR) techniques, while being twice as precise for \textsuperscript{130}Sn. These new mass excesses were added to a SkyNet network calculation to determine their impact on r-process abundances and to find the best astrophysical conditions to reproduce the Solar System r-process abundance pattern. Finally, by treating lighter and heavier elements separately, we assess the relative frequency of events producing elements in a cold versus a hot r-process scenario.

The Mpemba effect is a thermodynamic anomaly in which a system farther away in temperature from equilibrium thermalizes before one that is initially closer. The effect has been experimentally observed across a wide range of systems, including water, colloids, and trapped ions. It has recently been the focus of numerous studies aimed at understanding its mechanisms and developing multiple applications. Despite extensive work in the field, clearly determining which types of systems exhibit the Mpemba effect remains an open question. To address this, we derive simple necessary conditions on the transition rates for the Mpemba effect in a Markovian 3-level system and show that they can be applied to study the Mpemba effect in an N-level system. Multiple time scales govern thermalization in these systems. This allows the evolution to occur more quickly across larger temperature differences, explaining the Mpemba effect. We apply our protocol to evaluate which types of systems exhibit the Mpemba effect and, in doing so, explain why the Mpemba effect in Markovian systems remains a thermodynamic anomaly. In particular, due to the maximum entropy principle, our conditions allow us to discard the sub-Ohmic and Ohmic spectra. The latter describes a wide range of physical and chemical phenomena, which will not exhibit the Mpemba effect. Moreover, our results provide a clear path to determine the minimal physical requirements for the Mpemba effect, and we apply them to understand its underlying mechanisms better. Finally, our protocol could help identify relevant parameters for experiments, numerical simulations and diverse applications.

We implement a variational quantum algorithm for Gibbs state preparation of a transverse-field Ising model on IonQ's quantum computers. To this end, we train the variational parameters via classical simulation and perform state tomography on the quantum devices to evaluate the fidelity of the prepared Gibbs state. As a main result, we find that fidelity decreases (non-monotonically) as a function of the inverse temperature $β$ of the system. Fidelity also decreases as a function of the size of the system. Interestingly, we find that a Gibbs state prepared for a specified $β$ is a better representative of a Gibbs state prepared for a $\textit{lower}$ $β$; or in other words, thermal fluctuations in the quantum hardware lead to digital heating, that is, an increase in the temperature of the prepared Gibbs state above what was intended.

Photomultiplier tubes (PMTs) are used in Imaging Atmospheric Cherenkov Telescopes (IACTs) to detect Cherenkov light produced by air showers induced by gamma rays in the atmosphere. The afterpulsing rate of the PMTs for the Large-Sized Telescopes (LSTs) of the Cherenkov Telescope Array Observatory (CTAO) was found to increase if they were kept unused in storage. In contrast, PMTs that had been operated in the first LST showed a slight decrease in the rate. This decrease could be explained by a reduction of residual gas caused by ion feedback, although the detailed mechanism remained unclear. In this study, to investigate factors responsible for the evolution in the afterpulsing rate, we operated several PMTs under different high voltage and light illumination conditions. We monitored their rate daily for three weeks to compare their evolution under different conditions. We found that the reduction of afterpulses require both illumination and high-voltage operation. Notably, the reduction strongly depends on the applied high voltage and is closely correlated with the integrated anode current. Therefore, we conclude that the reduction of residual gas is mainly caused by ionization occurring at later dynodes of the PMTs, and the ions are trapped by the dynodes. We also discuss a possible explanation of the reduction of afterpulsing rate by later dynodes.

The quantum phonon laser state is a vibrational state generated by phonon coherent amplification based on quantum mechanics. Its core is coherent excitation and manipulation of phonon quantum states by controlling phonon dynamics. This technology breaks classical limits of traditional phonon lasers, offering new methods for quantum information. Previous research on quantum phonon lasers focused on quantum van der Pol oscillators. As typical nonlinear quantum systems, they show significant value in trapped-ion systems. These breakthroughs extend nonlinear dynamics into the quantum domain and provide platforms for exploring quantum nonlinear phenomena. Although realized in two-ion systems, practical applications remain challenging. This paper explores how a single trapped ion generates quantum phonon laser states using a three-level model. By solving the quantum master equation numerically, steady-state characteristics are analyzed, focusing on quantum statistics including the Wigner function and second-order correlation function. An experimental scheme is proposed based on a single trapped 40Ca+ ion, using bichromatic blue-sideband and red-sideband lasers to generate quantum phonon laser states. By introducing the characteristic function of motional states, precise quantum state tomography is achieved. Additionally, a two-level model discusses the phonon laser threshold effect. However, the three-level model shows significantly different thresholds and more accurately describes the quantum phonon laser's physical mechanisms.

Large, 3D trapped ion crystals offer improved sensitivity in quantum sensing protocols, and are expected to be implemented as platforms in near-future experiments. However, numerical techniques used to study the laser cooling of such crystals are inefficient as the number of ions, $N$, in the crystal increases. Here we develop a powerful numerical framework to simulate laser cooling of up to $10^5$ ions stored in a Penning trap. We apply this framework to characterize and optimize the cooling of ellipsoidal 3D crystals. We document new pathways to enhanced cooling based on the addition of an axial component to the potential energy-dominated $\boldsymbol{E}\times\boldsymbol{B}$ modes. Furthermore, we observe greatly enhanced cooling of the perpendicular kinetic energy to below 1 mK in prolate ion crystals, enabling a simplified cooling beam setup for such crystals. We propose specific values of trap and laser beam parameters which lead to optimal cooling in a variety of examples. This work illustrates the feasibility of preparing large 3D crystals for high-sensitivity quantum science protocols, motivating their use in future experiments.

We study the spectra of collective low excitations of two atomic ion ensembles which are confined in a liner trap by addressing lases. When the left ensemble is driven by an external optical field, its corresponding response spectrum to the incident optical light shows a vibration-induced transparency phenomenon when the detuning of the laser addressing the ion is tuned to the first red sideband. In the case of the detuning tuned to the first blue sideband, the response spectrum shows a conversion from the absorption peak to the transparency window. Furthermore, we investigate the fluctuation spectra of the collective excitation modes of ion ensemble and show the similar phenomena.

Accurate characterization of coherent and non-Markovian errors remains a central challenge in quantum information processing, as conventional benchmarking techniques typically rely on Markovian and time-independent noise assumptions. In practice, however, quantum devices exhibit both systematic coherent miscalibrations and temporally correlated fluctuations, which complicate error diagnosis and mitigation. Here, we apply a technique based on tangent-space decomposition to characterize such error in single-qubit quantum gates implemented on a trapped ion platform. Small imperfections in a quantum operation are treated as perturbations of the target quantum map, represented as tangent vectors in the space of quantum channels. This formulations enables a natural decomposition of the deviation into three components corresponding to coherent, Markovian and non-Markovian processes.The relative weights of these components provide a quantitative measure of the contribution from each type of error mechanism, directly from a single tomographic snapshot. We experimentally validate this method on a single-qubit gates implemented on a trapped $^{40}$Ca$^+$ ion, where control is achieved through laser-driven optical transitions. By analyzing experimentally reconstructed process matrices, expressed in the Pauli Transfer Matrix and Choi representations, we identify and quantify non-Markovian effects arising from controlled injection of slow fluctuations in the experimental environment. We also characterize deterministic coherent miscalibrations using the same technique. This approach provides a physically transparent and experimentally accessible tool for diagnosing complex error sources in quantum control systems.

The application of mass-analyzed threshold ionization (MATI) for the state-selective preparation of molecular ions is presented. Based on photoexcitation of long-lived high-$n$ Rydberg states, molecular ions are prepared in a single rovibronic level by pulsed-field ionization. We present a theoretical analysis and a recipe for obtaining an optimal energy ratio between such selected ions and molecular ions in unwanted rovibronic states, created by direct photoionization. It is shown that the second-order chromatic aberration of a dc quadrupole bender can be used to isolate the state-selectively prepared molecular ions. The phase-space properties of ions prepared by MATI are ideally suited for axial injection into a linear radio-frequency trap. A modified approach for carrying out MATI within such an ion trap is also described.

Highly charged ions (HCIs) combine compact electronic structure with strong relativistic effects, offering both robustness against external perturbations and enhanced sensitivity to variations of the fine-structure constant. Recent advances in sympathetic cooling and trapping enable precision measurements of highly charged ions; however, fully exploiting their potential requires accurate theoretical predictions. In particular, reliable calculations of clock wavelengths are essential for experimentally locating HCI clock transitions. Here, we treat Cf17+ as a univalent ion and perform calculations within the relativistic coupled-cluster framework, iteratively including nonlinear single-double contributions and valence and core triple excitations. We also assess quantum-electrodynamic corrections and basis-set and partial-wave truncation effects. Our results establish the impact of different correlation contributions on the low-lying energy spectrum and provide a quantitatively reliable prediction of the 5f_5/2 - 6p_1/2 clock transition, highlighting the critical role of core-valence correlations and iterative triples for precision spectroscopy and optical clock development.

We present a quantum reservoir computing (QRC) framework based on a small-scale quantum system comprising at most six interacting qubits, designed for nonlinear financial time-series forecasting. We apply the model to predict future daily closing trading volumes of 20 quantum-sector publicly traded companies over the period from April 11, 2020, to April 11, 2025, as well as minute-by-minute trading volumes during out-of-market hours on July 7, 2025. Our analysis identifies optimal reservoir parameters that yield stock trend (up/down) classification accuracies exceeding $86 \%$. Importantly, the QRC model is platform-agnostic and can be realized across diverse physical implementations of qubits, including superconducting circuits and trapped ions. These results demonstrate the expressive power and robustness of small-scale quantum reservoirs for modeling complex temporal correlations in financial data, highlighting their potential applicability to real-world forecasting tasks on near-term quantum hardware.

We present a technique for measuring ion temperature using cavity-based electromagnetically induced transparency (EIT) applicable for cavity QED systems. This method enables efficient extraction of the ion's phonon occupation number following sub-Doppler cooling close to the motional ground state. The proposed method requires operation in the resolved-sideband regime, where individual motional states can be selectively addressed for all relevant transitions either by selecting appropriate energy levels for the three-level system or by employing strong confinement with high secular frequencies ($\sim 10 MHz$). It relies on monitoring the cavity probe transmission while scanning the probe laser frequency to establish cavity-induced EIT using a control beam, thereby significantly simplifying the measurement procedure. We establish a theoretical model that demonstrates the influence of the thermal state of the trapped ion vis-à-vis the EIT linewidth measured. We show through numerical simulations how the cavity-induced EIT transmission may be used as a thermometry tool to deduce the ion temperature as well as its motional state in the sub-Doppler cooling regime, even for systems that are in the weak coupling regime.

Trapped-ion lattice geometries, which determine the interactions between trapped-ion qubits, are typically governed by the balance of Coulomb repulsion forces with the external trapping potential. Here we demonstrate how the effective ion lattice geometry and resulting qubit-qubit interactions may be reconfigured in-situ, by shelving specific ions in metastable states outside the qubit subspace. Using a triangular lattice of three $^{171}$Yb$^{+}$ ions, we optically pump selected ions into the long-lived $^2F_{7/2}$ state. We then apply a global Ising-like Hamiltonian to the system and verify that the shelved qubits are fully removed from participation in the quantum dynamics. We characterize the metastable state lifetime in the presence of laser-driven ion-ion interactions, finding a deshelving rate that is orders of magnitude slower than the spin-spin interaction rate and scales quadratically with applied laser intensity.

Quantum networks, integrating quantum communication, quantum metrology, and distributed quantum computing, could provide secure and efficient information transfer, high-resolution sensing, and an exponential speed-up in information processing. Deterministic entanglement distribution over long distances is a prerequisite for scalable quantum networks, enabling the utilization of device-independent quantum key distribution (DI-QKD) and quantum teleportation to achieve secure and efficient information transfer. However, the exponential photon loss in optical fibres prohibits efficient and deterministic entanglement distribution. Quantum repeaters, incorporating entanglement swapping and entanglement purification with quantum memories, offer the most promising means to overcome this limitation in fibre-based quantum networks. Despite numerous pioneering efforts toward realizing quantum repeaters, a critical bottleneck remains, as remote memory-memory entanglement suffers from decoherence more rapidly than it can be established and purified over long distances. We overcome this by developing long-lived trapped-ion memories, an efficient telecom interface, and a high-visibility single-photon entanglement protocol. This allows us to establish and maintain memory-memory entanglement over a 10 km fibre within the average entanglement establishment time for the same distance. As a direct application, we demonstrate metropolitan-scale DI-QKD, distilling 1,917 secret keys out of 4.05*10^5 Bell pairs over 10 km. We further report a positive key rate over 101 km in the asymptotic limit, extending the achievable distance by more than two orders of magnitude. Our work provides a critical building block for quantum repeaters and marks an important step toward scalable quantum networks.

Bosonic modes constitute a central resource in a wide range of quantum technologies, providing long-lived degrees of freedom for the storage, processing, and transduction of quantum information. Such modes naturally arise in platforms including circuit quantum electrodynamics, quantum acoustodynamics, and trapped-ion systems. In these architectures, coherent control and high-fidelity readout of the bosonic degrees of freedom are achieved via coupling to an auxiliary qubit. When operated in the strong dispersive regime, this interaction enables parity measurements of the mode which, in combination with phase-space displacements, constitute a standard experimental tool for full Wigner-function tomography. Here, we propose a protocol based on displaced parity measurements that allows for the preparation of a variety of bosonic quantum states. As a first example, we demonstrate the generation of squeezed states, achieving up to ~9 dB of squeezing after only three parity measurements, and show that the protocol is robust against experimental imperfections. Finally, we generalize our approach to the preparation of other paradigmatic bosonic states, including cat and Gottesman-Kitaev-Preskill states.

Enhancing the conversion efficiency and maximum energy of laser-driven ion beams is a critical challenge for applications in hadron therapy and high-energy density physics. In this work, we present a comprehensive two-dimensional Particle-In-Cell (PIC) simulation study comparing Target Normal Sheath Acceleration (TNSA) from standard flat foils and novel annular sector (C-shaped) targets. Under identical ultra-intense laser irradiation (a0=10, tau=25 fs), the annular sector geometry demonstrates a substantial enhancement in acceleration performance driven by two synergistic mechanisms: electromagnetic cavity confinement and geometric plasma focusing. Our analysis reveals that the target void acts as an optical trap, sustaining oscillating electromagnetic fields for over 300fs via multiple internal reflections. This confinement results in a total laser energy absorption of 49% (compared to 16% for flat targets), which yields a peak electron temperature of 5.1 MeV more than double the 2.2MeV observed in flat targets. Furthermore, phase space diagnostics confirm that ion bunches accelerated from the converging cavity walls superimpose at the geometric center, creating a localized high-density focal spot. Consequently, the annular target increases the proton cut-off energy to 22MeV (vs. 12MeV for flat targets) and boosts Carbon ion energies beyond 60MeV. These findings establish that tailoring target curvature to exploit optical trapping and geometric focusing offers a robust pathway for developing compact, high-efficiency laser-ion sources.

Quantum many-body systems driven far from equilibrium can exhibit chaos, entanglement, and non-classical correlations, yet directly observing these phenomena in large, closed quantum systems remains challenging. Here we realize the Dicke model -- a fundamental description of light-matter interactions -- in a two-dimensional crystal of approximately 100 trapped ions. The ions' internal state is optically coupled to the center of mass vibrational mode via an optical spin-dependent force, enabling unitary many-body dynamics beyond the mean-field and few-body limits. In the integrable regime, where the phonons can be adiabatically eliminated, we observe a dynamical phase transition between ferromagnetic to paramagnetic spin phases. In contrast, when the spins and phonons are strongly coupled, we observe clear signatures of non-integrable chaotic dynamics, including erratic phase-space trajectories and the exponential growth of excitations and entanglement quantified by the one-body Rényi entropy. By quenching from an unstable fixed point in the near-integrable regime, quantum noise can generate correlated spin-phonon excitations. Our numerical calculations, in clear agreement with experiment, reveal the generation of two-mode spin-phonon squeezing, 2.6 dB below the standard quantum limit (4.6 dB relative to the initial thermal state), followed by generalized vacuum Rabi collapses and revivals. Our results establish large ion crystals as scalable analog quantum simulators of non-equilibrium light-matter dynamics and provide a controlled platform for experimental studies of information scrambling and entanglement in closed many-body systems.

Measurement-induced phase transitions (MIPT) give rise to novel dynamical states of quantum matter realized by balancing unitary evolution and measurements. We present large-scale numerical simulations of a trapped-ion native MIPT, argued to belong to the universality class described by the Haar non-unitary conformal field theory. First, through a finite-size analysis we obtained the critical measurement rate, and correlation length exponent, which falls close to the percolation value. Second, by leveraging a monotone computable via semi-definite programming, we uncover robust algebraic decay of genuine multiparty entanglement (GME) versus separation for 2, 3, and 4 parties. The corresponding critical exponents are lower-bounded by those of the multiparty mutual information, which we determine up to 4 parties, and conjecture to be (k+2) for k parties. Additionally, we derive lower bounds for both GME and multiparty mutual information.

Distributed quantum sensing leverages quantum correlations among multiple sensors to enhance the precision of parameter estimation beyond classical limits. Most existing approaches target phase estimation and rely on a shared phase reference between the signal and the probe, yet many relevant scenarios deal with regimes where such a reference is absent, making the estimation of force or field amplitudes the main task. We study this phase-insensitive regime for bosonic sensors that undergo identical displacements with common phases randomly varying between experimental runs. We derive analytical bounds on the achievable precision and show that it is determined by first-order normal correlations between modes in the probe state, constrained by their average excitations. These correlations yield a collective sensitivity enhancement over the standard quantum limit, with a gain that grows linearly in the total excitation number, revealing a distributed quantum advantage even without a global phase reference. We identify families of multimode states with definite joint parity that saturate this limit and can be probed efficiently via local parity measurements already demonstrated or emerging in several quantum platforms. We further demonstrate that experimentally relevant decoherence channels favor two distinct sensing strategies: splitting of a single-mode nonclassical state among the modes, which is robust to loss and heating, and separable probes, which are instead resilient to dephasing and phase jitter. Our results are relevant to multimode continuous platforms, including trapped-ion, solid-state mechanical, optomechanical, superconducting, and photonic systems.

We directly observe and spatially map an optical analog of the Magnus effect, where intrinsic spin-orbit-like coupling of light generates a spin-dependent transverse displacement of the atom-light interaction profile for a $^{40}$Ca$^+$ ion. Probed on a quadrupole transition using a tightly focused beam, we observe displacements of the maximum in the profile of the effective interaction by several 100 nm originating from intrinsic longitudinal electric field components beyond the paraxial approximation. The tight focus of the beam induces additional transverse polarization gradients, which we characterize through a phase-sensitive measurement and spatial maps for different beam configurations. The results establish the physical basis of polarization-gradient interactions relevant to optical tweezer-based quantum control.

Cyanooxomethylium, NCCO$^+$, a fundamental linear acylium ion, has been observed spectroscopically for the first time using action spectroscopy in ion trap apparatuses. A first low-resolution infrared spectrum was obtained between 500 to 1400 cm$^{-1}$ and 2000 to 2500 cm$^{-1}$ using the Free Electron Laser for Infrared eXperiments (FELIX) and the FELion apparatus, employing infrared predissociation of the weakly bound NCCO$^+$-Ne complex. Subsequently, high-resolution studies of the bare ion were performed with the COLtrap II setup, one targeted at the CN-stretching mode $ν_2$ around 2150 cm$^{-1}$ using leak-out spectroscopy and one at the pure rotational spectrum employing a leak-out infrared/millimeter-wave double resonance approach covering transition frequencies as high as 246 GHz. Spectroscopic detection and analysis were guided by high-level quantum-chemical calculations performed at the CCSD(T) level of theory. The collected data permit accurate frequency predictions to support future astronomical searches with sensitive radio telescopes.

In trapped-ion quantum simulators, effective spin-1/2 XY interactions can be engineered via laser-induced coupling between internal atomic states and collective phonon modes. In the simplest one-dimensional ($1d$) traps, these interactions decay as a power-law with distance $1/r^α$, with a tunable exponent $α$. For small $α$, the resulting long-range $1d$ XY model exhibits continuous symmetry breaking, in marked contrast to its nearest neighbor counterpart. In this paper, we examine this model near the phase transition at $α_c$ from the lens of the spin stiffness, or superfluid density. We develop a stochastic series expansion (SSE) quantum Monte Carlo (QMC) simulation and a generalized winding number estimator to measure the superfluid density in the presence of power-law interactions, which we test against exact diagonalization for small lattice sizes. Our results show how conventional superfluidity in the $1d$ XY model is enhanced in the long-range interacting regime. This is observed as a diverging superfluid density as $α\rightarrow 0$ in the thermodynamic limit, which we show is consistent with linear spin-wave theory. Finally, we define a normalized superfluid density estimator that clearly distinguishes the short, medium, and long-range interacting regimes, providing a novel QMC probe of the critical value $α_c$.

In the past few decades, X-ray astronomy satellites equipped with grating spectrometers and microcalorimeters have enabled high-resolution spectroscopic observations of astrophysical objects. The need for accurate atomic data has arose as we attempt detailed analysis of the high-resolution spectra they provide. This is because current spectral models, which heavily rely on theoretical calculations, entail non-negligible uncertainties. We employ a plasma spectroscopy device called electron beam ion trap (EBIT) to experimentally obtain precise atomic data. An EBIT with a design that allows combined operation with synchrotron radiation facilities was developed based on the Heidelberg Compact EBIT and installed at ISAS/JAXA for this purpose. We conducted a spectroscopic experiment using the JAXA-EBIT at the synchrotron radiation facility SPring-8, and successfully obtained high-resolution spectra of the L$α$ resonance transition of Ne-like Fe$^{16+}$ ions, 3C, as well as the K$α$ resonance transition of He-like O$^{6+}$ ions. We also measured another Ne-like Fe$^{16+}$ L$α$ resonance transition, 3G, and constrained an upper limit of the oscillator strength ratio of 3G to 3C, using our experimental results. The experimental values obtained in this study will be applied to observational studies of astrophysical objects as a part of the plasma spectral modeling.

Towards the scalable realization of a quantum computer, a quantum charge-coupled device (QCCD) based on ion shuttling has been considered a promising approach. However, the processes of detaching an ion from an array, reintegrating it, and driving non-uniform motion introduce severe heating, requiring significant time and laser power for re-cooling and stabilization. To mitigate these challenges, we propose a novel entangling scheme between a stationary ion qubit and a continuously transported mobile ion, which remains in uniform motion and minimizes motional heating. We theoretically demonstrate a gate error on the order of 0.01%, within reach of current technology. This approach enables resource-efficient quantum operations and facilitates long-distance entanglement distribution, where stationary trapped-ion arrays serve as memory units and mobile ions act as communication qubits passing beside them. Our results pave the way for an alternative trapped-ion architecture beyond the QCCD paradigm.

Control over the internal states of trapped ions makes them the ideal system to generate single and two-photon states. Coupling a single ion to an optical cavity enables efficient emission of single photons into a single spatial mode and grants control over their temporal shape, phase and frequency. Using the long coherence time of the ion's internal states and employing a scheme to protect the coherence of the ion-cavity interaction, we demonstrate the generation of a two-photon entangled state with full control over the phase. Initially, ion-photon entanglement is generated. A second photon is subsequently generated, mapping the ion's state onto the second photon. By adjusting the drive field the phase of the entangled state can be fully controlled. We implement this scheme in the most resource efficient way by utilizing a single $^{40}$Ca$^+$ ion coupled to an optical cavity and demonstrate the generation of a two-photon entangled stated with full phase control with a fidelity of up to 82\%.

Modulation and control of lasers and optical signals is necessary for trapped-ion and cold neutral atom quantum systems. Given the diversity of atomic species, experimental modalities, and architectures, integrated optical modulators designed to operate across the visible to near-infrared spectrum are a key step towards portable, robust, and compact quantum computers, clocks, and sensors. Integrated optical modulators that are wavelength-independent, CMOS-compatible, and capable of maintaining low waveguide losses and a high resonator quality factor, DC-coupled broadband frequency response, and low power consumption, are essential for scalable photonic integration. Yet progress towards these goals has remained limited. Here we demonstrate four types of integrated stress-optic lead zirconate titanate (PZT) silicon nitride modulators: a coil Mach-Zehnder modulator, a coil pure phase modulator, and bus-coupled and add-drop ring resonator modulators, with operation from 493 nm to 780 nm. The coil MZM operates at 532 nm with a V$π$ of 2.8V, a 0.4 MHz 3-dB bandwidth, and an extinction ratio of 21.5dB. The coil phase modulator operates at 493 nm with a V$π$ of 2.8V and low residual amplitude modulation of -34 dB at a 1kHz offset. The bus-coupled ring resonator modulator operates at 493 nm and the add-drop ring resonator modulator operates at 780 nm. The ring-based modulators have an intrinsic quality factor of 3.4 million and 1.9 million, a linear tuning strength of 0.9 GHz/V and 1 GHz/V, and a 3-dB bandwidth of 2.6 MHz and 10 MHz, respectively. All four modulator designs maintain the low optical waveguide loss of SiN, are DC coupled with broadband frequency response, operate independent of wavelength, and consume only tens of nW per actuator. Such solutions unlock the potential for further integration with other precision SiN components to realize chip-scale atomic and quantum systems.

At the heart of quark confinement and hadronization, the physics of flux strings has recently become a focal point in the field of quantum simulation of high-energy physics (HEP). Despite considerable progress, a detailed understanding of the behavior of flux strings in quantum simulation-relevant lattice formulations of gauge theories has remained limited to the lowest truncations of the gauge field, which are severely limited in their ability to draw conclusions about the quantum field theory limit. Here, we employ tensor network simulations to investigate the behavior of flux strings in a quantum link formulation of $2+1$D quantum electrodynamics (QED) with a spin-$1$ representation of the gauge field. We first map out the ground-state phase diagram of this model in the presence of two spatially separated static charges, revealing distinct microscopic processes responsible for string breaking, including a two-stage breaking mechanism not possible in the spin-$\frac{1}{2}$ formulation. Starting in different initial product state string configurations, we then explore far-from-equilibrium quench dynamics across various parameter regimes, demonstrating genuine $2+1$D real-time string breaking and glueball-like bound state formation, with the latter not possible in the spin-$\frac{1}{2}$ formulation. In and out of equilibrium, we consider different values and placements of the static charges. Finally, we provide efficient qudit circuits for a quantum simulation experiment in which our results can be observed in state-of-the-art ion-trap setups. Our findings lay the groundwork for quantum simulations of flux strings towards the quantum field theory limit.

In this paper, we investigate the non-Hermitian skin effect in a semi-infinite Fock-state lattice, where the inherent coupling scales as \sqrt{n}. By analytically solving a non-uniform, non-reciprocal SSH model, we demonstrate that the intrinsic inhomogeneous coupling, in combination with nonreciprocity, fundamentally modifies the conventional skin effect. Instead of accumulating at the physical boundary, all eigenmodes become compressed and skewed within a finite spatial range determined by the inhomogeneous profile-a phenomenon we term the confined non-Hermitian skin effect. Consequently, the evolution of the probability distribution on the lattice starting from a single site is doubly confined: it is spatially bounded to a finite range by the inhomogeneous coupling, and further restricted to a one-sided trajectory at the edge of this range by the non-reciprocity. Moreover, a feasible experimental scheme based on a single trapped ion is also proposed. This work reveals how engineered coupling profiles in synthetic dimensions can reshape non-Hermitian properties and enable new protocols for quantum state manipulation.

Penning trap mass measurements of $^{149}$La, $^{149}$Ce, and $^{149}$Pr were performed with the Canadian Penning Trap (CPT) at the CARIBU facility of Argonne National Laboratory using the phase-imaging ion-cyclotron-resonance technique. The resulting mass excess of $^{149}$La differs by 221 keV from a recent JYFLTRAP measurement, resulting in a significant change in the profile of the two-neutron separation energy for that isotopic chain. The mass excesses of $^{149}$Ce and $^{149}$Pr are determined with an eight-fold improvement in precision compared to previous time-of-flight ion-cyclotron-resonance measurements; the $^{149}$Ce value is consistent with AME2020, while the $^{149}$Pr mass excess is lower by 17.5 keV. The mass excesses of $^{149}$La and $^{149}$Pr reported in this work have been confirmed recently by a measurement with a multi-reflection time-of-flight mass spectrometer coupled to a $β$-time of flight detector at RIKEN, providing further validation of the present results.

While spin squeezing has been traditionally considered in all-to-all interacting models, recent works have shown that it can also occur in systems with power-law interactions, enabling direct tests in Rydberg atoms, trapped ions, ultracold atoms, and nitrogen-vacancy (NV) centers in diamond. For the latter, Wu et al. Nature 646 (2025) demonstrated that spin squeezing is heavily affected by positional disorder, reducing any capacity for a practical squeezing advantage, which requires scalability with the system size. In this Letter we explore the robustness of spin squeezing in two-dimensional lattices with a fraction of unoccupied lattice sites. Using semiclassical modeling, we demonstrate the existence of scalable squeezing in power-law interacting XXZ models up to a disorder threshold, above which squeezing is not scalable. We produce a phase diagram for scalable squeezing, and explain its absence in the aforementioned NV experiment. Our work illustrates the maximum disorder allowed for realizing scalable spin squeezing in a host of quantum simulators, highlights a regime with substantial tolerance to disorder, and identifies controlled defect creation as a promising route for scalable squeezing in solid-state systems.

Compared to other stable isotopes of $\rm{Yb}^+$, $^{173}\rm{Yb}^+$ has a richer hyperfine structure, which leads to more favorable clock transitions, spectroscopic techniques for probing new physics, and more sophisticated quantum computing architectures. However, to date, its electronic spectrum remains poorly characterized. Here, we report on efficient laser cooling, state preparation, and detection of a single trapped $^{173}\rm{Yb}^+$ ion. The previously unobserved $^2\!S_{1/2} \rightarrow {}^2\!D_{3/2}$ electric quadrupole transition at 436 nm is coherently excited, and the isotope shift between $^{171}\rm{Yb}^+$ and $^{173}\rm{Yb}^+$ on this transition is determined with an uncertainty of 1.4 Hz. Using microwave spectroscopy, we resolve the hyperfine structure (HFS) of the ${}^2\!D_{3/2}$ state with a relative uncertainty below $10^{-8}$. From the HFS measurement data, we infer for ${}^{173}$Yb a nuclear magnetic octupole moment $Ω= -0.062(8)\,({\rm b} \times μ_N)$ with uncertainty reduced by more than 2 orders of magnitude compared to previous studies. The data also allow us to determine hyperfine anomalies for the ${}^2\!S_{1/2}$ and ${}^2\!D_{3/2}$ states.

We develop a unified many-body theory of two-photon dark-state laser cooling, the workhorse for preparing trapped ions close to their motional quantum ground state. For ions with a $Λ$ level structure, driven by Raman lasers, we identify an ion-number-dependent crossover between weak and strong coupling where both the cooling rate and final temperature are simultaneously optimized. We obtain simple analytic results in both extremes: In the weak coupling limit, we show a Lorentzian spin-absorption spectrum determines the cooling rate and final occupation of the motional state, which are both independent of the number of ions. We also highlight the benefit of including an additional spin dependent force in this case. In the strong coupling regime, our theory reveals the role of collective dynamics arising from phonon exchange between dark and bright states, allowing us to explain the enhancement of the cooling rate with increasing ion number. Our analytic results agree closely with exact numerical simulations and provide experimentally accessible guidelines for optimizing cooling in large ion crystals, a key step toward scalable, high-fidelity trapped-ion quantum technologies.

We present a theoretical model for realizing squeezed lasing in a trapped-ion system without relying on engineered baths or tailored dissipative reservoirs. Our approach leverages the intrinsic ion-phonon interactions, where two trapped ions, each interacting with a shared vibrational mode, are driven on both red- and blue-sideband transitions. This enables the creation of a squeezed state of motion through the dynamic coupling between the ions' internal states and the phonon mode. Unlike traditional methods that require bath engineering, our model demonstrates that squeezed lasing can be achieved through a direct manipulation of ion-phonon interactions, with no external reservoirs required. We explore the steady-state behavior of the system, analyzing the onset of lasing, gain-loss balance, and the role of the squeezing parameter in shaping the phonon field's statistical properties. Furthermore, we show how external coherent drives can stabilize phase coherence and achieve controlled quadrature squeezing, offering a simple yet effective method for achieving squeezed lasing in quantum mechanical systems. Our findings provide new insights into the realization of squeezed states in phonon-based systems, with potential applications in quantum metrology and information processing.

Quantum Darwinism explains how tenets of classical reality, such as objectivity and repeatability, emerge within a quantum universe. As a mathematical framework, Quantum Darwinism also provides guiding principles that determine what physical models support emergent classical behavior, what specific observables obey classical laws, and much more. For instance, in a recent work we elucidated that the limit under which Kirkwood-Dirac quasiprobability distributions become effectively classical coincides with the regime where the underlying physical model obeys the rules of Quantum Darwinism. In the present work, we study the breaking of Quantum Darwinism in a specific model and how that translates to non-classical measurement statistics. Interestingly, this provides effective tools for benchmarking the genuine quantum characteristics of NISQ hardware, which we demonstrate with IonQ's trapped-ion and IBM's superconducting quantum computing platforms.

Laser-cooled ions confined in electromagnetic traps provide a unique, tunable mesoscopic system where the interplay of the trapping potential, nonlinear Coulomb interactions, and laser-ion scattering generates rich, collective dynamics. In this work, we engineer thermally activated switching between two oppositely oriented, square-pyramidal configurations of five laser-cooled ions in a Paul trap. For identical ions ($^{40}\mathrm{Ca}^{+}$), the inversions proceed via a \textit{Berry pseudo-rotation} mechanism with a low activation barrier, enabled by the permutation symmetry, in contrast to the \textit{umbrella inversion} observed in ammonia. The experimentally measured inversion rates, spanning two orders of magnitude, are accurately captured by the multidimensional Kramers-Langer theory, enabling thermometry of the Doppler-cooled ion cluster at $1.8 \pm 0.1$ mK. By substituting the apex ion with a heavier isotope ($^{44}\mathrm{Ca}^{+}$), we break the permutation symmetry and observe a suppression of thermally activated inversions. Numerical analysis reveals that this symmetry breaking closes the low-barrier channel, forcing the system to invert through a high-barrier \textit{turnstile rotation}. Thus, we demonstrate a structural analogue of molecular kinetic isotope effects, establishing trapped ions as a versatile platform to explore symmetry-controlled collective dynamics.

In fault-tolerant quantum computation, the preparation of logical states is a ubiquitous subroutine, yet significant challenges persist even for the simplest states required. In the present work, we present a unitary, scalable, distance-preserving encoding scheme for preparing Pauli eigenstates in surface codes. Unlike previous unitary approaches whose fault-distance remains constant with increasing code distance, our scheme ensures that the protection offered by the code is preserved during state preparation. Building on strategies discovered by reinforcement learning for the surface-17 code, we generalize the construction to arbitrary code distances and both rotated and unrotated surface codes. The proposed encoding relies only on geometrically local gates, and is therefore fully compatible with planar 2D qubit connectivity, and it achieves circuit depth scaling as $\mathcal{O}(d)$, consistent with fundamental entanglement-generation bounds. We design explicit stabilizer-expanding circuits with and without ancilla-mediated connectivity and analyze their error-propagation behavior. Numerical simulations under depolarizing noise show that our unitary encoding without ancillas outperforms standard stabilizer-measurement-based schemes, reducing logical error rates by up to an order of magnitude. These results make the scheme particularly relevant for platforms such as trapped ions and neutral atoms, where measurements are costly relative to gates and idling noise is considerably weaker than gate noise. Our work bridges the gap between measurement-based and unitary encodings of surface-code states and opens new directions for distance-preserving state preparation in fault-tolerant quantum computation.

We define a quantum charger as an interacting quantum system that transfers energy between two drives. The key figure of merit characterizing a charger is its charging power. Remarkably, the presence of long-range interactions within the charger can induce a collective steady-state charging mode that depends superlinearly on the size of the charger, exceeding the performance of noninteracting, parallel units. Using the driven Lipkin-Meshkov-Glick model and power-law interacting spin chains, we show that this effect persists up to a critical system size set by the breakdown of the high-frequency regime. We discuss optimal work output as well as experimentally accessible initial states. The superlinear charging effect can be probed in trapped-ion experiments, and positions interacting Floquet systems as promising platforms for enhanced energy conversion.

Quantum simulation of interacting many-body spin systems is routinely performed with cold trapped ions, and systems with hundreds of spins have been studied in one and two dimensions. In the most common realizations of these platforms, spin degrees of freedom are encoded in low-lying electronic levels, and interactions among the spins are mediated through crystal vibrations. Here we propose a new approach which enables the quantum simulation of two-dimensional spin systems with interaction strengths that are increased by orders of magnitude. This, together with the unprecedented longevity of trapped ions, opens an avenue for the exploration of phenomena that take place on long timescales, e.g., slow and collective relaxation in frustrated and kinetically constrained systems. Our platform makes use of the strong dipolar interactions among electronic Rydberg states and planar confinement provided by a Penning trap. We investigate how the strong electric and magnetic fields that form this trap affect the properties of the Rydberg states and show that spin-spin interaction strengths on the order of MHz are achievable under experimentally realistic conditions. As a brief illustration of the capabilities of this quantum simulator, we study the entanglement in a frustrated spin system realized by three ions.

Developing and deploying advanced Quantum Repeater (QR) technologies will be necessary to scale quantum networks to longer distances. Depending on the error mitigation mechanisms adopted to suppress loss and errors, QRs are typically classified into memory-based or all-photonic QRs; and each type of QR may be best suited for a specific type of underlying quantum technology, a particular scale of quantum networks, or a specific regime of operational parameters. We perform theoretical analysis and simulations of quantum repeaters and networks to investigate the relative performance and resource requirements of different quantum network paradigms. Our results will help guide the optimization of quantum hardware and components and shed light on the role of a robust control plane. We present our research findings on theoretical analysis and simulations of memory-based first-generation trapped-ion quantum repeaters and networks, and all-photonic entanglement-based quantum repeaters and networks. We study the relative performance in terms of entanglement generation rate and fidelity, as well as the resource requirements of these two different quantum network paradigms.

While quantum simulators promise to explore quantum many-body physics beyond classical computation, their capabilities are limited by the available native interactions in the hardware. On many platforms, accessible Hamiltonians are largely restricted to one- and two-body interactions, limiting access to multi-body Hamiltonians and to systems governed by simultaneous, non-commuting interaction terms that are central to condensed matter, quantum chemistry, and high-energy physics. We introduce and experimentally demonstrate a hybrid digital-analog protocol that overcomes these limitations by embedding analog evolution between shallow entangling-gate layers. This method produces effective Hamiltonians with simultaneous non-commuting three- and four-body interactions that are generated non-perturbatively and without Trotter error -- capabilities not practically attainable on near-term hardware using purely digital or purely analog schemes. We implement our scheme on a trapped-ion quantum processor and use it to realize a topological spin chain exhibiting prethermal strong zero modes persisting at high temperature, as well as models featuring three- and four-body interactions. Our hardware-agnostic and scalable method opens new routes to realizing complex many-body physics across quantum platforms.

As quantum computing advances toward the late-NISQ and early fault-tolerant eras, scalable and platform-independent benchmarks are essential for quantifying computational capacity in a classically verifiable manner. We introduce two volumetric benchmarks, Clifford Volume and Free Fermion Volume, that assess quantum hardware by testing the execution of random Clifford and free fermion operations. These two groups of unitaries possess a combination of properties that make them ideal for benchmarking: (i) each is individually efficient to simulate classically, enabling verification at scale; (ii) together they form a universal gate set; (iii) they serve as essential algorithmic primitives in practical applications (including shadow tomography and quantum chemistry); and (iv) their definitions are formulated abstractly, without explicit reference to hardware-specific features such as qubit connectivity or native gate sets. This framework thus enables scalable and fair cross-platform comparisons and tracks meaningful computational advancement. We demonstrate the practical feasibility of these benchmarks through extensive numerical simulations across realistic noise parameters and through experimental validation on Quantinuum's H2-1 trapped-ion quantum computer, which achieves a Clifford Volume of 34.

Quantum computers are believed to solve a class of computational problems that are based on modular arithmetic faster than classical computers. Among the arithmetic building blocks, comparison of integer pairs is a primitive. Here we report its demonstration in the Reimei quantum computer at RIKEN, whose trapped-ion architecture provides all-to-all qubit connectivity together with high gate fidelities. We observe high success probabilities for bit widths n = 3, 5, 7, and 9: Under a conventional output-only success criterion we obtain 95% at n=9; under a stricter criterion additionally requiring the ancilla to be correct, the success is 69% at n=9. These results demonstrate reliable quantum comparison at scales far beyond those previously achieved experimentally, not only for comparators but also in the broader context of quantum arithmetic circuits.

We report on the first feedback cooling of a single trapped ion below the Doppler limit of $\hbarΓ/2 k_\mathrm{B}$. The motion of a single ion is monitored in real-time and cooled up to 9-times below the Doppler cooling temperature by applying electronic feedback. Real-time motion detection is implemented by imaging the fluorescence photons emitted by the ion onto a knife edge and detecting the transmitted light, a method used so far to cool trapped nanoparticles. The intensity modulation of the fluorescence resulting from the ion motion is used to generate and apply the feedback signal and also to determine the ion temperature. The method benefits from a high rate of detected scattered photons, which can be a challenge, and which we address by using a parabolic mirror for collecting the fluorescence.

Estimating molecular ground-state energies is a central application of quantum computing, requiring both the preparation of accurate quantum states and efficient energy readout. Understanding the effect of hardware noise on these experiments is crucial to distinguish errors that have low impact, errors that can be mitigated, and errors that must be reduced at the hardware level. We ran a state preparation and energy measurement protocol on an ion-trap quantum computer, without any non-scalable off-loading of computational tasks to classical computers, and show that leakage errors are the main obstacle to chemical accuracy. More specifically, we apply adiabatic state preparation to prepare the ground state of a six-qubit encoding of the H3+ molecule and extract its energy using a noise-resilient variant of iterative quantum phase estimation. Our results improve upon the classical Hartree-Fock energy. Analyzing the effect of hardware noise on the result, we find that while coherent and incoherent noise have little influence, the hardware results are mainly impacted by leakage errors. Absent leakage errors, noisy numerical simulations show that with our experimental settings we would have achieved close to chemical accuracy, even shot noise included. These insights highlight the importance of targeting leakage suppression in future algorithm and hardware development.

We present a spectroscopic investigation of $^{169}\mathrm{Tm}^+$ that provides two key foundations for its use as a platform for advanced quantum applications. First, we establish the complete spectroscopic road map for optical cycling (including laser cooling) by performing high-resolution spectroscopy on $^{169}\mathrm{Tm}^+$ ions in an ion trap. We characterize the primary $313\,\mathrm{nm}$ and complementary $448/453\,\mathrm{nm}$ cycling transitions, identify the essential near-infrared repumping frequencies, and determine the magnetic-dipole hyperfine $A$ constants for all relevant levels. Second, we report a detailed characterization of a metastable state as a candidate for hosting a robust qubit, performing lifetime measurements and Zeeman-resolved microwave hyperfine spectroscopy with $\mathrm{kHz}$ precision.

We report a theoretical and experimental investigation of autoionizing resonances from the $5d6p\,{}^3\mathrm{D}_1^o$ manifold in neutral barium for efficient loading of ion traps. Our calculations predict large resonant cross sections for many narrow autoionizing resonances, but we find experimentally that for most of these, Doppler broadening during trap loading depresses the effective cross sections that can be achieved in practice. We identify and demonstrate a strong, broad transition at $531\,\mathrm{nm}$, and show that it furnishes an order-of-magnitude increase in trap loading efficiency compared to other demonstrated resonances.

We report on the sympathetic cooling and Coulomb crystallization of xenon highly charged ions (HCIs) with laser-cooled Ca$^+$ ions. The HCIs are produced in a compact electron beam ion trap, then charge selected, decelerated, and finally injected into a cryogenic linear Paul trap. There, they are captured into $^{40}$Ca$^+$ Coulomb crystals, and co-crystallized within them, causing dark voids in their fluorescence images. Fine control over the number of trapped ions and HCIs allows us to realize mixed-species crystals with arbitrary ordering patterns. By investigating Xe$^{q+}$--Ca$^+$ strings, we confirm the HCI charge states, measure their lifetime and characterize the mixed-species motional modes. Our system effectively combines the established quantum control toolbox for Ca$^+$ with the rich set of atomic properties of Xe highly charged ions, providing a resourceful platform for optical frequency metrology, searches for signatures of new physics, and quantum information science.

We present a room-temperature Extreme High Vacuum (XHV) system engineered to support the long-duration operation of a trapped-ion quantum processor. Background-gas collisions impose limitations on trapped-ion performance and scalability by interrupting algorithmic execution and, in some cases, ejecting ions from the trap. Using molecular-flow simulations, we optimize the chamber geometry, conductance pathways, and pumping configuration to maximize the effective pumping speed at the ion location. We perform high-temperature heat treatment of stainless steel vacuum components to achieve the desired outgassing rate, guided by quantitative relations of bulk diffusive processes, allowing us to reduce the \(\mathrm{H_2}\) outgassing load to the \(10^{-15}\,\mathrm{mbar\,l\,s^{-1}\,cm^{-2}}\) level. The final pressure in our chamber, measured by a hot cathode gauge, is \(1.5\times10^{-12}\,\mathrm{mbar}\), corresponding to the gauge's measurement limit. We measure the local pressure at the ion location by observing collision-induced reordering events in a long ion chain of mixed-isotope Yb\(^+\). From the observed reordering frequency, we extract the average interval between collisions to be \((1.9 \pm 0.1)\,\mathrm{hrs/ion}\). This corresponds to a local pressure of \((3.9 \pm 0.3)\times10^{-12}\,\mathrm{mbar}\) at the ion location, assuming that all collisions arise from background H\(_2\) molecules at room temperature. Our demonstration extends the continuous operation time of a quantum processor while maintaining the simplicity of a room-temperature system that does not require cryogenic apparatus.

This study investigates the effect of the ion-to-electron temperature ratio ($T_i/T_e$) on microturbulence driven transport in Quiescent H-mode (QH-mode) plasmas in the DIII-D tokamak. Utilizing the Gyrokinetic Toroidal Code (GTC) and the QH-mode equilibrium, we perform linear and nonlinear simulations to analyze transport properties and instability dynamics under variations of $T_i$ and $T_e$. Our results demonstrate that decreasing $T_i/T_e$ leads to a relative destabilization of trapped electron modes (TEM) over ion temperature gradient (ITG) modes, with the transition between these regimes dictated by $T_i/T_e$. When the electron temperature is increased at fixed ion temperature, we observe an increase in transport saturation levels. In contrast, decreasing the ion temperature at fixed electron temperature results in more modest transport enhancement. The radial correlation length, which characterizes eddy size, increases with rising $T_e$ and decreases with falling $T_i$, consistent with the observed trends in turbulent transport. Additionally, we examine the impact of impurity addition on turbulence and growth rates, finding that impurity presence does not significantly alter transport quantities compared to the impurity-free case. Finally, investigating helium as an alternative main ion species, we find that helium plasmas exhibit higher linear growth rates but result in lower transport saturation levels than deuterium plasmas, suggesting potential confinement benefits. These findings provide quantitative insights into the temperature ratio dependence in QH-mode plasmas and highlight the role of temperature profiles and zonal flows in influencing plasma confinement.

We characterise an efficient optically-heated neutral atom source for ion trapping. We observe loading rates of up to $24(3)\,\mathrm{s}^{-1}$ with heating powers below $85\,\mathrm{mW}$, and demonstrate loading of a single ion in under $30\,\mathrm{s}$ with $41.4(4)\,\mathrm{mW}$ of optical power in a room-temperature ion trap system with an ionisation probability of $1.50(5)\times10^{-5}$. We calibrate a thermal model for the source's internal temperature by imaging the fluorescence of a collimated flux of neutral calcium that effuses from the oven at various optical heating powers. We show that the thermal performance of this oven is mainly limited by radiative losses. We explore the effect of second-stage photo-ionisation laser power on the loading rate, and identify a path beyond the loading rates reported in this study. We predict that this source is also well-suited to a wide range of metals used in ion-trapping.

Transformers have gained popularity in machine learning due to their application in the field of natural language processing. They manipulate and process text efficiently, capturing long-range dependencies among data and performing the next word prediction. On the other hand, gate-based quantum computing is based on controlling the register of qubits in the quantum hardware by applying a sequence of gates, a process which can be interpreted as a low level text programming language. We develop a transformer model capable of transpiling quantum circuits from the qasm standard to other sets of gates native suited for a specific target quantum hardware, in our case the set for the trapped-ion quantum computers of IonQ. The feasibility of a translation up to five qubits is demonstrated with a percentage of correctly transpiled target circuits equal or superior to 99.98%. Regardless the depth of the register and the number of gates applied, we prove that the complexity of the transformer model scales, in the worst case scenario, with a polynomial trend by increasing the depth of the register and the length of the circuit, allowing models with a higher number of parameters to be efficiently trained on HPC infrastructures.

Integrated photonics in trapped-ion systems are critical for the realization of applications such as portable optical atomic clocks and scalable quantum computers. However, system-level integration of all required functionalities remains a key challenge. In this work, we demonstrate an autonomously operating optical clock having a short-term frequency instability of $3.14(5)\times 10^{-14} / \sqrtτ$ using an ensemble of four $^{171}\textrm{Yb}^{+}$ ions trapped in a multi-site surface-electrode trap at room temperature. All clock operations are performed with light delivered via on-chip waveguides. We showcase the system's resilience through sustained, autonomous operation featuring automated ion shuttling and reloading to mitigate ion loss during interleaved clock measurements. This work paves the way beyond component-level functionality to establish a viable and robust architecture for the next generation of portable, multi-ion quantum sensors and computers.

Controlled quantum mechanical motion of trapped atomic ions can be used to simulate and explore collective quantum phenomena and to process quantum information. Groups of cold atomic ions in an externally applied trapping potential self-organize into "Coulomb crystals" due to their mutual electrostatic repulsion. The motion of the ions in these crystals is strongly coupled, and the eigenmodes of motion all involve multiple ions. While this enables studies of many-body physics, it limits the flexibility and tunability of the system as a quantum platform. Here, we demonstrate an array of trapped ions in individual trapping sites whose motional modes can be controllably coupled and decoupled by tuning the local applied confining potential for each ion. We show that a single motional quantum, or phonon, can be coherently shared among two or three ions confined at the vertices of an equilateral triangle 30 $μ$m on a side. We can adiabatically tune the ion participation in the motional modes around a closed contour in configuration space, observing that the single-phonon wavefunction acquires a topological Berry phase if the contour encircles a conical intersection of motional eigenvalue surfaces. We observe this phase by single-phonon interference and study its breakdown as the motional mode tuning becomes non-adiabiatic. Our results show that precise, individual quantum control of ion motion in a two-dimensional array can provide unique access to quantum multi-body effects.

We propose the use of motional states of two interacting atoms trapped in a potential stroboscopically engineered by an optical tweezer as a means to implement a qubit-oscillator system, in analogy to those implemented in circuit quantum electrodynamics and trapped ions. In our setting, the center of mass degree of freedom of the atoms plays the role of a photon or phonon mode, while the interacting, relative mode acts as a qubit. No internal state is involved in our system, which makes this motional qubit robust to spin-dependent noise. We show that a universal set of bosonic operations, including displacement, rotation, squeezing, and the corresponding set of gates controlled by the qubit, can be implemented through precise temporal modulation of the optical tweezers. We numerically check that these gates can be generated with high fidelity, and discuss possible schemes for initial state preparation and final state readout. While we restrict the discussion to a single qubit-oscillator module, scalability can be achieved by coupling arrays of atoms via dipolar or Rydberg-dressed interactions.

Small-scale turbulence originating from microinstabilities limits the energy confinement time in magnetic confinement fusion. Here we develop a semi-analytical dispersion relation based on lowest-order solutions to the gyrokinetic equations in an asymptotic expansion in the ratio of transit (bounce) frequency to the mode frequency for ions (electrons), capable of describing two common instabilities: the ion temperature gradient (ITG) mode and trapped-electron mode (TEM), in the electrostatic limit. The dispersion relation, which is valid in arbitrary toroidal geometry, takes into account resonances with the magnetic ion and bounce-averaged electron drifts, incorporates non-local effects along the magnetic field line, is valid for arbitrary sign of the growth rate and magnetic curvature, and is shown to satisfy a variational property. Several common approximation models are introduced for both the magnetic drift and finite Larmor radius (FLR) damping, with the Padé approximation for FLR effect in particular resulting in remarkable agreement with the baseline dispersion relation model at significantly reduced costs. The baseline model is verified by comparing solutions of the dispersion relation model to high-fidelity linear gyrokinetic simulations, where the exact eigenfunction of the electrostatic potential from simulations is used as a trial function, showing good quantitative agreement for ITGs and TEMs in (shaped) tokamaks as well as low-magnetic-shear stellarators.

The propagation properties of ion-acoustic solitary and shock waves in the magnetized viscous plasma with nonthermal trapped electrons are investigated. The Cairns-Gurevich distribution as the electron distribution is considered to describe the plasma nonthermality and particle trapping. By adopting the reductive perturbation technique, we derived the nonlinear Schamel-Korteweg-de Vries-Burgers (SKdVB) equation, and then obtained the ion-acoustic shock and solitary wave solutions of the SKdVB equation for different limiting cases. It is found that the impact of nonthermal parameter α, external magnetic field Ω, obliqueness lz, wave speed U0, and the ion kinematic viscosity η0 can significantly change the characteristics of the shock and solitary waves. These results may be useful for better understanding the propagation of nonlinear structures in space (i.e. Earth's magnetosphere and ionosphere, auroral regions) and laboratory plasma with nonthermal trapped electrons.

The exceptional point has presented considerably interesting and counterintuitive phenomena associated with nonreciprocity, precision measurement, and topological dynamics. The Liouvillian exceptional point (LEP), involving the interplay of energy loss and decoherence inherently relevant to quantum jumps, has recently drawn much attention due to capability to fully capture quantum system dynamics and naturally facilitate non-Hermitian quantum investigations. It was also predicted that quantum jumps could give rise to third-order LEPs in two-level quantum systems for its high dimensional Liouvillian superoperator, which, however, has never been experimentally confirmed until now. Here we report the first observation of the third-order LEPs emerging from quantum jumps in an ultracold two-level trapped-ion system. Moreover, by combining decay with dephasing processes, we present the first experimental exploration of LEPs involving combinatorial effect of decay and dephasing. In particular, due to non-commutativity between the Lindblad superoperators governing LEPs for decay and dephasing, we witness the movement of LEPs driven by the competition between decay and dephasing occurring in an open quantum system. This unique feature of non-Hermitian quantum systems paves a new avenue for modifying nonreciprocity, enhancing precision measurement, and manipulating topological dynamics by tuning the LEPs.

Electron-on-neon (eNe) qubits have recently emerged as a compelling platform for quantum computing, which combines the vacuum isolation advantages of trapped-ion qubits with the scalability of superconducting circuits. In this system, electrons are trapped in vacuum above a solid neon film deposited on superconducting microwave resonators, where they exhibit strong coupling to the resonators, coherence times of ~0.1 ms, and single-qubit gate fidelities exceeding 99.97%. A central challenge, however, is the spontaneous binding of electrons to neon surface bumps. These bumps, originating from substrate roughness, vary in size: electrons on bumps of suitable sizes within the resonator can couple to microwave photons and function as qubits, whereas those on unfavorable bumps remain inactive yet contribute to background charge noise. Moreover, both the bump landscape and the sites where electrons bind differ from run to run, leading to variable qubit characteristics that hinder scalability. To address this challenging issue, we present an on-chip magnetic-levitation architecture in which arrays of solid-neon microparticles are suspended above the processor chip to act as electron carriers. This design eliminates substrate effects while retaining strong qubit-resonator coupling and supporting inter-qubit connectivity. Our analysis further shows that the qubit transition frequency can be tuned across the gigahertz range and its anharmonicity can reach ~0.8 GHz by tuning the resonator bias voltage. Together, these features suggest a promising pathway toward robust, reproducible, and scalable eNe-based quantum computing.

Many optimally scaling quantum simulation algorithms employ controlled time evolution of the Hamiltonian, which is typically the major bottleneck for their efficient implementation. This work establishes a compression protocol for encoding the controlled time evolution operator of translationally invariant, local Hamiltonians into a quantum circuit. It achieves a near-optimal in time $t$ scaling for circuit depth $\mathcal{O}(t \text{ polylog}(t N/ε))$, while reducing the control overhead from a multiplicative to an additive factor. We report that this compression protocol enables the implementation of Iterative Quantum Phase Estimation with as few as 414 CNOT gates for a frustrated quantum spin system on a 6$\times$6 triangular lattice and delivers ground state energy errors below 1% (with $\pm$ 1.5% variation, calculated with a hardware noise aware pipeline) on a 4$\times$4 triangular lattice using the noisy emulator of the Quantinuum H2 trapped ion device.

We present the basic performance and experimental results of an electron beam ion trap (JAXA-EBIT), newly introduced to the Japanese astronomical community. Accurate atomic data are indispensable for the reliable interpretation of high-resolution X-ray spectra of astrophysical plasmas. The JAXA-EBIT generates highly charged ions under well-controlled laboratory conditions, providing experimental benchmarks for atomic data. The JAXA-EBIT shows performance comparable to the Heidelberg compact EBIT through dielectronic recombination measurements of highly charged Ar ions. Furthermore, we conducted resonant photoexcitation spectroscopy of highly charged ions using the soft X-ray beamline BL17SU at the synchrotron radiation facility SPring-8. As a result, we successfully detected resonance transitions of He-like O$^{6+}$ and Ne-like Fe$^{16+}$. These results demonstrate the capability of the JAXA-EBIT for precise measurement of atomic data and show that it serves as a powerful tool for advancing astrophysical research.

We report a high-precision determination of the natural-abundance-averaged nuclear charge-radius difference between Yb and Lu using extreme ultraviolet (EUV) spectroscopy of highly charged ions (HCIs). By measuring the $D_1$ transition energies in Na- and Mg-like charge states of Lu and Yb confined in the Tokyo electron-beam ion trap, we extract meV-level energy shifts that are directly sensitive to nuclear-size effects. Transition-energy differences obtained from these spectra are compared with state-of-the-art relativistic many-body perturbation theory, including a new treatment of Mg-like ions. We develop a generalized framework to propagate uncertainties arising from nuclear deformation and surface diffuseness and evaluate corresponding nuclear-sensitivity coefficients. Combining Na- and Mg-like results yields mutually consistent radius differences, demonstrating the robustness of both the experimental calibration and the theoretical predictions. To determine absolute isotopic radii, we perform a generalized least-squares optimization incorporating our HCI constraints together with optical-isotope-shift data and muonic-atom results. This analysis establishes that the $^{175}$Lu charge radius is smaller than that of $^{174}$Yb, restoring the expected odd-even staggering across the $N=94$ isotonic chain. Our recommended value, $R(^{175}\text{Lu}) = 5.291(11)$ fm, reduces the uncertainty of the Lu radius by a factor of three compared with the previous electron-scattering result and resolves a long-standing anomaly in rare-earth nuclear systematics. This work demonstrates that EUV spectroscopy of HCIs provides a powerful and broadly applicable method for precision nuclear-structure studies in heavy, deformed nuclei. The techniques developed here enable future investigations of isotonic and isoelectronic sequences, including radioactive nuclides and higher-$Z$ systems.

Quantum machine learning (QML) has attracted growing interest with the rapid parallel advances in large-scale classical machine learning and quantum technologies. Similar to classical machine learning, QML models also face challenges arising from the scarcity of labeled data, particularly as their scale and complexity increase. Here, we introduce self-supervised pretraining of quantum representations that reduces reliance on labeled data by learning invariances from unlabeled examples. We implement this paradigm on a programmable trapped-ion quantum computer, encoding images as quantum states. In situ contrastive pretraining on hardware yields a representation that, when fine-tuned, classifies image families with higher mean test accuracy and lower run-to-run variability than models trained from random initialization. Performance improvement is especially significant in regimes with limited labeled training data. We show that the learned invariances generalize beyond the pretraining image samples. Unlike prior work, our pipeline derives similarity from measured quantum overlaps and executes all training and classification stages on hardware. These results establish a label-efficient route to quantum representation learning, with direct relevance to quantum-native datasets and a clear path to larger classical inputs.

Quantum coherence remains a fundamental challenge for advancing quantum technologies. Although dynamical decoupling can suppress decoherence noise, it frequently misestimates decoherence times due to control errors -- a previously underappreciated issue. Here, we present Hadamard phase cycling, a scalable non-Markovian quantum error mitigation method using group-structured phase configurations to filter spurious dynamics. Validated across molecular electron spins, nitrogen-vacancy centers in diamond, nuclear spins, trapped ions, and superconducting qubits, this technique enables accurate decoherence time characterization and enhanced state fidelity with linear complexity. Our results indicate that many reported ultralong decoherence times stem from artifacts like coherence-population mixing rather than genuine noise suppression. By ensuring dynamical authenticity, Hadamard phase cycling establishes a robust framework for reliable quantum control, paving the way for reassessment and advancement of coherence benchmarks in the NISQ era.

We introduce a non-abelian geometric quantum energy pump realized by a transitionless geometric quantum drive--a time-dependent Hamiltonian supplemented by a counterdiabatic term generated by a prescribed trajectory on a smooth control manifold--that coherently transports states within a degenerate subspace. When the coordinates of the trajectory are independently addressable by external drives, the net energy transferred between drives is set by the non-abelian Berry-curvature tensor. The trajectory-averaged pumping power is separately controlled by the initial state and by the Hamiltonian topology through the Euler class. We outline an implementation with artificial atoms, which are realizable on various platforms including trapped atoms/ions, superconducting circuits, and semiconductor quantum dots. The resulting energy pump can serve as a quantum transducer or charger, and as a metrological tool for measuring phase coherences in quantum states.

We propose and demonstrate an experimental scheme to engineer thermal baths with independently tunable temperatures and dissipation rates for the motional modes of a trapped-ion system. This approach enables robust thermal-state preparation and quantum simulations of open-system dynamics in bosonic and spin-boson models at well-controlled finite temperatures. We benchmark our protocol by experimentally realizing out-of-equilibrium dynamics of a charge-transfer model at different temperatures. We observe that, when the process occurs at a higher temperature, the transfer rate spectrum broadens, with reduced rates at small donor-acceptor energy gaps and enhanced rates at large gaps. We then employ our scheme to study local-temperature effects in a two-mode vibrationally assisted exciton transfer system, where we observe thermally activated interference pathways for excitation transfer.

Ultraintense pulses from X-ray free-electron lasers can drive, within femtoseconds, multiple processes in the inner shells of atoms and molecules in all phases of matter. The ensuing complex ionization pathways of outer-shell electrons from the neutral to the final highly charged states make a comparison with theory enormously difficult. We resolve these pathways by preparing highly charged ions in an electron beam ion trap before exposing them to the pulsed radiation. This reveals how relativistic fine-structure effects shift electronic energies, largely compensate the core-screening potential, and enable the consecutive, resonant absorption of two quasi-monochromatic X-ray photons that would generally be unfeasible. This doubly-resonant channel enhances the efficiency of two-photon ionization by more than two orders of magnitude, dominating in this regime the nonlinear interaction of light and matter with possible application for future precision X-ray metrology.

Scaling of quantum gates remains a central challenge in quantum information science. Ultrafast gates based on spin-dependent kicks provide a promising approach for trapped-ion systems. However, these gates require laser pulses with both high temporal tunability and stability, which are difficult to achieve with existing pulsed sources. Here, we propose a programmable pulsed source that allows flexible control of pulse intensity, waveform, and phase profiles. This enables precise manipulation of pulse sequences, thereby improving the fidelity of entangling gates. Furthermore, since the pulse parameters can be conveniently tuned, various coherent population-transfer schemes can be implemented adiabatic SDKs, thereby improving both the fidelity and robustness of fast quantum gate. Simulation results show that our programmable pulse system can achieve gate fidelities above 99.99% with strong robustness against variations in pulse intensity and single-photon detuning using stimulated Raman adiabatic rapid passage (STIRARP) protocols.

We develop a framework for extracting non-polynomial analytic functions of density matrices in randomized measurement experiments by a method of analytical continuation. A central advantage of this approach, dubbed stabilized analytic continuation (SAC), is its robustness to statistical noise arising from finite repetitions of a quantum experiment, making it well-suited to realistic quantum hardware. As a demonstration, we use SAC to estimate the von Neumann entanglement entropy of a numerically simulated quenched Néel state from Rényi entropies estimated via the randomized measurement protocol. We then apply the method to experimental Rényi data from a trapped-ion quantum simulator, extracting subsystem von Neumann entropies at different evolution times. Finally, we briefly note that the SAC framework is readily generalizable to obtain other nonlinear diagnostics, such as the logarithmic negativity and Rényi relative entropies.

Deterministic quasiperiodicity in quantum systems has long been associated with localization, criticality, or glassy behavior, and has therefore been believed to suppress long-range order rather than stabilize it. Here we demonstrate the opposite: quasiperiodicity in interactions--without any quasiperiodic potential, disorder, or geometric modulation--can generate coherent, ordered quantum phases. We study hard-core bosons in one dimension with quasiperiodic long-range interactions, V_{ij}=V_0 \cos(παi)\cos(παj), where n=α=(\sqrt{5}-1)/2 is the inverse golden ratio. Using large-scale path-integral quantum Monte Carlo simulations, we uncover thermodynamically stable incompressible plateaus at irrational densities tied to Fibonacci ratios. These plateaus exhibit sharp incommensurate Bragg peaks, signaling an emergent quasi-solid with long-range quasicrystalline density order. More strikingly, at nearby fillings and interaction strengths, we identify a quasi-supersolid phase that supports both Fibonacci density ordering and finite superfluid density--demonstrating that interaction-induced quasiperiodicity can stabilize supersolid coherence. Our results establish a new mechanism for realizing ordered quasicrystalline quantum matter, and provide realistic guidance for implementation in Rydberg atom arrays, multimode cavity-QED systems, and trapped-ion quantum simulators.

Wigner negativity and genuine multipartite entanglement (GME) are key nonclassical resources that enable computational advantages and broader quantum-information tasks. In this work, we prove two theorems for multimode continuous-variable systems that relate these nonclassical resources. Both theorems show that "enough" Wigner negativity -- either a large-enough Wigner negativity volume along a suitably-chosen two-dimensional slice, or a large-enough nonclassicality depth of the centre-of-mass of a system -- certifies the presence of GME. Moreover, violations of the latter inequality provide lower bounds of the trace distance to the set of non-GME states. Our results also provide sufficient conditions for generating GME by interfering a state with the vacuum through a multiport interferometer, complementing long-known necessary conditions. Beyond these fundamental connections, our methods have practical advantages for systems with native phase-space measurements: they require only measuring the Wigner function over a finite region, or measuring a finite number of characteristic function points. Such measurements are frequently performed with readouts common in circuit/cavity quantum electrodynamic systems, trapped ions and atoms, and circuit quantum acoustodynamic systems. As such, our GME criteria are readily implementable in these platforms.

We apply the recently proposed Sample-based Krylov Quantum Diagonalization (SKQD) method to lattice gauge theories, using the Schwinger model with a $θ$-term as a benchmark. SKQD approximates the ground state of a Hamiltonian, employing a hybrid quantum-classical approach: (i) constructing a Krylov space from bitstrings sampled from time-evolved quantum states, and (ii) classically diagonalizing the Hamiltonian within this subspace. We study the dependence of the ground-state energy and particle number on the value of the $θ$-term, accurately capturing the model's phase structure. The algorithm is implemented on trapped-ion and superconducting quantum processors, demonstrating consistent performance across platforms. We show that SKQD substantially reduces the effective Hilbert space, and although the Krylov space dimension still scales exponentially, the slower growth underscores its promise for simulating lattice gauge theories in larger volumes.

Many existing genuine multipartite entanglement (GME) witnesses for continuous-variable (CV) quantum systems typically rely on quadrature measurements, which is challenging to implement in platforms where the CV degrees of freedom can be indirectly accessed only through qubit readouts. In this work, we propose methods to implement GME witnesses through phase-space measurements in state-of-the-art experimental platforms, leveraging controlled Gaussian unitaries readily available in qubit-CV architectures. Based on two theoretical results showing that sufficient Wigner negativity can certify GME, we present five concrete implementation schemes using controlled parity, displacement, and beamsplitter operations. Our witnesses can detect paradigmatic GME states like the Dicke and multipartite $N00N$ states, which include the W states as a special case, and GHZ-type entangled cat states. We analyze the performance of these witnesses under realistic noise conditions and finite measurement resolution, showing their robustness to experimental imperfections. Crucially, our implementations require exponentially fewer measurement settings than full tomography, with one scheme requiring only a single measurement on auxiliary modes. The methods are readily applicable to circuit/cavity quantum electrodynamics, circuit quantum acoustodynamics, as well as trapped ions and atoms systems, where such dichotomic phase-space measurements are already routinely performed as native readouts.

Displacement sensing is a fundamental task in metrology. However, the development of quantum-enhanced sensors that fully utilize the available degrees of freedom in many-body quantum systems remains an outstanding challenge. We propose novel many-body displacement sensing schemes that use spin-dependent squeezed (SDS) states -- hybrid spin-boson states whose bosonic squeezed quadrature is conditioned on an auxiliary spin. We prove that SDS states are \emph{optimal}, i.e. their quantum Cramér-Rao bound saturates the Heisenberg limit. We propose explicit measurement sequences that can be readily implemented in systems such as trapped ions. We also introduce a scalable state-preparation protocol and numerically demonstrate the preparation of $8.7$~dB of spin-dependent squeezing $15$ times faster than the standard approach using second-order sidebands in trapped ions. The potential applications of our sensing protocols range from measuring single-photon scattering to searches for dark matter.

Understanding the emergence of novel collective behaviors in strongly interacting systems lies at the heart of quantum many-body physics. Valuable insight comes from examining how few-body correlations manifest in many-body systems, embodying the ``from few to many'' philosophy. An intriguing example is the set of universal relations in ultracold atomic gases, which connect a wide range of observables to a single quantity known as the contact. In this Letter, we demonstrate that universal relations manifest in a distinct class of quantum many-body systems, long-range quantum spin chains, which belong to a completely new universality class. Using effective field theory and the operator product expansion, we establish connections between the asymptotic behavior of equal-time spin correlation functions, the dynamical structure factor, and the contact density. The theoretical predictions for equal-time correlators are explicitly verified through numerical simulations based on matrix product states. Our results could be readily tested in state-of-the-art trapped-ion systems.

Electric-field-induced ion heating is a major obstacle in scalable trapped-ion quantum computing. We present a theoretical study of a novel 3D-printed ion trap with a skeleton electrode structure, designed to reduce heating by minimizing surface area near the ion. Compared to a conventional blade trap with identical confinement parameters, the skeleton trap achieves over 50% reduction in total heating rate. Patch-by-patch analysis reveals that heating is dominated by surfaces within 500 μm of the ion. For axial motion, the peak heating occurs approximately 110 μm away due to electric field directionality. We demonstrate that minor geometric optimization, in which the electrode gaps are realigned with these hotspots, can further suppress heating despite the associated increase in surface area. A linear relationship between ion-to-electrode distance and peak heating location is also established. These results highlight the potential of 3D-printed electrode designs for achieving both strong confinement and reduced noise in future quantum systems.

Probing quantum dynamics in the strong-field regime is critical for advancing our understanding of controlled quantum systems and developing robust quantum technologies. In this work, we experimentally investigate the dynamics of a trapped ion where the Rabi frequency (Omega) approaches the vibrational mode frequency (nu), pushing the system beyond the weak-field regime, where non-trivial quantum correlations emerge. We begin by setting the detuning (delta) - the frequency offset between the qubit transition and the driving field - to zero and varying Omega from low to high values, eventually reaching the vibrational frequency. Using quantum state tomography, we reconstruct the density matrix and track its evolution to assess non-Markovianity, revealing significant memory effects governed by the interplay between internal and motional degrees of freedom. Furthermore, by exploring the dynamics across various parameter pairs (Omega, delta), we find that non-Markovianity does not always increase monotonically with Omega for a fixed delta. Strikingly, when the condition delta squared plus Omega squared equals nu squared is met, the non-Markovianity exhibits a circular pattern of maxima. At this parameter combination, the system's Hamiltonian takes a form similar to the Jaynes-Cummings model, enabling the possibility of analytical insights into the observed dynamics. These results go beyond the conventional carrier and sideband regimes, uncovering novel features of strong-field quantum dynamics. Our findings establish a pathway for using trapped-ion platforms to investigate non-Markovianity, coherent control, and the fundamental behavior of open quantum systems in extreme regimes.

Quantum annealing is a framework for solving combinatorial optimization problems. While it offers a promising path towards a practical application of quantum hardware, its performance in real-world devices is severely limited by environmental noise that can degrade solution quality. We investigate the suppression of local field noise in quantum annealing protocols through the periodic application of dynamical decoupling pulses implementing global spin flips. As test problems, we construct minimal Multiple Object Tracking QUBO instances requiring only five and nine qubits, as well as cutting stock instances of five and six qubits. Moreover, using the Sherrington--Kirkpatrick model, we demonstrate the robustness of our protocol to problem structure and size. To further place our results in a practical context, we consider a trapped-ion platform based on magnetic gradient-induced coupling as a reference architecture, using it to define experimentally realistic noise and coupling parameters. We show that external magnetic field fluctuations, typical in such setups, significantly degrade annealing fidelity, while moderate dynamical decoupling pulse rates, which are achievable in current experiments, restore performance to near-ideal levels. Our analytical and numerical results reveal a universal scaling behavior, with fidelity determined by a generalized parameter combining noise amplitude and dynamical decoupling pulse interval. While our analysis is grounded in the trapped-ion platform, the proposed noise mitigation strategy and resulting performance improvements are applicable to a broad range of quantum annealing implementations and establish a practical and scalable route for error mitigation in near-term devices.

The $\mathbb{Z}_2$ lattice gauge theory is a paradigmatic model that exhibits gauge-field-mediated-confinement of pairs of particles into mesons, drawing connections to quantum chromodynamics. In the absence of any additional attractive interactions between particles, mesons are not known to bind in this model. Here, we show that resonant pair-production terms give rise to two separate mechanisms to form stable ``hadron'' bound states of two mesons: either induced by an effective attractive interaction, or a new dynamical binding mechanism induced by an effective repulsion. The repulsively bound hadron is a high-energy state stabilized by being energetically separated from the two-meson continuum through quantum fluctuations of the gauge fields. We study the dynamical formation of this bound state starting from local excitations. We use matrix product state techniques based on the time-evolving block decimation algorithm to perform our numerical simulations and analyze the effect of model parameters on hadron formation. Furthermore, we derive an effective model that explains its formation. Our findings are amenable to experimental observation on modern quantum hardware such as superconducting qubits, trapped ions, and Rydberg atom arrays.

Certifying nonclassical correlations typically requires access to all subsystems, presenting a major challenge in open quantum systems coupled to inaccessible environments. Recent works have shown that, in autonomous pure dephasing scenarios, quantum discord with the environment can be certified from system-only dynamics via the Hamiltonian ensemble formulation. However, this approach leaves open whether stronger correlations, such as entanglement, can be certified. Moreover, its reliance on Fourier analysis requires full-time dynamics, which is experimentally resource-intensive and provides limited information about when such correlations are established during evolution. In this work, we present a method that enables the certification of system-environment quantum entanglement solely from the reduced dynamics of the system. The method is based on the theory of mixed-unitary channels and applies to general non-autonomous pure dephasing scenarios. Crucially, it relaxes the need for full-time dynamics, offering a resource-efficient approach that also reveals the precise timing of entanglement generation. We experimentally validate this method on a Quantinuum trapped-ion quantum processor with a controlled-dephasing model. Finally, we highlight its potential as a tool for certifying gravitationally induced entanglement.

We introduce the 'smooth gate', an entangling method for trapped-ion qubits where residual spin-motion entanglement errors are adiabatically eliminated by ramping the gate detuning. We demonstrate electronically controlled two-qubit gates with an estimated error of $8.4(7)\times10^{-5}$ without ground-state cooling. We further show that the error remains $\lesssim 5\times10^{-4}$ for ions with average phonon occupation up to $\bar{n}=9.4(3)$ on the gate mode. These results indicate that trapped-ion quantum computation can achieve high fidelity at temperatures above the Doppler limit, which enables faster and simpler device operation.

We present two scalable and entanglement-free methods for estimating the collective state of an n-qubit quantum computer. The first method consists of a fixed set of five quantum circuits-regardless of the number of qubits-that avoid the use of entanglement as a measurement resource, relying instead on classical communication between selected pairs of qubits. The second method requires only 2n+1 circuits, each of which applies a single local gate to one of the n qubits during the measurement stage. Unlike traditional estimation methods, our approaches do not require any costly post-processing procedure to estimate a quantum state, enabling scalability to relatively large system sizes. We experimentally compare both methods on freely available IBM quantum processors, and observe how the state estimation varies with increasing number of qubits and shots. We further validated our results by estimating the 4-qubit entangled state of two remote ion-trap quantum processors, demonstrating that the optimized 2n+1 tomographic scheme achieves estimates consistent with standard methods while using exponentially fewer measurements.

Symmetry plays a fundamental role in many-body systems, both in and out of equilibrium. The quantum Mpemba effect (QME) - a phenomenon where systems initially farther from equilibrium can thermalize faster - can be understood in terms of how rapidly a symmetry, broken by initial conditions, is dynamically restored. In this work, we study the QME in a one-dimensional spin-1/2 XYZ model with power-law decaying interactions in the presence of a magnetic field. In the prethermal regime generated by large field strengths, the system develops a continuous U(1) symmetry, enabling the QME to emerge. However, due to the Hohenberg-Mermin-Wagner theorem, the QME can only arise when interactions are sufficiently short-ranged. This leads to an interplay between the external field, interaction range, and dynamical symmetry restoration. We systematically explore this interplay and analyze the dependence of the QME on the effective temperature set by the initial state. Our results demonstrate the tunability of the QME via long-range interactions, which can be probed in experimental platforms of trapped ions, polar molecules, and NV centers.

We demonstrate a new technique that adapts single-qubit randomized benchmarking to two-qubit Mølmer-Sørensen gates. We use the controllable gate phase to generate Cliffords that act on a two-state subspace, enabling benchmarking of two-qubit gates without single-qubit operations. In addition to quantifying the gate infidelity, the protocol provides valuable information about the type of error by distinguishing between those that conserve the two-state subspace and those that result in leakage out of it. We demonstrate the protocol for calibrating and validating all-electronic maximally entangling gates in a trapped-ion quantum computer, achieving a two-qubit gate error of $2.6 (2)\times10^{-4}$.

We report a proof-of-principle study demonstrating the first capture and time-of-flight spectrometry of highly charged ions (HCIs) produced following antiproton annihilations in a Penning-Malmberg trap. A multi-step nested-trap technique was developed using the \aegis\ experiment to identify annihilation-linked captured ions. The trapping and spectrometry of helium and argon ions demonstrates the approach. This work establishes a foundation for the in-trap synthesis of radioactive HCIs and the study of cold nuclear annihilation fragments, with the long-term goal of enabling a sensitive tool for probing the outer nuclear periphery.

Autonomous quantum machines (AQMs) execute tasks without requiring time-dependent external control. Motivations for AQMs include the restrictions imposed by classical control on quantum machines' coherence times and geometries. Most AQM work is theoretical and abstract; yet an experiment recently demonstrated AQMs' usefulness in qubit reset, crucial to quantum computing. To further reduce quantum computing's classical control, we propose realizations of (fully and partially) quantum-autonomous gates on three platforms: Rydberg atoms, trapped ions, and superconducting qubits. First, we show that a Rydberg-blockade interaction or an ultrafast transition can quantum-autonomously effect entangling gates on Rydberg atoms. One can perform $Z$ or entangling gates on trapped ions mostly quantum-autonomously, by sculpting a linear Paul trap or leveraging a ring trap. Passive lasers control these gates, as well as the Rydberg-atom gates, quantum-autonomously. Finally, circuit quantum electrodynamics can enable quantum-autonomous $Z$ and $XY$ gates on superconducting qubits. The gates can serve as building blocks for (fully or partially) quantum-autonomous circuits, which may reduce classical-control burdens.

Systematic control errors, specifically Rabi frequency fluctuations and frequency detuning, constitute a primary bottleneck for high-fidelity quantum gates across leading platforms. In this work, we present a robust pulse engineering framework for non-adiabatic holonomic quantum computing (NHQC) in qutrit systems, combining inverse engineering with time-dependent perturbation theory. We derive analytical conditions for pulse shaping that intrinsically eliminate second-order Rabi errors. Furthermore, our analysis reveals that second-order detuning errors are fundamentally linked to the accumulated population in the auxiliary excited state, making them impossible to eliminate in a single loop. To overcome this, we introduce a compensation pulse strategy that rigorously cancels these residual errors. Although this composite scheme doubles the gate duration, we demonstrate that the suppression of systematic errors yields a significant net gain in fidelity, achieving values exceeding 99.9% under realistic experimental imperfections ($ε=0.2$, $δ=2~\text{MHz}$). This framework provides a rigorous and experimentally feasible pathway for high-fidelity quantum control in superconducting circuits, trapped ions, and neutral atom systems.

Laser-driven operations are a common approach for engineering one- and two-qubit gates in trapped-ion arrays. Measuring key parameters of these lasers, such as beam sizes, intensities, and polarizations, is central to predicting and optimizing gate speeds and stability. Unfortunately, it is challenging to accurately measure these properties at the ion location within an ultra-high vacuum chamber. Here, we demonstrate how the ions themselves may be used as sensors to directly characterize the laser beams needed for quantum gate operations. Making use of the four-photon Stark Shift effect in $^{171}$Yb$^+$ ions, we measure the profiles, alignments, and polarizations of the lasers driving counter-propagating Raman transitions. We then show that optimizing the parameters of each laser individually leads to higher-speed Raman-driven gates with smaller susceptibility to errors. Our approach demonstrates the capability of trapped ions to probe their local environments and to provide useful feedback for improving system performance.

Competition between short- and long-range interactions underpins many emergent phenomena in nature. Despite rapid progress in their experimental control, computational methods capable of accurately simulating open quantum many-body systems with complex long-ranged interactions at scale remain scarce. Here, we address this limitation by introducing an efficient and scalable approach to dissipative quantum lattices in one and two dimensions, combining matrix product operators and time-dependent variational Monte Carlo. We showcase the versatility, effectiveness, and unique methodological advantages of our algorithm by simulating the non-equilibrium dynamics and steady states of spin-$\frac{1}{2}$ lattices with competing algebraically-decaying interactions for as many as $N=200$ sites, revealing the emergence of spatially-modulated magnetic order far from equilibrium. This approach offers promising prospects for advancing our understanding of the complex non-equilibrium properties of a diverse variety of experimentally-realizable quantum systems with long-ranged interactions, including Rydberg atoms, ultracold dipolar molecules, and trapped ions.

This study examines the distribution and evolution of lithium in both anode and cathode materials of commercial lithium-ion coin cells subjected to high C-rate cycling, providing insights into the mechanisms of lithium loss, trapping, and plating. Cells were cycled at 1C to 3C rates, and post-mortem analysis was performed using Li nuclear reaction analysis (Li-NRA), x-ray diffraction (XRD), and scanning electron microscopy (SEM) equipped with energy-dispersive x-ray spectroscopy (EDS). Li-NRA, using the resonant nuclear reaction between an incident high-energy proton and lithium, was used to measure the depth distribution of Li in the cathode and anode layers. The Li-NRA analysis revealed a surface lithium peak on the anode, likely associated with SEI formation and lithium plating, while the cathode exhibited a decrease in lithium content by ~19.7%. XRD analysis of the cycled cathode showed an expansion of the c-lattice parameter and peak shifts consistent with lithium depletion and structural deformation, supported by SEM imaging. In contrast, the dead graphite anode shows an enhanced peak at 43.3°, which corresponds to the presence of Li2Co3. 3-C rate cycling also led to capacity fade and an increase in internal resistance, highlighting the impact of lithium plating on cell performance.

Single ion optical clocks have shown systematic frequency uncertainties below $10^{-18}$, but typically require more than one week of averaging to achieve a corresponding statistical uncertainty. This time can be reduced with longer probe times, but comes at the cost of a higher time-dilation shift due to motional heating of the ions in the trap. We show that sympathetic ground-state cooling using electromagnetically-induced transparency (EIT) of an \Al clock ion via a co-trapped \Ca ion during clock interrogation suppresses the heating of the ions. \Al can be kept close to the motional ground state, independent from the chosen interrogation time, at a relative time dilation shift of $(-1.69\pm0.20)\times10^{-18}$. The \Ca cooling light introduces an additional light shift on the \Al clock transition of $(-9.27\pm 1.03)\times10^{-18}$. We project that the uncertainty of this light shift can be further reduced by nearly an order of magnitude. This sympathetic cooling enables seconds of interrogation time with $10^{-19}$ motional and cooling laser-induced uncertainties for \Al and can be employed in other ion clocks as well.

Entangling gates are an essential capability of quantum computers. There are different methods for implementing two-qubit gates, with respective advantages and disadvantages. We investigate the experimentally relevant differences and commonalities of laser-based $σ_z\otimesσ_z$ light-shift and $σ_φ\otimesσ_φ$ Moelmer-Soerensen gates, highlighting the phases of experimental control fields and their long-term stabilities, in the specific case of mixed-species gates. We implement these gates on qubits with very different magnetic field sensitivities, encoded in $^{43}\mathrm{Ca}^+$ and $^{88}\mathrm{Sr}^+$, achieving fidelities of $99.8\%$ for the $σ_z\otimesσ_z$ and $99.6\%$ for the $σ_φ\otimesσ_φ$ gate.

Synchronization is a hallmark of collective behavior that emerges when nonlinear systems interact, spanning scales from mechanical oscillators to planetary orbits. As a universal phenomenon it underpins the study of complex systems and has far-reaching technological implications. While classical synchronization has a long and rich history, it has not been observed experimentally between multiple quantum limit-cycle oscillators despite a decade of theoretical investigations. We realize synchronization between two quantum van der Pol oscillators by engineering dissipation in a mixed-isotope trapped-ion quantum simulator. The synchronized state is encoded in a fixed relative phase between the oscillators that is inaccessible to local measurements and only revealed through joint readout of both oscillators, in stark contrast to the classical case where synchronization can be observed via individual phase measurements. We further show that the relative phase can be precisely controlled, and that the chain of two oscillators can synchronize to an external field, suggesting applications in sensing. Our results provide a promising pathway for studying more complex synchronized quantum dynamics beyond two oscillators, where a theoretical treatment becomes increasingly challenging, and it remains to be understood whether genuinely quantum features persist in such cases.

We introduce an ion trap platform based on a 3D-printed micro-junction array, designed to implement quantum charge-coupled device (QCCD) architectures for large-scale quantum information processing (QIP). The integration of three-dimensionally structured micro Radio-Frequency (RF) electrodes above a surface-electrode trap enables flexible control of electric field profiles across both linear and junction regions. Through simulations, we demonstrate that the linear region exhibits deeper and more harmonic ion confinement with reduced RF drive power compared to conventional planar traps. Crucially, we identify a junction geometry that maintains uniform ion confinement during transport while substantially reducing the pseudopotential barrier. This reduction facilitates low-heating, high-fidelity transport of single- and multi-species ion crystals. Our results establish a viable route toward fault-tolerant quantum computing by enabling modular and scalable QCCD systems based on the state-of-the-art 3D-printing technologies.

Engineering coherent spatial superpositions of levitated large masses is an ongoing challenge. Borrowing from recent experimental work, we consider a charged mass of hundreds of nanometers size (``nanoparticle'') co-trapped with an ion in a Paul trap, and propose a scheme to manipulate its spatial state through the Coulomb interaction with the ion. We focus on the achievable delocalisation, only sketching the other challenges of the protocol (initial cooling, preservation of coherence for long-enough times, and detection). We prove that our scheme can displace coherently the nanoparticle by a few nanometers, with state-of-the-art parameters. Though smaller than the nanoparticle's size, this is much larger than the wavefunction of the trap's ground state. Thus the co-trapping scheme is in principle able to demonstrate macroscopic delocalisation of a charged nanoparticle.

Decoherence errors arising from noisy environments remain a central obstacle to progress in quantum computation and information processing. Quantum error correction (QEC) based on the Gottesman-Kitaev-Preskill (GKP) protocol offers a powerful strategy to overcome this challenge, with successful demonstrations in trapped ions, superconducting circuits, and photonics. Beyond active QEC, a compelling alternative is to engineer Hamiltonians that intrinsically enforce stabilizers, offering passive protection akin to topological models. Inspired by the GKP encoding scheme, we implement a superconducting qubit whose eigenstates form protected grid states - long envisioned but not previously realized - by integrating an effective Cooper-quartet junction with a quantum phase-slip element embedded in a high-impedance circuit. Spectroscopic measurements reveal pairs of degenerate states separated by large energy gaps, in excellent agreement with theoretical predictions. Remarkably, our observations indicate that the circuit tolerates small disorders and gains robustness against environmental noise as its parameters approach the ideal regime, establishing a new framework for exploring superconducting hardware. These findings also showcase the versatility of the superconducting circuit toolbox, setting the stage for future exploration of advanced solid-state devices with emergent properties.

We present a MATLAB script which can use GPU acceleration to simulate a trapped ion interacting with a low-density cloud of atoms. This script, called atomiongpu.m, can massively parallelize MD simulations of trajectories of a trapped ion and an atom starting far away. The script uses ode45gpu, which is our optimized and specialized implementation of the Runge-Kutta algorithm used in MATLAB's ODE solver ode45. We first discuss the physical system and show how ode45gpu can solve it up to 22x faster than MATLAB's ode45. Then, we show how to easily modify the inputs to atomiongpu.m to account for different kinds of atoms, ions, atom-ion interactions, trap potentials, simulation parameters, initial conditions, and computational hardware, so that atomiongpu.m automatically finds the probability of complex formation, the distribution of observables such as the scattering angle and complex lifetime, and plots of specific trajectories.

Simulating out-of-equilibrium dynamics of quantum field theories in nature is challenging with classical methods, but is a promising application for quantum computers. Unfortunately, simulating interacting bosonic fields involves a high boson-to-qubit encoding overhead. Furthermore, when mapping to qubits, the infinite-dimensional Hilbert space of bosons is necessarily truncated, with truncation errors that grow with energy and time. A qubit-based quantum computer, augmented with an active bosonic register, and with qubit, bosonic, and mixed qubit-boson quantum gates, offers a more powerful platform for simulating bosonic theories. We demonstrate this capability experimentally in a hybrid analog-digital trapped-ion quantum computer, where qubits are encoded in the internal states of the ions, and the bosons in the ions' motional states. Specifically, we simulate nonequilibrium dynamics of a (1+1)-dimensional Yukawa model, a simplified model of interacting nucleons and pions, and measure fermion- and boson-occupation-state probabilities. These dynamics populate high bosonic-field excitations starting from an empty state, and the experimental results capture well such high-occupation states. This simulation approaches the regime where classical methods become challenging, bypasses the need for a large qubit overhead, and removes truncation errors. Our results, therefore, open the way to achieving demonstrable quantum advantage in qubit-boson quantum computing.

In recent years, the presence of local potentials has significantly enriched and diversified the entanglement patterns in monitored free fermion systems. In our approach, we employ the stochastic Schrödinger equation to simulate a one-dimensional spinless fermion system under continuous measurement and local potentials. By averaging the steady-state entanglement entropy over many quantum trajectories, we investigate its dependence on measurement and localization parameters. We used a phenomenological model to interpret the numerical results, and the results show that the introduction of local potentials does not destroy the universality class of the entanglement phase transition, and that the phase boundary is jointly characterized by the measurement process and the localization mechanism. This work offers a new perspective on the characterization of the entanglement phase boundary arising from the combined effects of measurement and localization, and provides criteria for detecting this novel phase transition in cold atom systems, trapped ions, and quantum dot arrays.

Precision atomic and quantum experiments rely on ultra-stable narrow linewidth lasers constructed using table-top ultra-low expansion reference cavities. These experiments often require multiple lasers, operating at different wavelengths, to perform key steps used in state preparation and measurement required in quantum sensing and computing. This is traditionally achieved by disciplining a cavity-stabilized laser to a key atomic transition and then transferring the transition linewidth and stability to other lasers using the same reference cavity in combination with bulk-optic frequency shifting such as acousto-optic modulators. Transitioning such capabilities to a low cost photonic-integrated platform will enable a wide range of portable, low power, scalable quantum experiments and applications. Yet, today's bulk optic approaches pose challenges related to lack of cavity tunability, large free spectral range, and limited photonic integration potential. Here, we address these challenges with demonstration of an agile photonic-integrated 780 nm ultra-high-Q tunable silicon nitride reference cavity that performs multiple critical experimental steps including laser linewidth narrowing, high resolution rubidium spectroscopy, dual-stage stabilization to a rubidium transition, and stability transfer to other lasers. We achieve up to 20 dB of frequency noise reduction at 10 kHz offset, precision spectroscopy over a 250 MHz range, and dual-stage locking to rubidium with an Allan deviation of $8.5 \times 10^{-12}$ at 1 s and up to 40 dB reduction at 100 Hz. We further demonstrate the transfer of this atomic stability to a second laser, via the rubidium-disciplined cavity, and demonstrate multi-wavelength Rydberg electrometry quantum sensing. These results pave the path for integrated, compact, and scalable solutions for quantum sensing, computing and other atomic and trapped ion applications.

Optical clocks based on atoms and ions probe relativistic effects with unprecedented sensitivity by resolving time dilation due to atom motion or different positions in the gravitational potential through frequency shifts. However, all measurements of time dilation so far can be explained effectively as the result of dynamics with respect to a classical proper time parameter. Here we show that atomic clocks can probe effects where a classical description of the proper time dynamics is insufficient. We apply a Hamiltonian formalism to derive time dilation effects in harmonically trapped clock atoms and show how second-order Doppler shifts (SODS) due to the vacuum energy (vSODS), squeezing (sqSODS) and quantum corrections to the dynamics (qSODS) arise. We also demonstrate that the entanglement between motion and clock evolution can become observable in state-of-the-art clocks when the motion of the atoms is strongly squeezed, realizing proper time interferometry. Our results show that experiments with trapped ion clocks are within reach to probe relativistic evolution of clocks for which a quantum description of proper time becomes necessary.

A longstanding goal in quantum information science is to demonstrate quantum computations that cannot be feasibly reproduced on a classical computer. Such demonstrations mark major milestones: they showcase fine control over quantum systems and are prerequisites for useful quantum computation. To date, quantum advantage has been demonstrated, for example, through violations of Bell inequalities and sampling-based quantum supremacy experiments. However, both forms of advantage come with important caveats: Bell tests are not computationally difficult tasks, and the classical hardness of sampling experiments relies on unproven complexity-theoretic assumptions. Here we demonstrate an unconditional quantum advantage in information resources required for a computational task, realized on Quantinuum's H1-1 trapped-ion quantum computer operating at a median two-qubit partial-entangler fidelity of 99.941(7)%. We construct a task for which the most space-efficient classical algorithm provably requires between 62 and 382 bits of memory, and solve it using only 12 qubits. Our result provides the most direct evidence yet that currently existing quantum processors can generate and manipulate entangled states of sufficient complexity to access the exponentiality of Hilbert space. This form of quantum advantage -- which we call quantum information supremacy -- represents a new benchmark in quantum computing, one that does not rely on unproven conjectures.

Optical transitions of highly charged ions can be very sensitive to hypothetical beyond-the-Standard-Model phenomena. Those near the $5s-4f$ level crossing, where the $5s$ and $4f$ are degenerate are especially promising. We present predictions from atomic theory and measurements of Os$^{15,16,17+}$ at an electron beam ion trap for identification of several transitions suitable for searches for a hypothetical fifth force and possible violations of local Lorentz invariance. The electric quadrupole (E2) transitions of Os$^{16+}$ that were found are especially suitable for frequency metrology due to their small linewidth of 44 $μ$Hz. Our calculations show the need for including enough inner-shell excitations to predict transition rates between configurations, which can otherwise be overestimated. Ultimately, the predicted interconfiguration transitions were too weak to be detected.

Recent advances in quantum technologies have enabled quantum simulation of gauge theories -- some of the most fundamental frameworks of nature -- in regimes far from equilibrium, where classical computation is severely limited. These simulators, primarily based on neutral atoms, trapped ions, and superconducting circuits, hold the potential to address long-standing questions in nuclear, high-energy, and condensed-matter physics, and may ultimately allow first-principles studies of matter evolution in settings ranging from the early universe to high-energy collisions. Research in this rapidly growing field is also driving the convergence of concepts across disciplines and uncovering new phenomena. In this Review, we highlight recent experimental and theoretical developments, focusing on phenomena accessible in current and near-term quantum simulators, including particle production and string breaking, collision dynamics, thermalization, ergodicity breaking, and dynamical quantum phase transitions. We conclude by outlining promising directions for future research and opportunities enabled by available quantum hardware.

We report on efficient rovibrational state-selective loading of single H$_2^+$ molecular ions into a cryogenic linear Paul trap using (2+1) resonance-enhanced multi-photon ionization (REMPI). The H$_2^+$ ions are created by resonant two-photon excitation of H$_2$ molecules from the $X\;^1Σ_g^+$ state to the $E,F\;^1Σ_g^+$ state, followed by non-resonant one-photon ionization. The H$_2^+$ ions are produced from residual gas and sympathetically cooled by a co-trapped, laser-cooled $^9$Be$^+$ ion. By tuning the wavelength of the REMPI laser, we observe the loading of single H$_2^+$ ions via the ($ν' = 0$, $L' = 0, 1, 2, 3$) rovibrational levels of the $E,F\;^1Σ_g^+$ intermediate state. We measure the success probability for the production of H$_2^+$ in the ($ν^+ = 0$, $L^+ = 1$) state via the ($ν' = 0$, $L' = 1$) level to be 85(6)% by quantum logic spectroscopy (QLS) of the hyperfine structure of this rovibrational state. Furthermore, we load an H$_2^+$ ion via the ($ν' = 0$, $L' = 2$) level and confirm its rovibrational state to be ($ν^+ = 0$, $L^+ = 2$) by QLS. We perform QLS probes on the ion over 19 h and observe no decay of the rotationally excited state. Our work demonstrates an efficient state-selective loading mechanism for single-ion, high-precision spectroscopy of hydrogen molecular ions.

Optical crosstalk due to imperfect addressing in trapped-ion entangling gates generates unwanted non-local entanglement between target ions and their neighbors that is difficult to mitigate using standard quantum error correction. We present a method to design entangling operations that are inherently insensitive to crosstalk by engineering the effective qubit coupling matrix. By controlling the geometric phases generated in the motional modes of the ion string, we construct a coupling matrix that selectively excludes crosstalk-affected neighbor ions from the entangling operation. This approach requires no knowledge of the amount of crosstalk present and avoids the need for additional gate operations or modifications to the optical setup. We numerically demonstrate the construction of crosstalk-insensitive entangling pulses for target ion pairs within an equispaced 20-ion string and provide experimental validation of crosstalk-insensitive entanglement in a three-ion string.

We demonstrate the operation of a dual-frequency Paul trap and characterize its performance by storing either electrons or calcium ions while applying two quadrupole fields simultaneously which oscillate at $Ω_\textrm{fast} = 2π\times 1.6$ GHz and $Ω_\textrm{slow} = 2π\times 2$ MHz. The particles are loaded and stored in the trap under various conditions followed by detection employing an electron multiplier tube. We find that tens of electrons or ions can be trapped for up to ten milliseconds and a small fraction remains trapped even after hundreds of milliseconds. During dual-frequency operation we find that while the number of trapped electrons rapidly decreases with increase of the $Ω_\textrm{slow}$ field amplitude, the number of trapped ions shows no dependence on the $Ω_\textrm{fast}$ field amplitude as supported by our extensive numerical simulations. We aim to use a similar trap for synthesising antihydrogen from antiprotons and positrons. Accordingly, we discuss open challenges such as the co-trapping of oppositely charged species and particle trap duration.

We propose and demonstrate four procedures for three-dimensional micromotion compensation by combining two methods: the RF-photon correlation method and the displacement method based on trap RF amplitude modulation. In ion traps, the structure of the electrodes or the vacuum chamber may restrict the laser beam incidence direction, and causes the limitation in the compensation scheme. We present four protocols, ensuring that at least one of them can be applied to experimental systems with various individual constraints. We also discuss the compensation accuracy and practical applicability of each of these four approaches. This work provides a practical guideline for performing full three-axis micromotion compensation and contributes to the advancement of endcap traps, which are highly suitable for single-ion trapping.

Error mitigation is essential for unlocking the full potential of quantum algorithms and accelerating the timeline toward quantum advantage. As quantum hardware progresses to push the boundaries of classical simulation, efficient and robust error mitigation methods are becoming increasingly important for producing accurate and reliable outputs. However, existing error-mitigation approaches face a fundamental tradeoff between practical performance and reliability: heuristic methods such as zero-noise extrapolation (ZNE) enjoy faster runtime but lack accuracy guarantees, while rigorous techniques such as probabilistic error cancellation (PEC) provide unbiased estimates at prohibitive computational cost. We introduce a characterization-based, rigorously-grounded quantum error mitigation and error suppression framework (QESEM) that resolves this tradeoff by leveraging the accuracy guarantees of quasi-probabilistic mitigation with dramatically reduced overhead. We explain the innovative methods underlying QESEM and demonstrate its capabilities in the largest utility-scale error mitigation experiment based on an unbiased method. This experiment simulates the kicked transverse field Ising model with far-from-Clifford parameters on an IBM Heron device. We further validate QESEM's versatility across arbitrary quantum circuits and devices through high-accuracy error-mitigated molecular VQE circuits executed on IBM Heron and IonQ trapped-ion devices. Compared with multiple variants of the widely used zero-noise extrapolation method, QESEM consistently achieves higher accuracy while avoiding the prohibitive runtime overhead associated with PEC. These results mark a significant step forward in accuracy and reliability for running quantum circuits on current devices across diverse applications. Finally, we provide projections of QESEM's performance on near-term devices toward quantum advantage.

We report measurements of the K$α$ emission from the astrophysically very abundant Ca XIX (He-like ion) and its satellite lines resonantly excited by dielectronic recombination (DR). We achieve an electron-energy resolution of 8 eV in a cryogenic electron beam ion trap, and determine the energies of the exciting electrons and the emitted photons up to the KLn ($n\le 8$) manifold with $0.05\%$ and $0.1\%$ respective uncertainties. For the KLL satellites, energies agree very well with our predictions using the Flexible Atomic Code (FAC) and previous state-of-the-art calculations. Our calculations also agree with our experimental direct excitation cross-sections for K$α$ within their $10\%$ uncertainty. We extract DR coefficient rates and find good agreement with values tabulated in the OPEN-ADAS database. As an application, we experimentally benchmark Ca XIX atomic data used to model high-temperature astrophysical plasmas by comparing FAC synthetic spectra with recent XRISM observations revealing the contributions of DR satellites to the Ca XIX lines.

A Multi-Reflection Time-of-Flight Mass Spectrometer (MR-ToF-MS) has been commissioned at the Ion-Guide Isotope Separator On-Line (IGISOL) facility. It consists of six electrode pairs that form a nearly energy-isochronous potential and a pulsed drift-tube to trap the ions between the electrodes. Time-of-flight peak widths down to 22 ns full-width at half-maximum and mass-resolving powers of $\approx 1.5 \times 10^5$ within 20 ms have been demonstrated. The obtained time-focus and mass-resolving power depend sensitively on the trapping energy, energy spread and the number of revolutions of the ions. The mass-resolving power is affected by the temporal and energy spread of the ions entering the MR-ToF-MS, and fluctuations in the electrode voltages due to temperature variations. The longitudinal emittance corresponding to the temporal and energy spread of $^{39}$K is estimated to be 175 eVns based on the data, close to the expected 186(10) eVns. The time-of-flight temperature sensitivity is found to be -5.55(30) ppm/K. In addition to atomic mass measurements of short-lived exotic nuclides, the MR-ToF-MS can be used as a fast mass separator for various other experiments at IGISOL and as an ion counter for laser spectroscopy and yield measurements.

We explore a novel strategy for detecting the radiative decay of very weakly interacting particles by leveraging the extreme sensitivity of quantum devices, such as superconducting transmon qubits and trapped ion systems, to faint electromagnetic signals. By modeling the effective electric field induced by the decay photons, we evaluate the response of quantum sensors across two particle physics scenarios: the cosmic neutrino background and two-component dark matter. We assess the discovery potential of these devices and outline the parameter space accessible under current experimental capabilities. Our analysis demonstrates that quantum sensors can probe radiative decays of dark matter candidates using existing technology, while probing neutrino magnetic moments beyond current limits will require scalable quantum architectures with enhanced coherence.

Ion Coulomb crystals are ordered structures formed by laser-cooled ions in traps that are characterized by interparticle distances of several micrometers and energy scales on the order of $μ$eV. Their crystalline structure emerges from the interplay between Coulomb repulsion and the external confining potential, which can be readily tuned. Moreover, individual ions can be precisely manipulated with lasers and imaged via resonance fluorescence. These unusual and unique properties make ion crystals a powerful platform for studying phases of matter in the strongly correlated regime and at low temperatures where their dynamics is manifestly quantum mechanical. This review examines the theoretical framework and experimental characterization of ion Coulomb crystals from a condensed-matter perspective. We discuss their dynamical and thermodynamic properties in one, two, and three dimensions, and review recent investigations into their out-of-equilibrium behavior. We provide outlooks on future directions for exploring novel condensed matter phenomena with trapped ion crystals, as well as for exploiting these features for scientific and technical applications.

Efficient quantum-state detection is crucial for many precision control experiments, such as the ongoing effort to probe the electron's electric dipole moment using trapped molecular $^{232}\mathrm{ThF}^+$ ions at JILA. While quantum state detection through state-selective photodissociation has been successfully implemented on this molecule, progress has been hindered by low dissociation efficiency. In this work, we perform spectroscopy on the molecule to identify excited states that facilitate more efficient photodissociation. For the most favorable transition, we achieve a dissociation efficiency of 57(14)% with quantum state selectivity. Additionally, we discuss several state detection protocols that leverage favorable excited states that will facilitate simultaneous readout of all EDM relevant states, allowing further improvement of overall statistics.

The effects of noise are one of the most important factors to consider when it comes to quantum computing in the noisy intermediate-scale quantum computing (NISQ) era that we are currently in. Therefore, it is important not only to gain more knowledge about the noise sources appearing in current quantum computing hardware in order to suppress and mitigate their contributions, but also to evaluate whether a given quantum algorithm can achieve reasonable results on a given hardware. To accomplish this, we need noise models that can describe the real hardware with sufficient accuracy. Here, we present a noise model that has been evaluated on superconducting hardware platforms and could be adapted to other common architectures such as trapped-ion or neutral atom devices. We then benchmark our model by simulating a 20-qubit superconducting quantum computer, and compare the accuracy of our model to similar approaches from the literature and demonstrate an improvement in the overall prediction accuracy.

Cross-beam energy transfer (CBET) between two lasers is investigated through theoretical analysis and two-dimensional hybrid simulations over sub-nanosecond to nanosecond timescales and millimeter spatial scales. A finite frequency-difference range for CBET development is derived. Ion acoustic wave (IAW) damping is found to broaden this range while reducing the growth rate of stimulated Brillouin scattering (SBS). CBET exhibits distinct nonlinear behaviors across different laser-intensity regimes. Denoting $I_{14}=1\times 10^{14} \mathrm{W/cm^2}$ for a laser wavelength of $351 \mathrm{nm}$, at moderate intensities ($1<I/I_{14}<8$), CBET grows weakly and saturates at a low level due to pump depletion. In the strongly coupled SBS regime ($I/I_{14} \gtrsim 8$), harmonic IAW and nonlinear wave-particle interactions emerge. The generation of harmonic IAW reduces the normal IAW mode, while ion-trapping-induced spectral broadening of normal IAW mode causes frequency mismatch, leading to nonlinear reduction of CBET. After the saturation of harmonic mode, ion trapping broadens harmonic IAW spectrum and weakens it, triggering a secondary growth stage of CBET. After approximately $60 \mathrm{ps}$, CBET approaches quasi-steady-state. The maximum total energy transfer occurs at a frequency difference below the linear matching condition due to the trapping-induced IAW redshift. Based on these two intensity regimes, piecewise scalings of the quasi-saturated total energy transfer rate with $I/I_{14}$ are obtained and shown to be robust against spot size. Speckle effects reduce high-intensity overlap and thus the energy transfer rate. The effects of plasma temperature, density, and flow velocity on CBET are also examined.

Narrow linewidth stabilized lasers are central to precision applications that operate across the visible to short-wave infrared wavelengths, including optical clocks, quantum sensing and computing, ultra-low noise microwave generation, and fiber sensing. Today, these spectrally pure sources are realized using multiple external cavity tabletop lasers locked to bulk-optic free-space reference cavities. Integration of this technology will enable portable precision applications with improved reliability and robustness. Here, we report wavelength-flexible design and operation, over more than an octave span, of an integrated coil-resonator-stabilized Brillouin laser architecture. Leveraging a versatile two-stage noise reduction approach, we achieve low linewidths and high stability with chip-scale laser designs based on the ultra-low-loss, CMOS-compatible silicon nitride platform. We report operation at 674 and 698 nm for applications to strontium neutral and trapped-ion clocks, quantum sensing and computing, and at 1550 nm for applications to fiber sensing and ultra-low phase noise microwave generation. Over this range we demonstrate frequency noise reduction from 1 Hz to 10 MHz resulting in 1.0 Hz -17 Hz fundamental and 181 Hz - 630 Hz integral linewidths and an Allan deviation of 6.5 x 10-13 at 1 ms for 674 nm, 6.0 x 10-13 at 15 ms for 698 nm, and 2.6 x10-13 at 15 ms for 1550 nm. This represents the lowest achieved linewidths and highest stability for integrated stabilized Brillouin lasers over an order of magnitude improvement in operating wavelength range. These results unlock the potential of integrated, ultra-low-phase-noise stabilized lasers for precision applications and further integration in systems-on-chip solutions.

State-dependent conformational changes play a central role in molecular dynamics, yet they are often difficult to observe or simulate due to their complexity and ultrafast nature. One alternative approach is to emulate such phenomena using quantum simulations with cold, trapped ions. In their electronic ground state, these ions form long-lived Wigner crystals. When excited to high-lying electronic Rydberg states, the ions experience a modified trapping potential, resulting in a strong coupling between their electronic and vibrational degrees of freedom. In an ion crystal, this vibronic coupling creates electronic state-dependent potential energy surfaces that can support distinct crystal structures -- closely resembling the conformational changes of molecules driven by electronic excitations. Here, we present the first experimental observation of this effect, by laser-coupling a single ion at the centre of a three-ion crystal to a Rydberg state. By tuning the system close to a structural phase transition, the excitation induces a state-dependent conformational change, transforming the Wigner crystal from a linear to a zigzag configuration. This structural change leads to a strong hybridisation between vibrational and electronic states, producing a clear spectroscopic signature in the Rydberg excitation. Our findings mark the first experimental step towards using Rydberg ions to create and study artificial molecular systems. change leads to a strong hybridisation between vibrational and electronic states, producing a clear spectroscopic signature in the Rydberg excitation. Our findings mark the first experimental step towards using Rydberg ions to create and study artificial molecular systems.

A scaled trapped-ion quantum computer will require efficient fluorescence collection across a large area. Here we propose and demonstrate a compact monolithically integrated system featuring a metalens fabricated on the backside of a surface ion trap. A 40$\times$100 $μ$m aperture enables a simulated point-source collection efficiency of 0.91% and a measured point-source detection efficiency of 0.58%. Increasing the aperture area to 40$\times$600 $μ$m boosts the simulated collection efficiency to 3.17%$-$comparable to that of a conventional objective with a numerical aperture of 0.35. Further improvements are possible by co-optimizing the electrode and aperture geometry. An undercut of the electrode substrate at the aperture ensures a large distance between the ion and dielectric substrate without compromising collection efficiency. The metalens directly collimates the collected fluorescence, eliminating the need for a high numerical aperture objective. An array of such readout zones will offer a compact, scalable solution for high-fidelity parallel readout in next-generation trapped-ion quantum processors.

We implement a quantum generalization of a neural network on trapped-ion and IBM superconducting quantum computers to classify MNIST images, a common benchmark in computer vision. The network feedforward involves qubit rotations whose angles depend on the results of measurements in the previous layer. The network is trained via simulation, but inference is performed experimentally on quantum hardware. The classical-to-quantum correspondence is controlled by an interpolation parameter, $a$, which is zero in the classical limit. Increasing $a$ introduces quantum uncertainty into the measurements, which is shown to improve network performance at moderate values of the interpolation parameter. We then focus on particular images that fail to be classified by a classical neural network but are detected correctly in the quantum network. For such borderline cases, we observe strong deviations from the simulated behavior. We attribute this to physical noise, which causes the output to fluctuate between nearby minima of the classification energy landscape. Such strong sensitivity to physical noise is absent for clear images. We further benchmark physical noise by inserting additional single-qubit and two-qubit gate pairs into the neural network circuits. Our work provides a springboard toward more complex quantum neural networks on current devices: while the approach is rooted in standard classical machine learning, scaling up such networks may prove classically non-simulable and could offer a route to near-term quantum advantage.

Quantum simulations of lattice gauge theories (LGTs) with both dynamical matter and gauge fields provide a promising approach to studying strongly coupled problems beyond classical computational reach. Yet, implementing gauge-invariant encodings and real-time evolution remains experimentally challenging. Here, we demonstrate a resource-efficient encoding of a $\mathbb{Z}_2$ LGT using a hybrid qubit-oscillator trapped-ion quantum device, where qubits represent gauge fields and vibrational modes naturally encode bosonic matter fields. This architecture utilises synthetic dimensions to construct higher-dimensional lattice geometries and combines digital and analogue techniques to prepare initial states, realise gauge-invariant real-time evolution, and measure the relevant observables. We experimentally probe dynamics obeying Gauss's law in a $\mathbb{Z}_2$ link and extend this to a loop geometry, marking the first steps towards higher-dimensional LGTs. In this quasi-2D setup, we observe Aharonov-Bohm interference for the first time with dynamical gauge fields encoding magnetic flux, demonstrating the interplay between charge and flux. Our results chart a promising path for scalable quantum simulations of bosonic gauge theories and outline a roadmap for realising exotic LGTs in higher dimensions.

We explore how recent advances in the manipulation of single-ion wave packets open new avenues for detecting weak magnetic fields sourced by ultralight dark matter. A trapped ion in a ``Schrödinger cat'' state can be prepared with its spin and motional degrees of freedom entangled and be used as a matter-wave interferometer that is sensitive to the Aharonov-Bohm-like phase shift accumulated by the ion over its trajectory. The result of the spin-motion entanglement is a parametrically-enhanced sensitivity to weak magnetic fields as compared with an un-entangled ion in a trap. Taking into account the relevant boundary conditions, we demonstrate that a single trapped ion can probe unexplored regions of kinetically-mixed dark-photon dark matter parameter space in the $10^{-15}~\text{eV} \lesssim m_{A'} \lesssim 10^{-14}$~eV mass window. We also show how such a table-top quantum device will also serve as a complementary probe of axion-like particle dark matter in the same mass window.

Three-dimensional (3D) crystals offer a route to scale up trapped ion systems for quantum sensing and quantum simulation applications. However, engineering coherent spin-motion couplings and effective spin-spin interactions in large crystals poses technical challenges associated with decoherence and prolonged timescales to generate appreciable entanglement. Here, we explore the possibility to speed up these interactions in 3D crystals via parametric amplification. We derive a general Hamiltonian for the parametric amplification of spin-motion coupling that is applicable to crystals of any dimension in both rf Paul traps and Penning traps. Unlike in lower dimensional crystals, we find that the ability to faithfully (uniformly) amplify the spin-spin interactions in 3D crystals depends on the physical implementation of the spin-motion coupling. We consider the light-shift (LS) gate, and the so-called phase-insensitive and phase-sensitive Mølmer-Sørensen (MS) gates, and find that only the latter gate can be faithfully amplified in general 3D crystals. We discuss a situation where non-uniform amplification can be advantageous. We also reconsider the impact of counter-rotating terms on parametric amplification and find that they are not as detrimental as previous studies suggest.

Information can improve heat engine performance, but the underlying principles are still not so clear. Here we introduce a Carnot information machine (CIE) and obtain a quantitative relationship between the engine performance and information. We demonstrate that the presence of information changes allows the CIE to operate as a heat engine in the regime where the standard Carnot cycle is prohibited, ensures that the efficiency of the CIE is greater than or equal to the standard Carnot efficiency, and significantly enables it to achieve 100\% efficiency with positive work extraction for arbitrary two-level systems. We explicitly demonstrate these features using a spin-1/2 system and propose an experimental implementation scheme based on a trapped $^{40}\mathrm{Ca}^+$ ion.

The classical Kramers-Henneberger transformation connects, via a series of unitary transformations, the dynamics of a quantum particle of mass $m$ located in a trap at position $α(t)$, with the dynamics of a charge $e$ moving in an electric field $e{\cal{E}}(t)=-m\ddotα(t)$ within the dipole approximation. In this paper, we extend the classical Kramers-Henneberger transformation to the quantum electrodynamic and quantum optical realm, by explicitly treating the trap location quantum mechanically, thus taking into account the quantum fluctuations of the time-dependent displacement force. Compared to the classical case, we show that quantum electrodynamic corrections appear, and we propose an optomechanical realization for the quantized position of the trap to show that such corrections can manifest in state-of-the-art experiments. These results open the path to novel quantum simulation of quantum electrodynamics and quantum optics of attoscience and ultrafast physics by using ultracold trapped atoms and ions.

Two-dimensional planar ion crystals in a Penning trap are a platform for quantum information science experiments. However, the low-frequency planar modes of these crystals are not efficiently cooled by laser cooling, which can limit the utility of the drumhead modes for quantum information processing. Recently, it has been shown that nonlinear mode coupling can enhance the cooling of the low-frequency planar modes. Here, we demonstrate in numerical simulations that this coupling can be dynamically tuned by adiabatically changing the rotation frequency of the ion crystal during experiments. Furthermore, we show that this technique can, in addition, produce lower temperatures for the low-frequency planar modes via an adiabatic cooling process. This result allows cooling of the planar modes to sub-millikelvin temperatures, resulting in improved spectral resolution of the drumhead modes at experimentally relevant rotation frequencies, which is crucial for quantum information processing applications.

We determine the exact asymptotic many-body wavefunction of a spin-$s$ Richardson-Gaudin model with a coupling inversely proportional to time, for time evolution starting from the ground state at $t = 0^+$ and for arbitrary $s$. Contrary to common belief, the resulting wavefunction cannot be derived from the spin-$1/2$ case by merging spins, but instead requires independent treatment for each spin size. The steady state is non-thermal and, in contrast to the spin-$1/2$ case, does not conform to a natural Generalized Gibbs Ensemble. We show that mean-field theory is exact for any product of a finite number of spin operators on different sites. We discuss how these findings can be probed in cavity QED and trapped ion experiments.

We report on the $γ$-ray emission above 100~MeV from the GOES M3.3 flare SOL2012-06-03. The hard X-ray (HXR) and microwave emissions have typical time profiles with a fast rise to a well-defined peak followed by a slower decay. The $>$100~MeV emission during the prompt phase displayed a double-peaked temporal structure with the first peak following the HXR and microwaves, and the second one, about three times stronger, occurring $17 \pm 2$ seconds later. The time profiles seem to indicate two separate acceleration mechanisms at work, where the second $γ$-ray peak reveals a potentially pure or at least largely dominant ion acceleration. The Atmospheric Imaging Assembly imaging shows a bright elliptical ribbon and a transient brightening in the north-western (NW) region. Nonlinear force-free extrapolations at the time of the impulsive peaks show closed field lines connecting the NW region to the south-eastern part of the ribbon and the magnetic topology revealed clusters of nulls. These observations suggest a spine-and-fan geometry, and based on these observations we interpret the second $γ$-ray peak as being due to the predominant acceleration of ions in a region with multiple null points. The $>$100 MeV emission from this flare also exhibits a delayed phase with an exponential decay of roughly 350 seconds. We find that the delayed emission is consistent with ions being trapped in a closed flux tube with gradual escape via their loss cone to the chromosphere.

Kitaev's honeycomb model is a paradigmatic exactly solvable system hosting a quantum spin liquid with non-Abelian anyons and topologically protected edge modes, offering a platform for fault-tolerant quantum computation. However, real candidate Kitaev materials invariably include complex secondary interactions that obscure the realization of spin-liquid behavior and demand novel quantum computational approaches for efficient simulation. Here we report quantum simulations of a 22-site Kitaev honeycomb lattice on a trapped-ion quantum processor, without and with non-integrable Heisenberg interactions that are present in real materials. We develop efficient quantum circuits for ground-state preparation, achieving high accuracy with energy errors equivalent to an effective temperature of 0.2 (in units of the Kitaev interactions), consistent with the experimentally relevant spin-liquid regime. Starting from these states, we apply controlled perturbations and measure time-dependent spin correlations along the system's edge. In the non-Abelian phase, we observe chiral edge dynamics consistent with a non-zero Chern number, a hallmark of topological order, which vanishes upon transition to the Abelian toric code phase. Extending to the non-integrable Kitaev-Heisenberg model, we find that weak Heisenberg interactions preserve chiral edge dynamics, while stronger couplings suppress them, signaling the breakdown of topological protection. Our work demonstrates a viable route for probing dynamical signatures of topological order in quantum spin liquids using programmable quantum hardware, opening new pathways for quantum simulation of strongly correlated materials.

The excitation energy of $ {}^{229m} \mathrm{Th} $ is extremely low at $ 8.4 \, \mathrm{eV} $; thus, this isotope exhibits changes in its decay modes depending on the chemical state, specifically the outermost electronic states. However, the reported half-lives of the $ γ$-ray transition are not consistent among the previous experiments. In this study, we investigate the chemical states of $ {}^{229m} \mathrm{Th} $ by density functional theory calculations. Based on these results, we evaluate the relationship between the experimental half-life of each sample and the electronic state of $ \mathrm{Th} $. The calculation results indicate that ion trap method, $ \mathrm{Ca} \mathrm{F}_2 $ model and $ \mathrm{Mg} \mathrm{F}_2 $ one decay only via the $ γ$-ray transition, whereas $ \mathrm{Li} \mathrm{Sr} \mathrm{Al} \mathrm{F}_6 $ one decays via the $ γ$-ray transition and has a possibility of decay via internal conversion and electron bridge.

A flagship application of quantum computers is the simulation of other quantum systems, including quantum field theories. In this article, we show how quantum computers can be employed to naturally calculate Feynman diagrams and their interferences in Quantum Chromodynamics (QCD). We simulate the colour parts of the interactions directly on the quantum computer, while the kinematic parts are for now pre-computed classically. For processes where some of the external particles are identical, we find the first hints of a potential quantum advantage. We validate our techniques using simulated quantum computers. Furthermore, for toy examples we also demonstrate our algorithms on a 56-qubit trapped-ion quantum computer. The work constitutes a further key step towards a full quantum simulation of generic perturbative QCD processes.

Nonlinear classical mechanics has established rich phenomena. These include limit tori defined by toroidal attractors supporting quasiperiodic motion with incommensurate frequencies. We study the fate of such structures in open quantum systems using two coupled driven-dissipative Kerr cavities modeled via the Lindblad master equation. Combining Liouvillian spectral theory with the truncated Wigner approximation, we characterize the quantum-to-classical crossover. In the classical limit, two pairs of purely imaginary Liouvillian eigenvalues signal persistent quasiperiodic modes. Quantum fluctuations induce small negative real parts to these eigenvalues, giving rise to finite lifetimes and leading to the quantum melting of the torus. The associated Liouvillian gaps vanish algebraically in the classical limit, indicating a dynamical critical crossover with spontaneous breaking of time-translational symmetry. Quantum trajectory analysis reveals that this melting is driven by fluctuation-induced dephasing. Using a circular-variance-based order parameter, we uncover universal scaling in system size and time. These results establish quantum melting of limit tori as a distinct and robust non-equilibrium critical phenomenon, with clear experimental signatures in trapped ions and superconducting circuits.

We describe a 88Sr+ ion trap apparatus with the capability to produce high-quality 408 nm photons aimed at distributed quantum computing and networking applications. This instrument confines ion chains using a surface electrode trap with a two-dimensional magneto-optical trap as an atomic source. Several laser systems spanning 400-1100 nm are used to achieve high fidelity state preparation and readout. Photons are produced via the decay of an exited state, which is accessed using a custom 408 nm laser system that produces 150 ps optical pulses using non-linear photonics. We demonstrate single photon production through a Hanbury Brown-Twiss measurement for one to six ions.

With the advent of advanced quantum processors capable of probing lattice gauge theories (LGTs) in higher spatial dimensions, it is crucial to understand string dynamics in such models to guide upcoming experiments and to make connections to high-energy physics (HEP). Using tensor network methods, we study the far-from-equilibrium quench dynamics of electric flux strings between two static charges in the $2+1$D $\mathbb{Z}_2$ LGT with dynamical matter. We calculate the probabilities of finding the time-evolved wave function in string configurations of the same length as the initial string. At resonances determined by the the electric field strength and the mass, we identify various string breaking processes accompanied with matter creation. Away from resonance strings exhibit intriguing confined dynamics which, for strong electric fields, we fully characterize through effective perturbative models. Starting in maximal-length strings, we find that the wave function enters a dynamical regime where it splits into shorter strings and disconnected loops, with the latter bearing qualitative resemblance to glueballs in quantum chromodynamics (QCD). Our findings can be probed on state-of-the-art superconducting-qubit and trapped-ion quantum processors.

We investigate quantum quenches starting from a critical point and experimentally probe the associated defect statistics using a trapped-ion quantum simulator of the transverse-field Ising model. The cumulants of the defect number distribution exhibit universal scaling with quench depth, featuring Gaussian behavior at leading order and systematic subleading corrections. Our results are in excellent agreement with both exact and approximate theoretical predictions, establishing quench-depth scaling as a powerful and precise experimental benchmark for nonequilibrium quantum critical dynamics.

We put forth a hitherto unexplored control strategy that enables high-fidelity fast transport of an unstable quantum wavepacket even in the presence of bath-induced dissipation. The wavepacket, which is confined within any shallow (anharmonic) potential trap is steered in acceleration, so as to maximize the transfer fidelity. This strategy can generally optimize any non-Markovian bath-dressed continuous-variable system dynamics. It can simultaneously cope with wavepacket leakage via non-adiabatic transitions and bath-induced dissipation in an optimal fashion. It can outperform methods based on counterdiabatic fields (shortcuts to adiabaticity) particularly for fast non-adiabatic transport. Transport fidelity is maximized even for trajectories exceeding the speed of bath-excitation propagation, e.g. for supersonic transfer through phonon baths. This general approach is illustrated for optimized transfer of impurities in Bose-Einstein condensates. It is applicable to both dissipative and non-dissipative transfer of trapped atoms and ions and molecular reaction products.

Fock-state lattice (FSL) offers a powerful quantum simulator for topological phenomena due to the unbounded scalability and ease of implementation. Nevertheless, the unique topological properties induced by its site-dependent coupling have remained elusive, mainly due to the challenge of handling an infinite state space without translational symmetry. Here, we rigorously analyze the topological features of a semi-infinite FSL-based Su-Schrieffer-Heeger (SSH) model, in both Hermitian and non-Hermitian realms, by mapping it to the solvable Jaynes-Cummings (JC) model via a unitary displacement transformation. We find a more stable topological zero mode than the conventional SSH model, originating from the bound state at the inherent domain wall under anisotropic conditions. With gain and loss introduced, we predict a non-Hermitian bound effect (NHBE), i. e., any state overlapping with the bound state will quickly stabilize to the domain wall, with the minimal stabilization time occurring in the vicinity of exceptional point (EP). The paritytime (PT ) phase transition can be observed by the oscillating-to-steady crossover of dynamics in the subspace orthogonal to the bound state. Furthermore, a concrete experimental proposal based on the trapped-ion setup is provided.

We study the impact of an unshielded dielectric $\unicode{x2013}$ here, a bare optical fiber $\unicode{x2013}$ on a $^{40}$Ca${^+}$ ion held several hundred $μ$m away in a cryogenic surface electrode trap. We observe distance-dependent stray electric fields of up to a few kV/m due to the dielectric, which drift on average less than 10% per month and can be fully compensated with reasonable voltages on the trap electrodes. We observe ion motional heating rates attributable to the dielectric of $\approx$30 quanta per second at an ion-fiber distance of 215(4) $μ$m and $\approx$1.5 MHz motional frequency. These results demonstrate the viability of using unshielded, trap-integrated dielectric objects such as miniature optical cavities or other optical elements in cryogenic surface electrode ion traps.

Quantum control protocols are typically devised in the time domain, leaving their spectral behavior to emerge only a posteriori. Here, we invert this paradigm. Starting from a target frequency-domain filter, we employ the dynamical-invariant framework to derive the continuous driving fields that enact the chosen spectral response on a qubit. This approach, Quantum Invariant Filtering (QIF), maps arbitrary finite-impulse responses, including multi-band and phase-sensitive profiles, into experimentally feasible Hamiltonian modulations. Implemented on a single nitrogen-vacancy center in diamond, the method realizes the prescribed passbands with high fidelity, suppresses noise, and preserves coherence for milliseconds, two orders of magnitude longer than Carr-Purcell-Meiboom-Gill sequences, while remaining robust to 50% drive-amplitude errors. Our results establish QIF as a broadly applicable framework for enhanced quantum control and sensing across diverse physical platforms, including superconducting qubits, trapped ions, and nuclear magnetic resonance systems.

We present a fully quantum mechanical description of a free $^6$Li atom scattering from a trapped $^{171}$Yb$^+$ ion in one dimension. By reformulating the system in polar coordinates and employing the adiabatic representation, we extract a set of coupled adiabatic potentials representing the atom interacting with the ion in different trap states. In an approach similar to quantum defect theory (QDT), we leverage the vast difference in energy scale between the interaction, the trap, and the scattering energy to encapsulate the short-range atom-ion scattering behavior in a single phase parameter. The presence of trapped $({}^{171}\text{Yb}^6\text{Li})^+$ molecular-ion states leads to a series of roughly evenly spaced resonances in the scattering cross section. The predicted distribution of resonances at low collision energies is at odds with the expectation of quantum chaos and the Bohigas-Giannoni-Schmit (BGS) conjecture.

Preparation of high-fidelity logical magic states has remained as a necessary but daunting step towards building a large-scale fault-tolerant quantum computer. One approach is to fault-tolerantly prepare a magic state in one code and then switch to another, a method known as code switching. We experimentally demonstrate this protocol on an ion-trap quantum processor, yielding a logical magic state encoded in an error-correcting code with state-of-the-art logical fidelity. Our experiment is based on the first demonstration of code switching between color codes, from the fifteen-qubit quantum Reed-Muller code to the seven-qubit Steane code. We prepare an encoded magic state in the Steane code with $82.58\%$ probability, with an infidelity of at most $5.1(2.7) \times 10^{-4}$. The reported infidelity is lower than the leading infidelity of the physical operations utilized in the protocol by a factor of at least $2.7$, indicating the quantum processor is below the pseudo-threshold. Furthermore, we create two copies of the magic state in the same quantum processor and perform a logical Bell basis measurement for a sample-efficient certification of the encoded magic state. The high-fidelity magic state can be combined with the already-demonstrated fault-tolerant Clifford gates, state preparation, and measurement of the 2D color code, completing a universal set of fault-tolerant computational primitives with logical error rates equal or better than the physical two-qubit error rate.

Electromagnetically Induced Transparency (EIT) cooling is a well-established method for preparing trapped ion systems in their motional ground state. However, isolating a three-level system, as required for EIT cooling, is often challenging or impractical. Nonetheless, multilevel systems can inherently host dark states. In this work, we extend the EIT cooling framework to such multilevel systems. We develop a formalism to accurately determine the cooling rate in the weak sideband coupling regime and provide an approximate estimate for cooling rates beyond this regime, without the need for explicit simulation of the motional degree of freedom. We clarify the connection between the cooling rate and the absorption spectrum, offering a pathway for efficient near-ground-state cooling of ions with complex electronic structures.

We propose an entanglement protocol where ions illuminated by optical tweezers serve as control qubits. We experimentally demonstrate this proposal with a controlled M$ø$lmer-S$ø$rensen operation on a three-ion chain, analogous to the canonical Toffoli gate. Our demonstration features cases in which the control qubit was in one of its logical basis states, and not in their superposition, due to dephasing by tweezer beam intensity fluctuations. Finally, we discuss how our protocol generalizes to a broad class of unitary operations and larger qubit systems, enabling a single-pulse implementation of $n$-controlled unitaries.

This work explores how the generalized uncertainty principle, a theoretical modification of the Heisenberg uncertainty principle inspired by quantum gravity, affects neutrino flavor oscillations. By extending the standard two-flavor neutrino model, we show that the oscillation probability acquires an additional phase term that depends on the {square roots of the individual neutrino masses}, introducing new features beyond the conventional mass-squared differences. To account for the non-Hermitian nature of the resulting dynamics, we employ parity-time ($PT$) symmetric quantum mechanics, which allows for consistent descriptions of systems with {balanced gain and loss mechanisms}. We analyze the feasibility of observing these effects in current and future neutrino experiments, such as DUNE, JUNO, IceCube, ORCA--KM3NeT, MINOS, Daya Bay, Hyper-Kamiokande, and KATRIN, and find that the predicted modifications could fall within the sensitivity of current experiments. Moreover, we propose that analog quantum simulation platforms, such as cold atoms, trapped ions, and photonic systems, offer a promising route to test these predictions under controlled conditions. Our findings suggest that neutrino oscillations may serve as an effective probe of quantum gravity effects, providing a novel connection between fundamental theory and experimental observables.

We present results from co-designed quantum simulations of the neutrinoless double-beta decay of a simple nucleus in 1+1D quantum chromodynamics using IonQ's Forte-generation trapped-ion quantum computers. Electrons, neutrinos, and up and down quarks are distributed across two lattice sites and mapped to 32 qubits, with an additional 4 qubits used for flag-based error mitigation. A four-fermion interaction is used to implement weak interactions, and lepton-number violation is induced by a neutrino Majorana mass. Quantum circuits that prepare the initial nucleus and time evolve with the Hamiltonian containing the strong and weak interactions are executed on IonQ Forte Enterprise. Enabled by tuned model parameters, lepton-number violation is observed in real time, providing a clear signal of neutrinoless double-beta decay. This was made possible by co-designing the simulation to maximally utilize the all-to-all connectivity and native gate-set available on IonQ's quantum computers. Quantum circuit compilation techniques and co-designed error-mitigation methods, informed from executing benchmarking circuits with up to 2,356 two-qubit gates, enabled observables to be extracted with high precision. We discuss the potential of future quantum simulations to provide yocto-second resolution of the reaction pathways in these, and other, nuclear processes.

Quantum simulation offers a route to study open-system molecular dynamics in non-perturbative regimes by programming the interactions among electronic, vibrational, and environmental degrees of freedom on similar energy scales. Trapped-ion systems possess this capability, with their native spins, phonons, and tunable dissipation integrated within a single platform. Here, we demonstrate an open-system quantum simulation of charge and exciton transfer in a multi-mode linear vibronic coupling model. Employing tailored spin-phonon interactions alongside reservoir engineering techniques, we emulate a system with two dissipative vibrational modes coupled to donor and acceptor electronic sites and follow its non-equilibrium dynamics. We continuously tune the system from the charge transfer (CT) regime to the vibrationally assisted exciton transfer (VAET) regime by controlling the vibronic coupling strengths. We find that degenerate modes enhance CT and VAET rates at large energy gaps, while non-degenerate modes activate slow-mode pathways that reduce the energy-gap dependence, thus enlarging the window for efficient transfer. These results show that the presence of one additional vibration introduces interfering vibrationally assisted pathways and reshapes non-perturbative quantum excitation transfer. Our work establishes a scalable and hardware-efficient route to simulating chemically relevant, many-mode vibronic processes with engineered environments, guiding the design of next-generation organic photovoltaics and molecular electronics.

We present a digital quantum computation of two-hadron scattering in a $Z_2$ lattice gauge theory in 1+1 dimensions. We prepare well-separated single-particle wave packets with desired momentum-space wavefunctions, and simulate their collision through digitized time evolution. Multiple hadronic wave packets can be produced using the efficient, systematically improvable algorithm of this work, achieving high fidelity with the target initial state. Specifically, employing a trapped-ion quantum computer (IonQ Forte), we prepare up to three meson wave packets using 11 and 27 system qubits, and simulate collision dynamics of two meson wave packets for the smaller system. Results for local observables are consistent with numerical simulations at early times, but decoherence effects limit evolution into long times. We demonstrate the critical role of high-fidelity initial states for precision measurements of state-sensitive observables, such as $S$-matrix elements. Our work establishes the potential of quantum computers in simulating hadron-scattering processes in strongly interacting gauge theories.

Although it is known that the $N=28$ spherical shell closure erodes, the strength of the closure with decreasing proton number $Z<20$ is an open question in nuclear structure. In this region of interest, direct high-precision mass measurements of neutron-rich $^{43-45}$Cl isotopes were performed at the Low Energy Beam and Ion Trap (LEBIT) when coupled to the National Superconducting Cyclotron Lab. The resulting mass excesses (MEs) are ME($^{43}$Cl) = -24114.4(1.7) keV, ME($^{44}$Cl) = -20450.8(10.6) keV, and ME($^{45}$Cl) = -18240.1(3.7) keV, and improve the uncertainty of these masses by up to a factor of ~40 compared to the previous values reported in the 2020 Atomic Mass Evaluation. Comparison to $\textit{ab initio}$ calculations using the Valence-Space In-Medium Similarity Renormalization Group (VS-IMSRG) shows good agreement up to and including the closure.

Interacting many-particle systems can self-organize into a rich variety of crystalline structures. While symmetry provides a powerful framework for predicting whether transitions between crystal states are continuous or discontinuous, collective lattice dynamics offer complementary insights into the microscopic mechanisms that drive these transitions. Trapped laser-cooled ions present a pristine and highly controllable few-body system for studying this interplay of symmetry and dynamics. Here, we use real-time fluorescence imaging while deforming the trap potential to observe a variety of structural transitions in three-dimensional (3D), unit-cell-like ion clusters. We identify a set of transitions signaled by parity-odd octupole order parameters, and probe their distinct dynamical signatures. Our observations reveal the softening of a collective Higgs-like mode indicating spontaneous symmetry-breaking, hysteresis resulting from a catastrophe where a metastable state vanishes abruptly, and stochastic switching between metastable states of differing symmetries. We also uncover a remarkable coincidence of symmetry-breaking and discontinuous transitions, analogous to a thermodynamic triple point. Our results establish 3D trapped-ion clusters as a versatile platform to engineer complex potential energy landscapes, opening new avenues for studies of reaction kinetics, geometric frustration, and related phenomena in mesoscopic platforms.

We report on comprehensive laboratory studies of the K-shell dielectronic recombination (DR) resonances of Fe XXV - XXI ions that prominently contribute to the hard X-ray spectrum of hot astrophysical plasmas. By scanning a monoenergetic electron beam to resonantly excite trapped Fe ions in an electron beam ion trap, and achieving a high electron-ion collision energy resolution of ~7 eV, we resolve their respective KL$n$ satellites up to n'=11. By normalization to known radiative recombination cross sections we also determine their excitation cross sections and that of the continuum with uncertainties below 15%, and verify our results with an independent normalization based on previous measurements. Our experimental data excellently confirm the accuracy and suitability of distorted-wave calculations obtained with the Flexible Atomic Code (FAC) for modeling astrophysical and fusion plasmas.

The liquid-vapor transition is a classic example of a discontinuous (first-order) phase transition. Such transitions underlie many phenomena in cosmology, nuclear and particle physics, and condensed-matter physics. They give rise to long-lived metastable states, whose decay can be driven by either thermal or quantum fluctuations. Yet, direct experimental observations of how these states collapse into a stable phase remain elusive in the quantum regime. Here, we use a trapped-ion quantum simulator to observe the real-time dynamics of ``bubble nucleation'' induced by quantum fluctuations. Bubbles are localized domains of the stable phase which spontaneously form, or nucleate, and expand as the system is driven across a discontinuous quantum phase transition. Implementing a mixed-field Ising spin model with tunable and time-dependent interactions, we track the microscopic evolution of the metastable state as the Hamiltonian parameters are varied in time with various speeds, bringing the system out of equilibrium. Site-resolved measurements reveal the emergence and evolution of finite-size quantum bubbles, providing direct insight into the mechanism by which the metastable phase decays. We also identify nonequilibrium scaling behavior near the transition, consistent with a generalized Kibble-Zurek mechanism. Our results demonstrate the power of quantum simulators to probe out-of-equilibrium many-body physics, including quantum bubble nucleation, a key feature of discontinuous quantum phase transitions, with application to studies of matter formation in the early universe.

In this study, we employed Fourier-based quantum phase estimation (QPE) to calculate X-ray absorption spectroscopy (XAS) spectra. The primary focus of this study is the calculation of the XAS spectra of transition metal $L_{2,3}$-edges, which are dominated by strong correlation effects. First, the Fe $L_{2,3}$-edge X-ray absorption near-edge structure of FePO$_4$ is calculated using a noiseless simulator. The present computation involves a comparison of three types of input states: a uniform superposition state, optimal entangled input state, and Slater function state. Subsequently, we investigated the resolution error of the QPE and statistical error attributed to the measurements. It was revealed that post-processing to introduce Lorentzian broadening reduces the statistical error, which becomes a significant problem for a large number of qubits. Subsequently, we implemented QPE on a trapped-ion quantum computer, encompassing three orbitals within the active space. To this end, we implemented QPE using dynamic circuits to reduce ancilla qubits and [[k+2, k, 2]] quantum error detection code to mitigate the quantum noise inherent in current quantum computers. As a result, it was demonstrated that hardware noise was reduced, and spectra close to the noiseless ones were obtained.

Trapped-ion quantum computing requires precise optical control for individual qubit manipulation. However, conventional free-space optics face challenges in alignment stability and scalability as the number of qubits increases. Integrated photonics offers a promising alternative, providing miniaturized optical systems on a chip. Here, we propose a design for a multimode photonic circuit integrated with a surface-electrode ion trap capable of targeted and reconfigurable light delivery. Three closely positioned ions can be addressed using a focusing grating coupler that emits multimode light through electrode openings to ions trapped 80 $μ$m above the chip. Simulations show that the couplers achieve diffraction-limited spot with a 4.3 $μ$m beam waist along the trap axis and 2.2 $μ$m perpendicular to the trap axis. Controlled interference of the TE$_{\text{10}}$ and TE$_{\text{20}}$ modes results in crosstalk of -20 dB to -30 dB at ion separations of 5-8 $μ$m when addressing ions individually, and down to -60 dB when two of the three ions are addressed simultaneously. Additionally, the higher-order TE modes can offer a novel mechanism for driving spin-motion coupling transitions, potentially enabling alternative approaches to quantum gates and simulations. The proposed integrated platform offers a viable path for constructing large-scale trapped-ion systems, leveraging the benefits of nanophotonic design for precise and reliable ion manipulation.

We derive a generalized quantum Langevin equation and its fluctuation-dissipation relation describing the quantum dynamics of a tagged particle interacting with a medium (environment), where both the particle and the environment are driven by an external time-dependent (e.g. oscillating) field. We specialize on the case of a charged tagged particle interacting with a bath of charged oscillators, under an external AC electric field, although the results are much more general and can be applied to any type of external time-dependent fields. We derive the corresponding quantum Langevin equation, which obeys a modified fluctuation-dissipation relation (FDR) where the AC field plays an explicit role. The modified FDR is non-Markovian even if the undriven particle-bath system is Markovian without the external field. We provide an illustration of the usefulness of these results and derive a new form of the quantum Nyquist noise for the voltage fluctuations in electrical circuits under AC conditions (finite frequency), which is the most general since it also accounts for the response of the heat bath (e.g. lattice ions) to the applied AC electric field in the GHz-THz region, of relevance for 5G/6G wireless technologies. This generalized quantum fluctuation-dissipation relation for driven systems can also find other applications ranging from quantum noise in quantum optics to quantum computing with trapped ions.

Metastable qubits in atomic systems can enable large-scale quantum computing by simplifying hardware requirements and adding efficient erasure conversion to the pre-existing toolbox of high-fidelity laser-based control. For trapped atomic ions, the fundamental error floor of this control is given by spontaneous Raman and Rayleigh scattering from short-lived excited states. We measure spontaneous Raman scattering rates out of a metastable $D_{5/2}$ qubit manifold of a single trapped $^{40}$Ca$^+$ ion illuminated by 976 nm light that is -44 THz detuned from the dipole-allowed transition to the $P_{3/2}$ manifold. This supports the calculation of error rates from both types of scattering during one- and two-qubit gates on this platform, thus demonstrating that infidelities $<10^{-4}$ are possible.

A trapped ion immersed in a neutral bath shows long-lived atom-ion complexes that significantly alter its chemical properties, and, thus the ion stability. In this work, we present a general study of trapped ion-atom scattering with the ion modeled as a charge distribution defined by the spatial extent of its ground-state wavefunction. After mapping the time-dependent problem onto a time-independent framework, we investigate the role of the trap, the atomic species, atom-ion interaction, and collision energy in shaping the chaotic dynamics of the system. We find that the probability of atom-ion complex formation directly measures its chaoticity. Therefore, our results establish a clear relationship between the emergence of chaotic scattering and the presence of ion-atom complexes.

The Petz recovery map provides a near-optimal reversal of quantum noise, yet proposals for its implementation are only recent. We propose a physical realization of the exact state-specific Petz map in an ion trap for qubit decoherence channels. Our circuit constructions require at most $1 (2)$ ancilla qubits and $3 (20)$ CNOT gates for channels with Kraus rank $2 (>2)$. We analyze typical ion trap errors and construct corresponding Petz maps, simulating their performance under realistic noise modeled by residual spin-motion coupling. Quantum circuits are provided for depolarizing, dephasing, and amplitude damping channels. Focusing on single-shot recovery, suited for present-day devices, we also quantify the precision of prior knowledge required to achieve a recovery error below 0.01 across varying decoherence levels and state purities.

The MORA experimental setup is designed to measure the triple-correlation D parameter in nuclear beta decay. The D coefficient is sensitive to possible violations of time-reversal invariance. The experimental configuration consists of a transparent Paul trap surrounded by a detection setup with alternating beta and recoil-ion detectors. The octagonal symmetry of the detection setup optimizes the sensitivity of positron-recoil-ion coincidence rates to the D correlation, while reducing systematic effects. MORA utilizes an innovative in-trap laser polarization technique. The design and performance of the ion trap, associated beamline elements, lasers and beta and recoil-ion detectors, are presented. Recent progress towards the polarization proof-of-principle is described.

We report a single-ion optical atomic clock with fractional frequency uncertainty of $5.5\times10^{-19}$ and fractional frequency stability of $3.5 \times10^{-16}/\sqrt{τ/\mathrm{s}}$, based on quantum logic spectroscopy of a single $^{27}$Al$^+$ ion. A co-trapped $^{25}$Mg$^+$ ion provides sympathetic cooling and quantum logic readout of the $^{27}$Al$^+$ $^1$S$_0\leftrightarrow^3$P$_0$ clock transition. A Rabi probe duration of 1 s, enabled by laser stability transfer from a remote cryogenic silicon cavity across a 3.6 km fiber link, results in a threefold reduction in instability compared to previous $^{27}$Al$^+$ clocks. Systematic uncertainties are lower due to an improved ion trap electrical design, which reduces excess micromotion, and a new vacuum system, which reduces collisional shifts. We also perform a direction-sensitive measurement of the ac magnetic field due to the RF ion trap, eliminating systematic uncertainty due to field orientation.

This paper introduces a novel device-independent quantum self-testing protocol designed specifically for multipartite quantum communication. By exploiting the quantum rigidity in Bell nonlocality, the protocol enables the certification of genuinely entangled subspaces without reliance on device assumptions. Additionally, we investigate its potential to enhance the security of the Global Positioning System (GPS) against malicious cyberattacks. The study concludes with a comprehensive analysis of the experimental requirements, comparing superconducting and trapped-ion qubit architectures in terms of full-circuit fidelity and total gate time for generating a five-qubit code in the context of the noisy intermediate-scale quantum (NISQ) era.

The St. Benedict ion trapping system, which aims to measure the $β-ν$ angular correlation parameter in superallowed-mixed mirror transitions, is under construction at the University of Notre Dame. These measurements will provide much-needed data to improve the accuracy of the $V_{ud}$ element of the CKM matrix. One of the major components of this system is the radio frequency quadrupole cooler-buncher, which is necessary to create low-emittance ion bunches for injection into the measurement Paul trap. The off-line commissioning of the cooler-buncher, using a potassium ion source, determined that the device could produce cooled ion bunches characterized by a 50-ns full-width-half-maximum time width. The commissioning results also determined the trapping efficiency to be 93(1)$\%$ and the trapping half-life to be 20.0(5) s.

In this study, we employ the variational quantum eigensolver algorithm with a multireference unitary coupled cluster ansatz to report the ground state energy of the BeH2 molecule in a geometry where strong correlation effects are significant. We consider the two most important determinants in the construction of the reference state for our ansatz. We remove redundancies in order to execute a redundancy-free calculation. In view of the currently available noisy quantum hardware, we carry out parameter optimization on a classical computer and measure the energy with optimized parameters on a quantum computer. Furthermore, in order to carry out our intended 12-qubit computation with error mitigation and post-selection on a noisy intermediate scale quantum era trapped ion hardware (the commercially available IonQ Forte-I), we perform a series of resource reduction techniques to a. decrease the number of two-qubit gates by 99.84% (from 12243 to 20 two-qubit gates) relative to the unoptimized circuit, and b. reduce the number of measurements via the idea of supercliques, while losing 2.69% in the obtained ground state energy relative to that computed classically for the same resource-optimized problem setting.

Continuously parameterized two-qubit gates are a key feature of state-of-the-art trapped-ion quantum processors as they have favorable error scalings and show distinct improvements in circuit performance over more restricted maximally entangling gatesets. In this work, we provide a comprehensive and pedagogical discussion on how to practically implement these continuously parameterized Mølmer-Sørensen gates on the Quantum Scientific Computing Open User Testbed (QSCOUT), a low-level trapped-ion processor. To generate the arbitrary entangling angles, $θ$, we simply scale the amplitude of light used to generate the entanglement. However, doing so requires careful consideration of amplifier saturation as well as the variable light shifts that result. As such, we describe a method to calibrate and cancel the dominant fourth-order effects, followed by a dynamic virtual phase advance during the gate to cancel any residual light shifts, and find a linear scaling between $θ$ and the residual light shift. Once, we have considered and calibrated these effects, we demonstrate performance improvement with decreasing $θ$. Finally, we describe nuances of hardware control to transform the XX-type interaction of the arbitrary-angle Mølmer-Sørensen gate into a phase-agnostic and crosstalk-mitigating ZZ interaction.

Imaginary-time evolution, an important technique in tensor network and quantum Monte Carlo algorithms on classical computers, has recently been adapted to quantum computing. In this study, we focus on probabilistic imaginary-time evolution (PITE) algorithm and derive its formulation in the context of state-vector-based simulations, where quantum state vectors are directly used to compute observables without statistical errors. We compare the results with those of shot-based simulations, which estimate observables through repeated projective measurements. Applying the PITE algorithm to the Heisenberg chain, we investigate optimal initial conditions for convergence. We further demonstrate the method on the transverse-field Ising model using a state-of-the-art trapped-ion quantum device. Finally, we explore the potential of error mitigation in this framework, highlighting practical considerations for near-term digital quantum simulations.

Under specific conditions, a rotating saddle potential can confine the motion of a particle on its surface. This time-varying hyperbolic potential shares key characteristics with the RF electric quadrupole ion trap (RF Paul trap), making it a valuable mechanical analog. Previous work has primarily focused on symmetric saddles, characterized by equal curvatures along the trapping and anti-trapping directions. However, most applications of RF Paul traps-such as atomic clocks, quantum computing, and quantum simulations-require asymmetry in the quadrupole potential to break the degeneracy of motional modes, which is essential for processes like laser cooling and other quantum manipulations. In this paper, we investigate the motion of trapped particles in asymmetric rotating saddles. We demonstrate that even minor asymmetries, including those arising from manufacturing imperfections, can significantly affect particle trajectories and stability. Our analysis includes both theoretical modeling and experimental measurements. We derive the equations of motion for asymmetric saddles and solve them to explore stability and precession effects. Additionally, we present lifetime measurements of particles in saddles with varying degrees of asymmetry to map key features of the a-q stability diagram, including counterintuitive demonstrations of stability for saddles with negative asymmetry. This study underscores the importance of incorporating asymmetry into mechanical models of ion traps to better reflect real-world implementations. Although motivated primarily by RF Paul traps, these asymmetry-related results are also relevant to emerging gravitational analogs, such as rotating saddle potentials in certain binary black hole systems.

The abundance of elements heavier than iron produced via the astrophysical rapid-neutron capture process depends sensitively on the atomic mass of the involved nuclei as well as the behavior of a few special types of nuclear isomers called astromers. High-precision mass measurements of $^{119}$Cd, $^{119}$Ag and their respective isomeric states have been performed with the Phase Imaging-Ion Cyclotron Resonance (PI-ICR) method with a precision of $δm/m \approx 10^{-8}$ using the Canadian Penning Trap (CPT). The ground state mass excess, as well as the excitation energy, agrees with recent Penning Trap measurements from JYFLTRAP. Network calculations using these new measurements revealed that, contrary to previous expectations, $^{119m}$Ag behaves as an astromer which significantly affects the population of $^{119}$Ag.

Quantum-logic spectroscopy has become an increasingly important tool for the state detection and readout of trapped atomic and molecular ions which do not possess easily accessible closed-cycling optical transitions. In this approach, the internal state of the target ion is mapped onto a co-trapped auxiliary ion. This mapping is typically mediated by normal modes of motion of the two-ion Coulomb crystal in the trap. The present study investigates the role of spectator modes not directly involved in a measurement protocol relying on a state-dependent optical-dipole force. We identify a Debye-Waller-type effect that modifies the response of the two-ion string to the force. We show that cooling the spectator modes of the string allows for the detection of the rovibrational ground state of an N$_2^+$ molecular ion with a computed statistical fidelity exceeding 99.99%, improving on previous experiments by more than an order of magnitude while also halving the experimental time. This enhanced sensitivity enables the simultaneous identification of multiple rotational states with markedly weaker signals.

We propose a series of dissipation-assisted entanglement generation protocols that can be implemented on a trapped-ion quantum simulator. Our approach builds on the single-site molecular electron transfer (ET) model recently realized in the experiment [So et al. Sci. Adv. 10, eads8011 (2024)]. This model leverages spin-dependent boson displacement and dissipation controlled by sympathetic cooling. We show that, when coupled to external degrees of freedom, the ET model can be used as a dissipative quantum control mechanism, enabling the precise tailoring of both spin and phonon steady state of a target sub-system. We derive simplified analytical formalisms that offer intuitive insights into the dissipative dynamics. Using realistic interactions in a trapped-ion system, we develop a protocol for generating $N$-qubit and $N$-boson $W$ states. Additionally, we generalize this protocol to realize generic $N$-qubit Dicke states with tunable excitation numbers. Finally, we outline a realistic experimental setup to implement our schemes in the presence of noise sources.

In the study of ion-atom interactions, the ion often remain trapped during the experiments. However, the effects of the trapping potential of the ion on ion-neutral interactions remain largely unexplored. Although trap-assisted ion-neutral complex formation has been experimentally studied and described by applying semiclassical theories where the ion is treated as a point charge particle, the potential effect of a delocalized charge distribution of a confined ion due to its quantum mechanical wavefunction has not been considered. To remedy this, in the present theoretical work we substitute the point charge of the ion with a delocalized charged distribution according to its motional ground state in the trap. Our results show that the trapping frequency and hence the spatial extension of the ion's ground-state wavefunction drastically affects the elastic and transport cross sections in interactions with neutral atoms. Stimulated by these results, we propose experimental procedures to verify the effects of the delocalize charge distribution in ion-atom interactions via measuring the heating rate of the ion due to the energy transfer in atomic collisions. Our novel approach brings new possibilities for investigating ion-neutral systems and, through them, new perspectives on ionic polarons and potentially a better understanding of trap-induced losses in ion-neutral experiments.

We propose the realization of a mechanically squeezed Kerr oscillator with a single ion in a tapered trap. We show that the motion coupling between the axial and radial modes caused by the trap geometry leads to Kerr nonlinearity of the radial mode with magnitude controlled by the trap frequencies. This allows the realization of non-Gaussian quantum gates, which play a significant role in the universal set of continuous variable quantum gates. Furthermore, we show that, because of the nonlinearity of the ion trap, applying an off-resonant time-varying electric field along the trap axis causes a motion squeezing of the radial mode. Finally, we discuss the motion mode frequency spectrum of an ion crystal in a tapered trap. We show that the frequency gap between the motion modes increases with trap nonlinearity, which benefits the realization of faster quantum gates.

While quantum computers have the potential to perform a wide range of practically important tasks beyond the capabilities of classical computers, realizing this potential remains a challenge. One such task is to use an untrusted remote device to generate random bits that can be certified to contain a certain amount of entropy. Certified randomness has many applications but is fundamentally impossible to achieve solely by classical computation. In this work, we demonstrate the generation of certifiably random bits using the 56-qubit Quantinuum H2-1 trapped-ion quantum computer accessed over the internet. Our protocol leverages the classical hardness of recent random circuit sampling demonstrations: a client generates quantum "challenge" circuits using a small randomness seed, sends them to an untrusted quantum server to execute, and verifies the server's results. We analyze the security of our protocol against a restricted class of realistic near-term adversaries. Using classical verification with measured combined sustained performance of $1.1\times10^{18}$ floating-point operations per second across multiple supercomputers, we certify $71,313$ bits of entropy under this restricted adversary and additional assumptions. Our results demonstrate a step towards the practical applicability of today's quantum computers.

Recent advances in laser excitation of the low-energy nuclear isomer transition in $^{229}$Th have opened avenues for developing nuclear clocks, a novel quantum technology with exceptional performance and sensitivity to exotic physics. Here we explore the host-dependence of the nuclear clock frequency, focusing on the isomer shift induced by the difference in the nuclear charge distribution between the ground and excited nuclear states. We combine relativistic many-body methods of atomic structure with periodic density functional theory to evaluate the isomer shifts in solid-state hosts. We elucidate the critical importance of the ``relaxation'' effect in evaluating the isomer shifts. Our analysis predicts nuclear clock frequencies for various solid-state and trapped ion platforms: $ ω_\text{clk}(\text{solid state}) = 2,020,407,384(40) \, \text{MHz}$, $ω_\text{clk}(^{229}\text{Th}^{4+}) = 2,020,407,648(70) \, \text{MHz}$, and $ ω_\text{clk}(^{229}\text{Th}^{3+}) = 2,020,407,114(70) \, \text{MHz}$. We also determine the nuclear transition energy for the bare $^{229}$Th nucleus to be $ω_\text{nuc} = 8.272(22) \,\text{eV}$. Our calculated valence-band isomer shifts for different host materials constrain the nuclear transition frequencies to an 80 MHz-wide frequency window, aiding experimental searches for the $^{229}$Th nuclear transition in novel materials.

In contrast to monolithic devices, modular, networked quantum architectures are based on interconnecting smaller quantum hardware nodes using quantum communication links, and offer a promising approach to scalability. Virtual distillation (VD) is a technique that can, under ideal conditions, suppress errors exponentially as the number of quantum state copies increases. However, additional gate operations required for VD introduce further errors, which may limit its practical effectiveness. In this work, we analyse three practical implementations of VD that correspond to edge cases that maximise space-time tradeoffs. Specifically, we consider an implementation that minimises the number of qubits but introduces significantly deeper quantum circuits, and contrast it with implementations that parallelise the preparation of copies using additional qubits, including a constant-depth implementation. We rigorously characterise their circuit depth and gate count requirements, and develop explicit architectures for implementing them in networked quantum systems -- while also detailing implementations in early fault-tolerant quantum architectures. We numerically compare the performance of the three implementations under realistic noise characteristics of networked ion trap systems and conclude the following. Firstly, VD effectively suppresses errors even for very noisy states. Secondly, the constant-depth implementation consistently outperforms the implementation that minimises the number of qubits. Finally, the approach is highly robust to errors in remote entangling operations, with noise in local gates being the main limiting factor to its performance.

This paper reports on the use of a convolutional neural network (CNN) methodology to analyse fluorescence images of calcium-ion Coulomb crystals in the gas phase. A transfer-learning approach is adopted using the publicly available RESNET50 model. It is demonstrated that by training the neural network on around 500,000 simulated images, we are able to determine ion-numbers not only for a verification set of 100,000 simulated images, but also for experimental calcium-ion images from two different laboratories using a wide range of ion-trap parameters. Absolute ion numbers in the crystal were determined for the experimental data with a percentage error of approximately 10%. This analysis can be performed in a few seconds for an individual crystal image, and therefore the method enables the objective, and efficient, analysis of such images in real time, thereby facilitating time-dependent kinetic measurements on ion-molecule chemistry. The approach adopted also shows promising performance for identifying Ca+ ion numbers in images of mixed-species crystals.

We report $β$-detected nuclear magnetic resonance ($β$-NMR) measurements of implanted $^{8}$Li$^{+}$ in a synthetic single crystal of $α$-SiO$_2$ (quartz). At 6.55 Tesla, the spectrum is comprised of a large amplitude broad resonance and a quadrupolar multiplet that is only revealed by an RF comb excitation. The quadrupole splitting is surprisingly small, increases with temperature, and provides information on the implantation site. Supercell density functional theory calculations show that the small EFG is consistent with an in-channel interstitial site (Wyckoff 3$a$). The spin-lattice relaxation is unexpectedly fast and strongly temperature dependent with a diffusive peak above 200 K and a second more prominent relaxation peak at lower temperature. Analysis of the diffusive relaxation yields an activation barrier 178(43) meV for the isolated Li$^{+}$, in the range of other measurements and calculations. To account for many of the other features of the data, it is suggested that some of the implanted ions trap an electron forming the neutral Li$^{0}$, which is stable over a narrow range of temperatures.

We analyze the use of the Solovay Kitaev (SK) algorithm to generate an ensemble of one qubit rotations over which to perform randomized compilation. We perform simulations to compare the trace distance between the quantum state resulting from an ideal one qubit $R_{Z}$ rotation and discrete SK decompositions. We find that this simple randomized gate synthesis algorithm can reduce the approximation error of these rotations in the absence of gate errors in simulation by at least a factor of two compared to a naive gate synthesis algorithm. We test the technique under the effects of a simple coherent noise model and find that it can mitigate coherent noise. We also run our algorithm on Sandia National Laboratories' QSCOUT trapped-ion device and find that randomization is able to help in the presence of realistic noise sources.

Spin squeezed states provide a seminal example of how the structure of quantum mechanical correlations can be controlled to produce metrologically useful entanglement. Such squeezed states have been demonstrated in a wide variety of artificial quantum systems ranging from atoms in optical cavities to trapped ion crystals. By contrast, despite their numerous advantages as practical sensors, spin ensembles in solid-state materials have yet to be controlled with sufficient precision to generate targeted entanglement such as spin squeezing. In this work, we present the first experimental demonstration of spin squeezing in a solid-state spin system. Our experiments are performed on a strongly-interacting ensemble of nitrogen-vacancy (NV) color centers in diamond at room temperature, and squeezing (-0.5 $\pm$ 0.1 dB) is generated by the native magnetic dipole-dipole interaction between NVs. In order to generate and detect squeezing in a solid-state spin system, we overcome a number of key challenges of broad experimental and theoretical interest. First, we develop a novel approach, using interaction-enabled noise spectroscopy, to characterize the quantum projection noise in our system without directly resolving the spin probability distribution. Second, noting that the random positioning of spin defects severely limits the generation of spin squeezing, we implement a pair of strategies aimed at isolating the dynamics of a relatively ordered sub-ensemble of NV centers. Our results open the door to entanglement-enhanced metrology using macroscopic ensembles of optically active spins in solids.

Strongly correlated topological phases of matter are central to modern condensed matter physics and quantum information technology but often challenging to probe and control in material systems. The experimental difficulty of accessing these phases has motivated the use of engineered quantum platforms for simulation and manipulation of exotic topological states. Among these, the Laughlin state stands as a cornerstone for topological matter, embodying fractionalization, anyonic excitations, and incompressibility. Although its bosonic analogs have been realized on programmable quantum simulators, a genuine fermionic Laughlin state has yet to be demonstrated on a quantum processor. Here, we realize the ν = 1/3 fermionic Laughlin state on IonQ's Aria-1 trapped-ion quantum computer using an efficient and scalable Hamiltonian variational ansatz with 369 two-qubit gates on a 16-qubit circuit. Employing symmetry-verification error mitigation, we extract key observables that characterize the Laughlin state, including correlation hole and chiral edge modes, with strong agreement to exact diagonalization benchmarks. This work establishes a scalable quantum framework to simulate material-intrinsic topological orders and provides a starting point to explore its dynamics and excitations on digital quantum processors.

Stray electric fields induce excess micromotion in ion traps, limiting experimental performance. We present a new micromotion-compensation technique that utilizes a dark ion in a bright-dark-bright linear ion crystal. Stray electric fields in the radial plane of the trap deform the crystal axially. We exploit the mode softening near the transition to the zig-zag configuration to increase our sensitivity dramatically. We corroborate our results with a modified ion-displacement compensation method using a single bright ion. Our modification allows us to compensate stray fields on the 2D radial plane from a 1D measurement of the ion position on the camera. Both methods require only a fixed imaging camera and continuous ion-fluorescence detection. As such, they can be readily implemented in virtually any ion-trapping experiment without additional hardware modifications.

We present a quantum averaging theory (QAT) for analytically modeling unitary gate dynamics in driven quantum systems beyond the rotating-wave approximation. QAT addresses the simultaneous presence of distinct timescales by generating a rotating frame with a dynamical phase operator that toggles with the high-frequency dynamics and yields an effective Hamiltonian for the slow degree of freedom. By accounting for the fast-varying effects, we demonstrate that high-fidelity two-qubit gates in strongly driven systems are achievable by going beyond the validity of first-order approximations. The QAT results rapidly converge with numerical calculations of a fast-entangling Mølmer-Sørensen trapped-ion-qubit gate in the strong coupling regime, illustrating QAT's ability to simultaneously provide both an intuitive, effective-Hamiltonian model and high accuracy.

Atom-cavity systems offer unique advantages for building large-scale distributed quantum computers by providing strong atom-photon coupling while allowing for high-fidelity local operations of atomic qubits. However, in prevalent schemes where the photonic state is encoded in polarization, cavity birefringence introduces an energy splitting of the cavity eigenmodes and alters the polarization states, thus limiting the fidelity of remote entanglement generation. To address this challenge, we propose a scheme that encodes the photonic qubit in the frequency degree-of-freedom. The scheme relies on resonant coupling of multiple transverse cavity modes to different atomic transitions that are well-separated in frequency. We numerically investigate the temporal properties of the photonic wavepacket, two-photon interference visibility, and atom-atom entanglement fidelity under various cavity polarization-mode splittings and find that our scheme is less affected by cavity birefringence. Finally, we propose practical implementations in two trapped ion systems, using the fine structure splitting in the metastable D state of $\mathrm{^{40}Ca^{+}}$, and the hyperfine splitting in the ground state of $\mathrm{^{225}Ra^{+}}$. Our study presents an alternative approach for cavity-based quantum networks that is less sensitive to birefringent effects, and is applicable to a variety of atomic and solid-state emitter-cavity interfaces.

As a crucial resource in the field of quantum metrology, spin squeezing can facilitate highly precise measurements that surpass the limitations imposed by classical physics. However, the quantum advantage of spin squeezing is significantly compromised by decoherence, thus impeding its practical implementation. Here, by investigating the influence of local dissipative environment on spin squeezing beyond the conventional Born-Markov approximation, we find a mechanism to protect spin squeezing from decoherence and show that robust spin squeezing can be achieved in the steady state. We outline an experimental proposal to verify our prediction in a trapped-ion platform. Overcoming the challenges set by decoherence in spin squeezing, our work provides guidance to realize high-precision sensing in realistic environments and sheds light on the effect of non-Markovian environment on quantum systems.

We present a high-precision mass measurement of the proton-rich nucleus 23Si, performed with the LEBIT Penning trap at the Facility for Rare Isotope Beams (FRIB) utilizing the time-of-flight ion cyclotron resonance (TOF-ICR) technique. We determined a mass excess of 23362.9(5.8) keV, which agrees with a recent storage-ring measurement from CSRe but has a factor 20 improved precision. 23Si is hence the nucleus with the most precisely known mass of all nuclei with an isospin projection of Tz =-5/2. We performed shell-model calculations with the USDC and USDCm Hamiltonians to study binding energy differences and Thomas-Ehrmann shifts in mirror systems with an isospin up to T = 5/2. Our experimental result and other recently reported masses of neutron-deficient sd-shell nuclei agree well with the theoretical predictions, demonstrating that isospin symmetry breaking in sd-shell nuclei, even at high isospin values, is well described by modern shell-model calculations.

We investigate the structural properties and melting behavior of two-dimensional ion crystals in an RF trap, focusing on the effects of ion temperature and trap potential symmetry. We identify distinct crystal structures that form under varying trapping conditions and temperatures through experimental observations and theoretical analyses. As the temperature increases or the trap potential becomes more symmetric, we observe a transition from a lattice arrangement to elongated ring-like formations aligned along the trap axes. Our experimental and theoretical efforts enhance our understanding of phase transitions in low-dimensional, confined systems, offering insights into the controlled formation of quantum crystals for applications in quantum simulations and many-body physics.

When two non-relativistic particles interact resonantly in three dimensions, an infinite tower of three-body bound states emerges, exhibiting a discrete scale invariance. This universal phenomenon, known as the Efimov effect, has garnered extensive attention across various fields, including atomic, nuclear, condensed matter, and particle physics. In this letter, we demonstrate that the Efimov effect also manifests in long-range quantum spin chains. The long-range coupling modifies the low-energy dispersion of magnons, enabling the emergence of continuous scale invariance for two-magnon states at resonance. This invariance is subsequently broken to discrete scale invariance upon imposing short-range boundary conditions for the three-magnon problem, leading to the celebrated Efimov bound states. Using effective field theory, we theoretically determine how the ratio of two successive binding energies depends on the interaction range, which agrees with the numerical solution of the bound-state problem. We further discuss generalizations to arbitrary spatial dimensions, where the traditional Efimov effect serves as a special case. Our results reveal universal physics in dilute quantum gases of magnons that can be experimentally tested in trapped-ion systems.

We experimentally demonstrate an unambiguous quantum state discrimination of two qubit states under a non-Hermitian Hamiltonian with parity-time-reversal ($\mathcal{PT}$) symmetry in a single trapped $^{40}$Ca$^+$ ion. We show that any two non-orthogonal states can become orthogonal subjected to time evolution of a $\mathcal{PT}$-symmetric Hamiltonian in both the $\mathcal{PT}$-symmetry preserving and broken regimes, thus can be discriminated deterministically. For a given pair of candidate states, we show that the parameters of the Hamiltonian must be confined in a proper range, within which there exists an optimal choice to realize quantum brachistochrone for the fastest orthogonalization. Besides, we provide a clear geometric picture and some analytic results to understand the main conclusions. Our work shows a promising application of non-Hermitian physics in quantum information processing.

We measured the $g$-factor of the excited state $^3\text{P}_1$ in $\text{Ca}^{14+}$ ion to be $g = 1.499032(6)$ with a relative uncertainty of $4\times10^{-6}$. The magnetic field magnitude is derived from the Zeeman splitting of a $\text{Be}^+$ ion, co-trapped in the same linear Paul trap as the highly charged $\text{Ca}^{14+}$ ion. Furthermore, we experimentally determined the second-order Zeeman coefficient $C_2$ of the $^3\text{P}_0$ - $^3\text{P}_1$ clock transition. For the $m_J=0\rightarrow m_{J'}=0$ transition, we obtain $C_2 = 0.39\pm0.04\text{HzmT}^{-2}$, which is to our knowledge the smallest reported for any atomic transition to date. This confirms the predicted low sensitivity of highly charged ions to higher-order Zeeman effects, making them ideal candidates for high-precision optical clocks. Comparison of the experimental results with our state-of-the art electronic structure calculations shows good agreement, and demonstrates the significance of the frequency-dependent Breit contribution, negative energy states and QED effects on magnetic moments.

Photon recoil is one of the fundamental limitations for high-fidelity control of trapped-atom qubits such as neutral atoms and trapped ions. In this work, we derive an analytical model for efficiently evaluating the motion-induced infidelity in remote entanglement generation protocols. Our model is applicable for various photonic qubit encodings such as polarization, time bin, and frequency, and with arbitrary initial motional states, thus providing a crucial theoretical tool for realizing high-fidelity quantum networking. For the case of tweezer-trapped neutral atoms, our results indicate that operating in the bad-cavity regime with cavity decay rate exceeding atom-photon coupling rate, and near-ground-state cooling with motional quanta below 1, are desired to suppress the motion-induced infidelity sufficiently below the 1% level required for efficient quantum networking. Finite temperature effects can be mitigated efficiently by detection time filtering at the moderate cost of success probability and network speed. These results extend the understanding of infidelity sources in remote entanglement generation protocols, establishing a concrete path towards fault-tolerant quantum networking with scalable trapped-atom qubit systems.

We study the use of global drives with multiple frequency components to improve the efficiency of trapped ion quantum simulations and computations. We show that such `multi-mode' global drives, when combined with a linear number of single-qubit rotations, generate universal Ising-type interactions with shorter overall runtimes than corresponding two-qubit gate implementations. Further, we show how this framework may be extended to efficiently generate $n-$body interactions between any subset $n$ of the ion qubits. Finally, we apply these techniques to encode the Quantum Fourier Transform using quadratically-fewer entangling operations, with quadratically smaller runtime, compared with traditional approaches.

Quantum dynamics on curved spacetime has never been directly probed beyond the Newtonian limit. Although we can describe such dynamics theoretically, experiments would provide empirical evidence that quantum theory holds even in this extreme limit. The practical challenge is the minute spacetime curvature difference over the length scale of the typical extent of quantum effects. Here we propose a quantum network of alkaline earth(-like) atomic processors for constructing a distributed quantum state that is sensitive to the differential proper time between its constituent atomic processor nodes, implementing a quantum observable that is affected by post-Newtonian curved spacetime. Conceptually, we delocalize one clock between three locations by encoding the presence or absence of a clock into the state of the local atoms. By separating three atomic nodes over $\sim$km-scale elevation differences and distributing one clock between them via a W-state, we demonstrate that the curvature of spacetime is manifest in the interference of the three different proper times that give rise to three distinct beat notes in our non-local observable. We further demonstrate that $N$-atom entanglement within each node enhances the interrogation bandwidth by a factor of $N$. We discuss how our system can probe new facets of fundamental physics, such as the linearity, unitarity and probabilistic nature of quantum theory on curved spacetime. Our protocol combines several recent advances with neutral atom and trapped ions to realize a novel quantum probe of curved spacetime uniquely enabled by quantum networks.

We describe how the annihilation of antiprotons can be utilized to generate highly charged isomeric ions in an ion-trap setup. We identify optical transitions in the hyperfine splitting of Hydrogen-like atoms composed of an isomer and a single electron in the ground state. We identify promising candidates in the isomers of Y, Nb, Rh, In, and Sb, for which the hyperfine transition lies in the infrared and whose excited state level lifetime is in the hundreds of milliseconds, which is suitable for metrology applications.

Ion trap system is a leading candidate for quantum network privileged by its long coherence time, high-fidelity gate operations, and the ion-photon entanglement that generates an ideal pair of a stationary memory qubit and a flying communication qubit. Rapid developments in nonlinear quantum frequency conversion techniques have enhanced the potential for constructing a trapped ion quantum network via optical fiber connections. The generation of long-distance entanglement has been demonstrated with ions such as Ca$^{+}$ and Ba$^{+}$, which emit photons in visible or near-infrared range naturally. On the other hand, as the qubit-native photons reside in ultra-violet (UV) spectrum, the Yb$^{+}$ ion has not been considered as a strong competitor for telecommunication qubits despite extensive research on it. Here, we demonstrate an efficient difference-frequency conversion of UV photons, emitted from a trapped Yb$^{+}$ ion, into a visible range. We provide experimental evidence that confirms the converted photons are radiated from the Yb$^{+}$ ion. Our results provide a crucial step toward realizing a long-distance trapped ion quantum network based on Yb$^{+}$ ions through quantum frequency conversion.

A scheme for implementing quantum batteries in a realizable and controllable platform based on a trapped ion chain driven by a mechanical oscillator is proposed. The effects of the hopping interaction between the two-level ions and the coupling interaction between the ions and the external mechanical oscillator on the charging process of the battery are investigated. The importance of the counter-rotating wave terms in the system's Hamiltonian, which are often ignored, is analyzed, and it is found that the charging energy and the ergotropy of the battery are dramatically affected by the counter-rotating wave terms. The quantum phase transition of the two-level system is restrained by the counter-rotating wave terms due to the destruction of the quantum coherence. Lastly, the power-law dependence of the charging process on the distance between the ions is discussed. Our theoretical analysis provides a solid foundation for the development of a practical quantum battery.

The calibration of high-quality two-qubit entangling gates is an essential component in engineering large-scale, fault-tolerant quantum computers. However, many standard calibration techniques are based on randomized circuits that are only quadratically sensitive to calibration errors. As a result, these approaches are inefficient, requiring many experimental shots to achieve acceptable performance. In this work, we demonstrate that robust phase estimation can enable high-precision, Heisenberg-limited estimates of coherent errors in multi-qubit gates. Equipped with an efficient estimator, the calibration problem may be reduced to a simple optimization loop that minimizes the estimated coherent error. We experimentally demonstrate our calibration protocols by improving the operation of a two-qubit controlled-Z gate on a superconducting processor, and we validate the improved performance with gate set tomography. Our methods are applicable to gates in other quantum hardware platforms such as ion traps and neutral atoms, and on other multi-qubit gates, such as CNOT or iSWAP.

The absolute photodetachment cross-section characterizes the photostability of atomic and molecular anions against photodestruction by neutralization. The measurement of this quantity has been reported only for atomic and simple molecular ions. In 2006, Wester's group introduced a novel ion-trap-based technique to measure the absolute photodetachment cross-section [S. Trippel et al., Phys. Rev. Lett. 97, 193003 (2006)] of OH^-. In the present work, we propose a novel methodology to streamline this technique to reduce the measurement time by several orders of magnitude by combining a single experimental rate measurement with a simulated column density distribution of the trapped ions. We validated our approach by reproducing the cross-section reported for OH^- at 632.8 nm. Using this technique, we report the first such measurement for a molecule of biological interest, deprotonated indole, at a laser wavelength of 403 nm. The proposed scheme is anticipated to have a significant and transformative impact on the development of a comprehensive database for photodetachment and photodissociation cross-sections of molecular ions. Furthermore, these measurements have the potential to drive the development of cutting-edge computational codes for cross-section calculations, enabling an unprecedentedly detailed understanding of electron dynamics in large molecules and the light-matter interaction.

A direct measurement of the ground-state-to-ground-state electron-capture decay $Q$ ($Q_{\rm EC}$) value of $^{97}$Tc has been conducted employing the high resolving power phase-imaging ion-cyclotron-resonance technique with the double Penning trap mass spectrometer JYFLTRAP. The resulting $Q_{\rm EC}$ value for $^{97}$Tc is 324.82(21) keV, exhibiting a precision approximately 19 times higher than the value adopted in the newest Atomic Mass Evaluation (AME2020) and differing by 1.2$σ$. Furthermore, by combining this refined $Q$ value with nuclear energy-level data for the decay-daughter $^{97}$Mo, a potential ultra-low Q-value transition, possibly of allowed type, $^{97}$Tc (9/2$^{+}$, ground state) $\rightarrow$ $^{97}$Mo$^{*}$ (320(1) keV), was evaluated for future long-term neutrino-mass determination experiments. The ground-state-to-excited-state electron-capture decay $Q$ value ($Q^{*}_{\rm EC}$) of this transition was determined to be 4.8(10) keV, confirming it to be energetically allowed with a confidence level of exceeding 4$σ$. The captures of electrons occupying the L and higher shells for this transition are energetically allowed, giving a value of 2.0(10) keV for the closest distance of $Q^{*}_{\rm EC}$ to the allowed binding energy of the L1 shell. To predict partial half-lives and energy-release distributions for this transition, the atomic self-consistent many-electron Dirac--Hartree--Fock--Slater method and the nuclear shell model have been employed. Dominant correction terms such as exchange and overlap corrections, as well as shake-up and shake-off effects, were included in the final results. Moreover, the normalized distribution of released energy in the electron-capture decay of $^{97}$Tc to excited states of $^{97}$Mo, is compared with that of $^{163}$Ho, which is being used for electron-neutrino-mass determination.

The interplay between coherence and system-environment interactions is at the basis of a wide range of phenomena, from quantum information processing to charge and energy transfer in molecular systems, biomolecules, and photochemical materials. In this work, we use a Frenkel exciton model with long-range interacting qubits coupled to a damped collective bosonic mode to investigate vibrationally assisted transfer processes in donor-acceptor systems featuring internal substructures analogous to light-harvesting complexes. We find that certain delocalized excitonic states maximize the transfer rate and that the entanglement is preserved during the dissipative transfer over a wide range of parameters. We investigate the reduction in transfer caused by static disorder, white noise, and finite temperature and study how transfer efficiency scales as a function of the number of dimerized monomers and the component number of each monomer, finding which excitonic states lead to optimal transfer. Finally, we provide a realistic experimental setting to realize this model in analog trapped-ion quantum simulators. Analog quantum simulation of systems comprising many and increasingly complex monomers could offer valuable insights into the design of light-harvesting materials, particularly in the non-perturbative intermediate parameter regime examined in this study, where classical simulation methods are resource-intensive.

Monitored many-body systems can exhibit a phase transition between entangling and disentangling dynamical phases by tuning the strength of measurements made on the system as it evolves. This phenomenon is called the measurement-induced phase transition (MIPT). Understanding the properties of the MIPT is a prominent challenge for both theory and experiment at the intersection of many-body physics and quantum information. Realizing the MIPT experimentally is particularly challenging due to the postselection problem, which demands a number of experimental realizations that grows exponentially with the number of measurements made during the dynamics. Proposed approaches that circumvent the postselection problem typically rely on a classical decoding process that infers the final state based on the measurement record. But the complexity of this classical process generally also grows exponentially with the system size unless the dynamics is restricted to a fine-tuned set of unitary operators. In this work we overcome these difficulties. We construct a tree-shaped quantum circuit whose nodes are Haar-random unitary operators followed by weak measurements of tunable strength. For these circuits, we show that the MIPT can be detected without postselection using only a simple classical decoding process whose complexity grows linearly with the number of qubits. Our protocol exploits the recursive structure of tree circuits, which also enables a complete theoretical description of the MIPT, including an exact solution for its critical point and scaling behavior. We experimentally realize the MIPT on Quantinuum's H1-1 trapped-ion quantum computer and show that the experimental results are precisely described by theory. Our results close the gap between analytical theory and postselection-free experimental observation of the MIPT.

The Mølmer-Sørensen (MS) gate is a two-qubit controlled-phase gate in ion traps that is highly valued due to its ability to preserve the motional state of the ions. However, its fidelity is obstructed by errors affecting the motion of the ions as well as the rotation of the qubits. In this work, we propose an amplitude-modulated composite MS gate which features high fidelity robust to gate timing, detuning and coupling errors and is also tolerant of a.c. Stark shifts and drifting detuning errors.

We present an experimental method for the characterization of the kinetic energies of ions confined in a 22-pole radio frequency trap by inducing a small potential barrier using the surrounding ring electrodes, allowing the selective extraction of ions. Energy sampling experiments have been performed on buffer gas thermalized He$^+$ ions at trap temperatures between 10-180 K, resulting in distinct extraction curves as a function of the potential barrier, and a differentiated behavior depending on the escape time from the trap. The experiments are complemented by Monte Carlo simulations of the ion trajectories inside the calculated trap potential and allow us to investigate the properties of the sampling method, the role of ion motion coupling, and the impact of residual buffer gas collisions on the observed results. The technique has also been successfully applied to identify energetic H$_3^+$ ions produced in an exothermic reaction inside the trap. Upon calibration, this method can provide relative kinetic energy distributions or be used to filter the maximum desired kinetic energy of the ions inside the trap.

Quantum games, like quantum algorithms, exploit quantum entanglement to establish strong correlations between strategic player actions. This paper introduces quantum game-theoretic models applied to trading and demonstrates their implementation on an ion-trap quantum computer. The results showcase a quantum advantage, previously known only theoretically, realized as higher-paying market Nash equilibria. This advantage could help uncover alpha in trading strategies, defined as excess returns compared to established benchmarks. These findings suggest that quantum computing could significantly influence the development of financial strategies.

This study investigates the dynamics of quantum information and computational resources using a tractable model of coupled harmonic oscillators. We precisely characterize the interplay between mutual information, synchronization, and circuit complexity, demonstrating that they serve as complementary yet distinct measures of quantum correlations. Our analysis reveals how coupling strength, detuning, and external magnetic fields modulate these quantities, with synchronization and mutual information exhibiting marked divergence in nonlinear regimes. By employing exact Gaussian methods, we compute the circuit depth required to prepare target states and connect increased fidelity to more regular dynamical behavior. Furthermore, we analyze single-ion transport in a harmonic trap, comparing sudden and adiabatic protocols. We introduce a nonadiabaticity metric to quantify the fidelity-complexity trade-off, showing that smooth control sequences significantly minimize operational errors by suppressing excitations. These results provide a refined understanding of quantum correlations and offer concrete principles for optimizing control strategies in quantum technologies.

We explore the interplay of quantum computing and machine learning to advance experimental protocols for observing measurement-induced phase transitions (MIPT) in quantum devices. In particular, we focus on trapped ion monitored circuits and apply the cross entropy benchmark recently introduced by [Li et al., Phys. Rev. Lett. 130, 220404 (2023)], which can mitigate the post-selection problem. By doing so, we reduce the number of projective measurements -- the sample complexity -- required per random circuit realization, which is a critical limiting resource in real devices. Since these projective measurement outcomes form a classical probability distribution, they are suitable for learning with a standard machine learning generative model. In this paper, we use a recurrent neural network (RNN) to learn a representation of the measurement record for a native trapped-ion MIPT, and show that using this generative model can substantially reduce the number of measurements required to accurately estimate the cross entropy. This illustrates the potential of combining quantum computing and machine learning to overcome practical challenges in realizing quantum experiments.

The potential applications of dilute magnetic oxides (DMOs) in magneto-optic and spintronic devices have attracted significant attention, although understanding their magnetic behavior is complex due to intricate interactions of intrinsic defects. The present study aims to investigate the effect of different annealing environments on the magnetic properties of polycrystalline transition metal cation (Co and Y) doped CeO2 DMO with a 5% doping concentration of transition metal (TM). The objective is to investigate the defect interactions within the lattice through a comprehensive investigation involving structural characterizations, magnetic measurements, and first principle calculations. The results show that the Ar/H2 annealing environment induced more oxygen vacancies than air-annealed samples. Consequently, field-dependent magnetization measurements revealed above-room-temperature ferromagnetism (RTFM) in both un-doped and TM-doped CeO2. The ferromagnetic (FM) properties of CeO2 resulted from carrier-trapped vacancy centers facilitating exchange interactions between the spins of magnetic ions. The Langevin field profile indicated that TM-doped CeO2 formed more bound magnetic polarons (BMPs) during annealing in an Ar/H2 environment, which contributed to the enhanced ferromagnetism. Similarly, enhancement in the magnetic properties with increasing oxygen vacancies is observed through first principle calculations. This suggests the potential for optimizing the magnetic properties of DMOs through controlled annealing processes.

We propose an experimental setup for manipulating the spontaneous emission of trapped ions, based on a spatial light modulator. Anticipated novelties include the potential to entangle more than two ions through a single photon detection event and control the visibility for spatially distinguishable emitters. The setup can be adapted to most of the existing ion traps commonly used in quantum technology.

We propose to combine neutral atom and trapped ion qubits in one scalable modular architecture that uses shuttling of individual neutral atoms in optical tweezers to realize atomic interconnects between trapped ion quantum registers. These interconnects are deterministic, and thus may be performed on-demand. The proposed protocol is as follows: a tweezer-trapped neutral atom qubit is brought close to a trapped ion in an ion chain serving as a module of a larger quantum computer, and an entangling gate is performed between the two qubits. Then the neutral atom is quickly moved to another, nearby trapped ion chain in the same modular ion trap and entangled with an ion in that chain, thus entangling the two separate ion chains. The optical dipole potential of the tweezer beam for the neutral atom does not measurably affect the trapped ions, while the RF ion trap does not affect the neutral atom. With realistic tweezer trap parameters, the neutral atom can be moved over millimeter scale distance in a few tens of microseconds, thus enabling a remote entanglement generation rate of over 10^3/s even with very modest assumptions for the atom-ion quantum gate speed, and possibly up to 10^4/s, which is two orders of magnitude higher than the current state-of-the-art with photonic interconnects.

Atomic and trapped-ion systems are the backbone of a new generation of quantum-based positioning, navigation, and timing (PNT) technologies. The miniaturization of such quantum systems offers tremendous technological advantages, especially the reduction of system size, weight, and power consumption. Yet, this has been limited by the absence of compact, standalone photonic integrated circuits (PICs) at the wavelengths suitable for these instruments. Mobilizing such photonic systems requires development of fully integrated, on-chip, active components at sub-micrometer wavelengths. We demonstrate heterogeneous photonic integrated circuits operating at 980 nm based on wafer-scale bonding of InGaAs quantum well active regions to tantalum pentoxide passive components. This high-yield process provides > 95 % surface area yield and enables integration of > 1300 active components on a 76.2 mm (3 inch) silicon wafer. We present a diverse set of functions, including semiconductor optical amplifiers, Fabry-Perot lasers, and distributed feedback lasers with 43 dB side-mode suppression ratio and > 250 GHz single-mode tuning range. We test the precise wavelength control and system level functionality of the on-chip lasers by pumping optical parametric oscillation processes in microring resonators fabricated on the same platform, generating short-wavelength signals at 778 nm and 752 nm. These results provide a pathway to realize fully functional integrated photonic engines for operation of compact quantum sensors based on atomic and trapped-ion systems.

The quantum chromodynamics (QCD) phase diagram, which reveals the state of strongly interacting matter at different temperatures and densities, is key to answering open questions in physics, ranging from the behavior of particles in neutron stars to the conditions of the early universe. However, classical simulations of QCD face significant computational barriers, such as the sign problem at finite matter densities. Quantum computing offers a promising solution to overcome these challenges. Here, we take an important step toward exploring the QCD phase diagram with quantum devices by preparing thermal states in one-dimensional non-Abelian gauge theories. We experimentally simulate the thermal states of SU(2) and SU(3) gauge theories at finite densities on a trapped-ion quantum computer using a variational method. This is achieved by introducing two features: Firstly, we add motional ancillae to the existing qubit register to efficiently prepare thermal probability distributions. Secondly, we introduce charge-singlet measurements to enforce color-neutrality constraints. This work marks the first lattice gauge theory quantum simulation of QCD at finite density and temperature for two and three colors, laying the foundation to explore QCD phenomena on quantum platforms.

Single-atom quantum sensors offer high spatial resolution and high sensitivity to electric and magnetic fields. Among them, trapped ions offer exceptional performance in sensing electric fields, which has been used in particular to probe these in the proximity of metallic surfaces. However, the flexibility of previous work was limited by the use of radio-frequency trapping fields, which has restricted spatial scanning to linear translations, and calls into question whether observed phenomena are connected to the presence of the radio-frequency fields. Here, using a Penning trap instead, we demonstrate a single ion probe which offers three-dimensional position scanning at distances between $50$ $μ\mathrm{m}$ and $450$ $μ\mathrm{m}$ from a metallic surface and above a $200\times200$ $μ\mathrm{m}^{2}$ area, allowing us to reconstruct static and time-varying electric as well as magnetic fields. We use this to map charge distributions on the metallic surface and noise stemming from it. The methods demonstrated here allow similar probing to be carried out on samples with a variety of materials, surface constitutions and geometries, providing a new tool for surface science.

Trapped-ion systems are a promising route toward the realization of both near-term and universal quantum computers. However, one of the pressing challenges is improving the fidelity of two-qubit entangling gates. These operations are often implemented by addressing individual ions with laser pulses using the Molmer-Sorensen (MS) protocol. Amplitude modulation (AM) is a well-studied extension of this protocol, where the amplitude of the laser pulses is controlled as a function of time. We present an analytical study of AM, using a Fourier series expansion to maintain the generality of the laser amplitude's functional form. We then apply this general AM method to gate-timing errors by imposing conditions on these Fourier coefficients, producing trade-offs between the laser power and fidelity at a fixed gate time. The conditions derived here are linear and can be used, in principle, to achieve arbitrarily high orders of insensitivity to gate-timing errors. Numerical optimization is then employed to identify the minimum-power pulse satisfying these constraints. Our central result is that the leading order dependence on gate timing errors is improved from $\mathcal{O}(Δt^2)$ to $\mathcal{O}(Δt^6)$ with the addition of one linear constraint on the Fourier coefficients and to $\mathcal{O}(Δt^{10})$ with two linear constraints without a significant increase in the average laser power. The increase approaches zero as more Fourier coefficients are included. In further studies, this protocol can be applied to other error sources and used in conjunction with other error-mitigation techniques to improve two-qubit gates.

We propose a teleportation protocol involving beam splitting operations and binary-outcome measurements, such as parity measurements. These operations have a straightforward implementation using the dispersive regime of the Jaynes-Cummings Hamiltonian, making our protocol suitable for a broad class of platforms, including trapped ions, circuit quantum electrodynamics and acoustodynamics systems. In these platforms homodyne measurements of the bosonic modes are less natural than dispersive measurements, making standard continuous variable teleportation unsuitable. In our protocol, Alice is in possession of two bosonic modes and Bob a single mode. An entangled mode pair between Alice and Bob is created by performing a beam splitter operation on a cat state. An unknown qubit state encoded by cat states is then teleported from Alice to Bob after a beamsplitting operation, measurement sequence, and a conditional correction. In the case of multiple measurements, near-perfect fidelity can be obtained. We discuss the optimal parameters in order to maximize the fidelity under a variety of scenarios.

The advancements of quantum processors offer a promising new window to study exotic states of matter. One striking example is the possibility of non-ergodic behaviour in systems with a large number of local degrees of freedom. Here we use a trapped-ion qudit quantum processor to study a disorder-free $S=1$ Floquet model, which becomes prethermal by dynamic localization due to local spin interactions. We theoretically describe and experimentally observe an emergent $3T$ subharmonic response, demonstrating the ability to witness non-ergodic dynamics beyond qubit systems. Our numerical simulations reveal the role played by multipartite entanglement through the Quantum Fisher Information, showing how this quantity successfully reflects the transition between ergodic and localized regimes in a non-equilibrium context. These results pave the way for the study of ergodicity-breaking mechanisms in higher-dimensional quantum systems.

Semiconductor quantum dots offer a promising platform for controlling spin qubits and realizing quantum logic gates, essential for scalable quantum computing. In this work, we utilize a variational quantum compiling algorithm to design efficient three-qubit gates using a time-independent Hamiltonian composed of only physical interaction terms. The resulting gates, including the Toffoli and Fredkin gates, demonstrate high fidelity and robustness against both coherent and incoherent noise sources, including charge and nuclear spin noise. This method is applicable to a wide range of physical systems, such as superconducting qubits and trapped ions, paving the way for more resilient and universal quantum computing architectures.

The kinetic stability of collisionless, sloshing beam-ion (45° pitch angle) plasma is studied in a 3D simple magnetic mirror, mimicking the Wisconsin High-temperature superconductor Axisymmetric Mirror (WHAM) experiment. The collisional Fokker-Planck code CQL3D-m provides a slowing-down beam-ion distribution to initialize the kinetic-ion/fluid-electron code Hybrid-VPIC, which then simulates free plasma decay without external heating or fueling. Over 1-10 $μ$s, drift-cyclotron loss-cone (DCLC) modes grow and saturate in amplitude. DCLC scatters ions to a marginally-stable distribution with gas-dynamic rather than classical-mirror confinement. Sloshing ions can trap cool (low-energy) ions in an electrostatic potential well to stabilize DCLC, but DCLC itself does not scatter sloshing beam-ions into said well. Instead, cool ions must come from external sources such as charge-exchange collisions with a low-density neutral population. Manually adding cool ~1 keV ions improves beam-ion confinement several-fold in Hybrid-VPIC simulations, which qualitatively corroborates prior measurements from real mirror devices with sloshing ions.

We report the achievement of single-qubit gates with sub-part-per-million error rates, in a trapped-ion $^{43}$Ca$^{+}$ hyperfine clock qubit. We explore the speed/fidelity trade-off for gate times $4.4\leq t_{g}\leq35~μ$s, and benchmark a minimum error per Clifford gate of $1.5(4) \times 10^{-7}$. Calibration errors are suppressed to $< 10^{-8}$, leaving qubit decoherence ($T_{2}\approx 70$ s), leakage, and measurement as the dominant error contributions. The ion is held above a microfabricated surface-electrode trap which incorporates a chip-integrated microwave resonator for electronic qubit control; the trap is operated at room temperature without magnetic shielding.

The accurate computational study of wavepacket nuclear dynamics is considered to be a classically intractable problem, particularly with increasing dimensions. Here we present two algorithms that, in conjunction with other methods developed by us, will form the basis for performing quantum nuclear dynamics in arbitrary dimensions. For one algorithm, we present a direct map between the Born-Oppenheimer Hamiltonian describing the wavepacket time-evolution and the control parameters of a spin-lattice Hamiltonian that describes the dynamics of qubit states in an ion-trap quantum computer. This map is exact for three qubits, and when implemented, the dynamics of the spin states emulate those of the nuclear wavepacket. However, this map becomes approximate as the number of qubits grow. In a second algorithm we present a general quantum circuit decomposition formalism for such problems using a method called the Quantum Shannon Decomposition. This algorithm is more robust and is exact for any number of qubits, at the cost of increased circuit complexity. The resultant circuit is implemented on IBM's quantum simulator (QASM) for 3-7 qubits. In both cases the wavepacket dynamics is found to be in good agreement with the classical result and the corresponding vibrational frequencies obtained from the wavepacket density time-evolution, are in agreement to within a few tenths of a wavenumbers.

Non-adiabatic processes near conical intersections are rooted in the stronger coupling between electronic and nuclear degrees of freedom. Using a system of two trapped Rydberg ions, their high polarizability and strong dipolar interactions allow to form a conical intersection, where dynamics takes place on a microsecond time scale. Rydberg lifetimes are typically from a few to tens of microseconds, which could affect the conical dynamics. We study the effect of the finite lifetime of the Rydberg state on the vibronic dynamics around the conical intersection via analyzing the master equation. Through mean field and numerical calculations, damping dynamics are found in both the phonon populations and electronic states depending on the initial states. It is found that oscillatory vibronic dynamics can be seen clearly within the Rydberg lifetime, permitting to observe the conical effect in the trapped Rydberg ion system.

Today's most advanced ion trap quantum computers have significant overhead due to the need for dual-species operation. Looking ahead, logical qubit register sizes will be limited by the encoding rate needed to correct generic Pauli errors. We address both of these issues by establishing high-fidelity control of metastable qubits, a key component of \textit{omg} or dual-type architectures, which enables converting a significant fraction of gate errors to erasures. We first implement an erasure conversion scheme which enables detection of $\sim 94\%$ of spontaneous Raman scattering errors during logic gates and nearly all errors from qubit decay. Second, we perform a two-ion geometric phase gate using far-detuned (-44\,THz) stimulated Raman transitions to produce an entangled state with a raw Bell state fidelity of 97.73\% and a SPAM-corrected Bell state fidelity of 98.61\%. When subtracting erasure errors, this fidelity becomes 99.16\%. These results, along with projections based on our detailed error budget, demonstrate metastable trapped-ion qubits as a platform for low-overhead, fault-tolerant quantum computing.

We propose a spin-motion state for high-precision quantum metrology with super-Heisenberg scaling of the parameter estimation uncertainty using a trapped ion system. Such a highly entangled state can be created using the Tavis-Cummings Hamiltonian which describes the interaction between a collective spin system and a single vibrational mode. Our method relies on an adiabatic evolution in which the initial motional squeezing is adiabatically transferred into collective spin squeezing. In the weak squeezing regime, we show that the adiabatic evolution creates a spin-squeezed state, which reduces the quantum projective noise to a sub-shot noise limit. For strong bosonic squeezing we find that the quantum Fisher information follows a super-Heisenberg scaling law $\propto N^{5/2}$ in terms of the number of ions $N$. Furthermore, we discuss the spin squeezing parameter which quantifies the phase sensitivity enhancement in Ramsey spectroscopic measurements and show that it also exhibits a super-Heisenberg scaling with $N$. Our work enables the development of high-precision quantum metrology based on entangled spin-boson states that lead to faster scaling of the parameter estimation uncertainty with the number of spins.

The Fermi-Hubbard model (FHM) is a simple yet rich model of strongly interacting electrons with complex dynamics and a variety of emerging quantum phases. These properties make it a compelling target for digital quantum simulation. Trotterization-based quantum simulations have shown promise, but implementations on current hardware are limited by noise, necessitating error mitigation techniques like circuit optimization and post-selection. A mapping of the FHM to a Z2 LGT was recently proposed that restricts the dynamics to a subspace protected by additional symmetries, and its ability for post-selection error mitigation was verified through noisy classical simulations. In this work, we propose and demonstrate a suite of algorithm-hardware co-design strategies on a trapped-ion quantum computer, targeting two key aspects of NISQ-era quantum simulation: circuit compilation and error mitigation. In particular, a novel combination of iteratively preconditioned gradient descent (IPG) and subsystem von Neumann Entropy compression reduces the 2-qubit gate count of FHM quantum simulation by 35%, consequently doubling the number of simulatable Trotter steps when used in tandem with error mitigation based on conserved symmetries, debiasing and sharpening techniques. Our work demonstrates the value of algorithm-hardware co-design to operate digital quantum simulators at the threshold of maximum circuit depths allowed by current hardware, and is broadly generalizable to strongly correlated systems in quantum chemistry and materials science.

Studies aiming to determine the astrophysical origins of nuclei produced by the rapid neutron capture process ($r$ process) rely on nuclear properties as inputs for simulations. The solar abundances can be used as a benchmark for such calculations, with the $r$-process rare-earth peak (REP) around mass number ($A$) 164 being of special interest due to its presently unknown origin. With the advancement of rare isotope beam production over the last decade and improvement in experimental sensitivities, many of these REP nuclides have become accessible for measurement. Masses are one of the most critical inputs as they impact multiple nuclear properties, namely the neutron-separation energies, neutron capture rates, $β$-decay rates, and $β$-delayed neutron emission probabilities. In this work, we report masses of 20 neutron-rich nuclides (along the Ba, La, Ce, Pr, Nd, Pm, Gd, Dy and Ho isotopic chains) produced at the CAlifornium Rare Isotope Breeder Upgrade (CARIBU) facility at Argonne National Laboratory. The masses were measured with the Canadian Penning trap (CPT) mass spectrometer using the Phase-Imaging Ion-Cyclotron-Resonance (PI-ICR) technique. We then use these new masses along with previously published CPT masses to inform predictions for a Markov Chain Monte Carlo (MCMC) procedure aiming to identify the astrophysical conditions consistent with both solar data and mass measurements. We show that the MCMC responds to this updated mass information, producing refined results for both mass predictions and REP abundances.

Trapped ions provide a highly controlled platform for quantum sensors, clocks, simulators, and computers, all of which depend on cooling ions close to their motional ground state. Existing methods like Doppler, resolved sideband, and dark resonance cooling balance trade-offs between the final temperature and cooling rate. A traveling polarization gradient has been shown to cool multiple modes quickly and in parallel, but utilizing a stable polarization gradient can achieve lower ion energies, while also allowing more tailorable light-matter interactions in general. In this paper, we demonstrate cooling of a trapped ion below the Doppler limit using a phase-stable polarization gradient created using trap-integrated photonic devices. At an axial frequency of $2π\cdot1.45~ \rm MHz$ we achieve $\langle n \rangle = 1.3 \pm 1.1$ in $500~μ\rm s$ and cooling rates of ${\sim}0.3 \, \rm quanta/μs$. We examine ion dynamics under different polarization gradient phases, detunings, and intensities, showing reasonable agreement between experimental results and a simple model. Cooling is fast and power-efficient, with improved performance compared to simulated operation under the corresponding running wave configuration.

We show that recent experiments in hybrid qubit-oscillator devices that measure the phase-space characteristic function of the oscillator via the qubit can be seen through the lens of functional calculus and path integrals, drawing a clear analogy with the generating functional of a quantum field theory. This connection suggests an expansion of the characteristic function in terms of Feynman diagrams, exposing the role of the real-time bosonic propagator, and identifying the external source functions with certain time-dependent couplings that can be controlled experimentally. By applying maximum-likelihood techniques, we show that the ``measurement'' of these Feynman diagrams can be reformulated as a problem of multi-parameter point estimation that takes as input a set of Ramsey-type measurements of the qubit. By numerical simulations that consider leading imperfections in trapped-ion devices, we identify the optimal regimes in which Feynman diagrams could be reconstructed from measured data with low systematic and stochastic errors. We discuss how these ideas can be generalized to finite temperatures via the Schwinger-Keldysh formalism, contributing to a bottom-up approach to probe quantum simulators of lattice field theories by systematically increasing the qubit-oscillator number.

As one of the main pillars of quantum technologies, quantum metrology aims to improve measurement precision using techniques from quantum information. The two main strategies to achieve this are the preparation of nonclassical states and the design of optimized measurement observables. We discuss precision limits and optimal strategies in quantum metrology and sensing with a single mode of quantum continuous variables. We focus on the practically most relevant cases of estimating displacements and rotations and provide the sensitivities of the most important classes of states that includes Gaussian states and superpositions of Fock states or coherent states. Fundamental precision limits that are obtained from the quantum Fisher information are compared to the precision of a simple moment-based estimation strategy based on the data obtained from possibly sub-optimal measurement observables, including homodyne, photon number, parity and higher moments. Finally, we summarize some of the main experimental achievements and present emerging platforms for continuous-variable sensing. These results are of particular interest for experiments with quantum light, trapped ions, mechanical oscillators, and microwave resonators.

The development of programmable quantum devices can be measured by the complexity of manybody states that they are able to prepare. Among the most significant are topologically ordered states of matter, which enable robust quantum information storage and processing. While topological orders are more readily accessible with qudits, experimental realisations have thus far been limited to lattice models of qubits. Here, we prepare a ground state of the Z3 toric code state on 24 qutrits in a trapped ion quantum processor with fidelity per qutrit exceeding 96.5(3)%. We manipulate two types of defects which go beyond the conventional qubit toric code: a parafermion, and its bound state which is related to charge conjugation symmetry. We further demonstrate defect fusion and the transfer of entanglement between anyons and defects, which we use to control topological qutrits. Our work opens up the space of long-range entangled states with qudit degrees of freedom for use in quantum simulation and universal error-correcting codes.

State-of-the-art noisy-intermediate-scale quantum (NISQ) processors are currently implemented across a variety of hardware platforms, each with their own distinct gatesets. As such, circuit compilation should not only be aware of, but also deeply connect to, the native gateset and noise properties of each. Trapped-ion processors are one such platform that provides a gateset that can be continuously parameterized across both one- and two-qubit gates. Here we use the Quantum Scientific Computing Open User Testbed (QSCOUT) to study noise-aware compilations focused on continuously parameterized two-qubit $\mathcal{ZZ}$ gates (based on the Mølmer-Sørensen interaction) using $\textbf{Superstaq}$, a quantum software platform for hardware-aware circuit compiler optimizations. We discuss the realization of $\mathcal{ZZ}$ gates with arbitrary angle on the all-to-all connected trapped-ion system. Then we discuss a variety of different compiler optimizations that innately target these $\mathcal{ZZ}$ gates and their noise properties. These optimizations include moving from a restricted maximally entangling gateset to a continuously parameterized one, swap mirroring to further reduce total entangling angle of the operations, focusing the heaviest $\mathcal{ZZ}$ angle participation on the best performing gate pairs, and circuit approximation to remove the least impactful $\mathcal{ZZ}$ gates. We demonstrate these compilation approaches on the hardware with randomized quantum volume circuits, observing the potential to realize a larger quantum volume as a result of these optimizations. Using differing yet complementary analysis techniques, we observe the distinct improvements in system performance provided by these noise-aware compilations and study the role of stochastic and coherent error channels for each compilation choice.

Trapped ions are among the most advanced platforms for quantum simulation and computation. Their capabilities can be further augmented by making use of electronically highly excited Rydberg states, which enable the realization of long-ranged electric dipolar interactions. Most experimental and theoretical studies so far focus on the excitation of ionic Rydberg states in linear Paul traps, which generate confinement by a combination of static and oscillating electric fields. These two fields need to be carefully aligned to minimize so-called micromotion, caused by the time-dependent electric field. The purpose of this work is to systematically understand the qualitative impact of micromotion on the Rydberg excitation spectrum, when the symmetry axes of the two electric fields do not coincide. Considering this scenario is not only important in the case of possible field misalignment, but becomes inevitable for Rydberg excitations in 2D and 3D ion crystals. We develop a minimal model describing a single trapped Rydberg ion, which we solve numerically via Floquet theory and analytically using a perturbative approach. We calculate the excitation spectra and analyze in which parameter regimes addressable and energetically isolated Rydberg lines persist, which are an important requirement for conducting coherent manipulations.

Sympathetic cooling of molecular ions through the Coulomb interaction with laser-cooled atomic ions is an efficient tool to prepare translationally cold molecules without, ideally, affecting the internal state of the molecular ions. However, the electric field due to the Coulomb interaction may induce rotational transitions that change the purity of initially quantum state prepared molecules. Here, we use estimates of rotational state changes in single collisions of diatomic ions with atomic ions [arXiv:1905.02130] to determine the overall rotational excitation accumulated over the sympathetic cooling. Considering two different experimental scenarios, that of a molecular ion co-trapped with a single atomic ion and a molecular ion immersed in a Coulomb crystal of atomic ions, we also estimate the cooling time.

Banded energy distributions of H$^{+}$, O$^{++}$, S$^{+++}$, and O$^+$ or S$^{++}$ ions between 100 eV to ~20 keV are consistently observed in Jupiter's magnetosphere mapping to M-shells between M=10-20. The bands correspond to flux enhancements at similar speeds for different ion species, providing the first evidence of simultaneous bounce-resonant acceleration of multiple ion species in Jupiter's magnetosphere. Ion enhancements occur for energies at which the bounce frequencies of the trapped ions matched integer harmonics of the System-III corotation frequency. The observations highlight a previously unknown interaction between corotation and bounce motion of <10 keV energy ions that is a fundamental and persistent process occurring in Jupiter's magnetosphere.

High-fidelity mid-circuit measurements, which read out the state of specific qubits in a multiqubit processor without destroying them or disrupting their neighbors, are a critical component for useful quantum computing. They enable fault-tolerant quantum error correction, dynamic circuits, and other paths to solving classically intractable problems. But there are almost no methods to assess their performance comprehensively. We address this gap by introducing the first randomized benchmarking protocol that measures the rate at which mid-circuit measurements induce errors in many-qubit circuits. Using this protocol, we detect and eliminate previously undetected measurement-induced crosstalk in a 20-qubit trapped-ion quantum computer. Then, we use the same protocol to measure the rate of measurement-induced crosstalk error on a 27-qubit IBM Q processor, and quantify how much of that error is eliminated by dynamical decoupling.

The ability to prepare molecular ions in selected quantum states enables studies in areas such as chemistry, metrology, spectroscopy, quantum information, and precision measurements. Here, we demonstrate $(2+1)$ resonance-enhanced multiphoton ionization (REMPI) of oxygen, both in a molecular beam and in an ion trap. The two-photon transition in the REMPI spectrum is rotationally resolved, allowing ionization from a selected rovibrational state of O$_2$. Fits to this spectrum determine spectroscopic parameters of the O$_2$ $d\,^1Π_g$ state and resolve a discrepancy in the literature regarding its band origin. The trapped molecular ions are cooled by co-trapped atomic ions. Fluorescence mass spectrometry nondestructively demonstrates the presence of the photoionized O$_2^+$. We discuss strategies for maximizing the fraction of ions produced in the ground rovibrational state. For $(2+1)$ REMPI through the $d\,^1Π_g$ state, we show that the Q(1) transition is preferred for neutral O$_2$ at rotational temperatures below 50~K, while the O(3) transition is more suitable at higher temperatures. The combination of state-selective loading and nondestructive detection of trapped molecular ions has applications in optical clocks, tests of fundamental physics, and control of chemical reactions.

Spontaneous particle-pair formation is a fundamental phenomenon in nature. It can, for example, appear when the potential energy between two particles increases with separation, as if they were connected by a tense string. Beyond a critical separation, new particle pairs can form, causing the string to break. String-breaking dynamics in quantum chromodynamics play a vital role in high-energy particle collisions and early universe evolution. Simulating string evolution and hadron formation is, therefore, a grand challenge in modern physics. Quantum simulators, well-suited for studying dynamics, are expected to outperform classical computing methods. However, the required experimental capabilities to simulate string-breaking dynamics have not yet been demonstrated, even for simpler models of the strong force. We experimentally probe, for the first time, the spatiotemporal dynamics of string-breaking in a (1+1)-dimensional $\mathbb{Z}_2$ lattice gauge theory using a fully programmable trapped-ion quantum simulator. We emulate external static charges and strings via site-dependent magnetic-field control enabled by a dual array of tightly focused laser beams targeting individual ions. First, we study how confinement affects isolated charges, finding that they freely spread without string tension but exhibit localized oscillations when tension is increased. Then, we observe and characterize string-breaking dynamics of a string stretched between two static charges after an abrupt increase in string tension. Charge pairs appear near the string edges and spread into the bulk, revealing a route to dynamical string-breaking distinct from the conventional Schwinger mechanism. Our work demonstrates that analog quantum simulators have achieved the necessary control to explore string-breaking dynamics, which may ultimately be relevant to nuclear and high-energy physics.

As quantum computing advances towards practical applications, reducing errors remains a crucial frontier for developing near-term devices. Errors in the quantum gates and quantum state readout could result in noisy circuits, which would prevent the acquisition of the exact expectation values of the observables. Although ultimate robustness to errors is known to be achievable by quantum error correction-based fault-tolerant quantum computing, its successful implementation demands large-scale quantum processors with low average error rates that are not yet widely available. In contrast, quantum error mitigation (QEM) offers more immediate and practical techniques, which do not require extensive resources and can be readily applied to existing quantum devices to improve the accuracy of the expectation values. Here, we report the implementation of a zero-noise extrapolation-based error mitigation technique on a silicon spin qubit platform. This technique has recently been successfully demonstrated for other platforms such as superconducting qubits, trapped-ion qubits, and photonic processors. We first explore three methods for amplifying noise on a silicon spin qubit: global folding, local folding, and pulse stretching, using a standard randomized benchmarking protocol. We then apply global folding-based zero-noise extrapolation to the state tomography and achieve a state fidelity of 99.96% (98.52%), compared to the unmitigated fidelity of 75.82% (82.16%) for different preparation states. The results show that the zero-noise extrapolation technique is a versatile approach that is generally adaptable to quantum computing platforms with different noise characteristics through appropriate noise amplification methods.

We describe an inexpensive and accessible instructional setup that explores particle trapping with a planar linear ion trap. The planar trap is constructed using standard printed circuit board manufacturing and is designed to trap macroscopic charged particles in air. Trapping, shuttling, and splitting are demonstrated to students using these particles, which are visible to the naked eye. Students control trap voltages and can compare properties of particle motion with an analytic model of the trap using a computer vision program for particle tracking. Learning outcomes include understanding the design considerations for planar AC traps, mechanisms underpinning particle ejection, the physics of micromotion, and methods of data analysis using standard computer vision libraries.

We explore the feasibility of gate-based hybrid quantum computing using both discrete (qubit) and continuous (qumode) variables on trapped-ion platforms. Trapped-ion systems have demonstrated record one- and two-qubit gate fidelities and long qubit coherence times, while qumodes, which can be represented by the collective vibrational modes of the ion chain, have remained relatively unexplored for their use in computing. Using numerical simulations, we show that high-fidelity hybrid gates and measurement operations can be achieved for existing trapped-ion quantum platforms. As an exemplary application, we consider quantum simulations of the Jaynes-Cummings-Hubbard model, which is given by a one-dimensional chain of interacting spin and boson degrees of freedom. Using classical simulations, we study its real-time evolution and develop a suitable variational quantum algorithm for ground state preparation. Our results motivate further studies of hybrid quantum computing in this context, which may lead to direct applications in condensed matter and fundamental particle and nuclear physics.

Spatial search is the problem of finding a marked vertex in a graph. A continuous-time quantum walk in the single-excitation subspace of an $n$ spin system solves the problem of spatial search by finding the marked vertex in $O(\sqrt{n})$ time. Here, we investigate a natural extension of the spatial search problem, marking multiple vertices of a graph, which are still marked with local fields. We prove that a continuous-time quantum walk in the $k$-excitation subspace of $n$ spins can determine the binary string of $k$ marked vertices with an asymptotic fidelity in time $O(\sqrt{n})$, despite the size of the state space growing as $O(n^k)$. Numerically, we show that this algorithm can be implemented with interactions that decay as $1/r^α$, where $r$ is the distance between spins, and an $α$ that is readily available in current ion trap systems.

As a step towards the ultimate goal of a high-precision mass measurement of doubly-magic $^{100}$Sn, the mass of $^{103}$Sn was measured at the Low Energy Beam and Ion Trap (LEBIT) located at the Facility for Rare Isotope Beams (FRIB). Utilizing the time-of-flight ion cyclotron resonance (ToF-ICR) technique, a mass uncertainty of 3.7~keV was achieved, an improvement by more than an order of magnitude compared to a recent measurement performed in 2023 at the Cooler Storage Ring (CSRe) in Lanzhou. Although the LEBIT and CSRe mass measurements of $^{103}$Sn are in agreement, they diverge from the experimental mass value reported in the 2016 version of the Atomic Mass Evaluation (AME2016), which was derived from the measured $Q_{β^+}$ value and the mass of $^{103}$In. In AME2020, this indirectly measured $^{103}$Sn mass was classified as a `seriously irregular mass' and replaced with an extrapolated value, which aligns with the most recent measured values from CSRe and LEBIT. As such, the smoothness of the mass surface is confidently reestablished for $^{103}$Sn. Furthermore, LEBIT's mass measurement of $^{103}$Sn enabled a significant reduction in the mass uncertainties of five parent isotopes which are now dominated by uncertainties in their respective $Q$-values.

Many-body quantum chaos has immense potential as a tool to accelerate the preparation of entangled states and overcome challenges due to decoherence and technical noise. Here, we study how chaos in the paradigmatic Dicke model, which describes the uniform coupling of an ensemble of qubits to a common bosonic mode, can enable the rapid generation of non-Gaussian entangled spin-boson states without fine tuning of system parameters or initial conditions. However, the complexity of these states means that unlocking their utility for quantum-enhanced sensing with standard protocols would require the measurement of complex or typically inaccessible observables. To address this challenge, we develop a sensing scheme based on interaction-based readout that enable us to implement near-optimal quantum-enhanced metrology of global spin rotations or bosonic dipslacements using only spin measurements. We show that our approach is robust to technical noise and imperfections and thus opens new opportunities to exploit complex entangled states generated by chaotic dynamics in current quantum science platforms such as trapped-ion and cavity-QED experiments.

The effects of an electrostatic logarithmic trap (ELT) on an ionic gas confined in a cylindric chamber are studied in detail, with special reference to the effects of the ion-ion Coulombic interactions and the resulting low-temperature thermodynamics. The collapse of the ions in radially localized states, about the axial cathode, is shown to cause an abrupt (but not critical) transition from non degeneration to strong degeneration, at a special temperature $T_c$. This transition could actually involve both Bosons and Fermions and is not to be confused with a Bose-Einstein condensation (BEC), which is excluded in principle. However, while for Bosons the resulting effects on the pressure are observable in the ultra high vacuum (UHV) regime, the Fermions' density should fall well below UHV, for the pressure change to be observable. This is because the ion-ion \emph{exchange} interactions increase the kinetic energy along the axial cathode, which makes the Fermi level and the non degeneration threshold temperature increase accordingly.

The quantum transverse Ising model and its extensions play a critical role in various fields, such as statistical physics, quantum magnetism, quantum simulations, and mathematical physics. Although it does not suffer from the sign problem in most cases, the corresponding quantum Monte Carlo algorithm performs inefficiently, especially at a large longitudinal field. The main hindrance is the lack of loop update method which can strongly decrease the auto-correlation between Monte Carlo steps. Here, we successfully develop a loop algorithm with a novel merge-unmerge process. It demonstrates a great advantage over the state-of-the-art algorithm when implementing it to simulate the Rydberg atom chain and Kagome qubit ice. This advanced algorithm suits various systems such as Rydberg atom arrays, trapped ions, quantum materials, and quantum annealers.

While commonly used entanglement criteria for continuous variable systems are based on quadrature measurements, here we study entanglement detection from measurements of the Wigner function. These are routinely performed in platforms such as trapped ions and circuit QED, where homodyne measurements are difficult to be implemented. We provide complementary criteria which we show to be tight for a variety of experimentally relevant Gaussian and non-Gaussian states. Our results show novel approaches to detect entanglement in continuous variable systems and shed light on interesting connections between known criteria and the Wigner function.

The mass of the electron-antineutrino can be determined in dedicated measurements of the $β$ spectral shape near the $β$ endpoint of a $β^-$ transition, with a low $Q$ value enhancing the sensitivity of the measurement. One such low-$Q$-value candidate is the transition between the $6^+$ isomer of $^{110}$Ag and the $5^+_2$ state in $^{110}$Cd ($Q^{\ast}_{β,m}=-0.12(131)$ keV). To reduce the uncertainty of the $Q$ value, we have used the phase-imaging ion-cyclotron-resonance technique with the JYFLTRAP double Penning trap and performed a high-precision atomic-mass measurement of $^{109}$Ag with $^{110}$Cd as a reference. Combined with the known spectroscopic data, we obtain a re-evaluated value $Q^{\ast}_{β,m}=405(135)$ eV, for the $^{110}\text{Ag}(6^+_\text{m}) \rightarrow {^{110}\text{Cd}}(5^+_2)$ transition. This represents the lowest $Q_β$ value for any allowed transition observed to date. In order to estimate the partial half-life ($t_{1/2}$) and branching ratio (Br) of the transition, nuclear shell-model calculations were performed using the $jj45pnb$ Hamiltonian in combination with state-of-the-art atomic calculations. The computed values $t_{1/2} = 2.23^{+5.24}_{-1.28} \times 10^7$ years and $\textrm{Br} = 3.07^{+4.16}_{-2.15} \times 10^{-8}$, along with the thermal-neutron capture on stable $^{109}$Ag as a viable production method, make $^{110}\textrm{Ag}^m$ a promising candidate for future antineutrino-mass measurements.

Trapped-ion hardware based on the Magnetic Gradient Induced Coupling (MAGIC) scheme is emerging as a promising platform for quantum computing. Nevertheless, in this -- as in any other -- quantum-computing platform, many technical questions still have to be resolved before large-scale and error-tolerant applications are possible. In this work, we present a thorough discussion of the structure and effects of higher-order terms in the MAGIC setup, which can occur due to anharmonicities in the external potential of the ion crystal (e.g., through Coulomb repulsion) or through curvature of the applied magnetic field. These terms generate systematic shifts in the leading-order interactions and take the form of three-spin couplings, two-spin couplings, local fields, as well as diverse phonon-phonon conversion mechanisms. We find that most of these are negligible in realistic situations, with only two contributions that need careful attention. First, there are undesired longitudinal fields contributing shifts to the resonance frequency, whose strength increases with chain length and phonon occupation numbers; while their mean effect can easily be compensated by additional $Z$ rotations, phonon number fluctuations need to be avoided for precise gate operations. Second, anharmonicities of the Coulomb interaction can lead to well-known two-to-one conversions of phonon excitations. Both of these error terms can be mitigated by sufficiently cooling the phonons to the ground-state. Our detailed analysis constitutes an important contribution on the way of making magnetic-gradient trapped-ion quantum technology fit for large-scale applications, and it may inspire new ways to purposefully design interaction terms.

Science is founded on the benchmarking of theoretical models against experimental measurements, with the challenge that for all but the simplest systems, the calculations required for high precision become extremely challenging. $\mathrm{H}_2^+$ is the simplest stable molecule, and its structure is calculable to high precision. However, studying $\mathrm{H}_2^+$ experimentally presents significant challenges: Standard control methods such as laser cooling are not applicable due to the long lifetimes of its rotational and vibrational states. Here we solve this issue by combining buffer gas cooling to quench the $\mathrm{H}_2^+$ rovibrational excitation with quantum logic operations between $\mathrm{H}_2^+$ and a co-trapped 'helper' ion to control the molecule's hyperfine structure. This enables us to perform pure quantum state preparation, coherent control, and non-destructive readout, which we use to demonstrate high-resolution microwave spectroscopy in the hyperfine structure of $\mathrm{H}_2^+$ with a precision of 2 Hz. Our results pave the way for high precision spectroscopy of $\mathrm{H}_2^+$ in both the microwave and optical domains. Due to the wide applicability of buffer gas cooling, our method provides a general tool for molecular ion species that are hard to control with quantum logic tools alone.

We present a novel protocol for high-fidelity qubit state preparation and measurement (SPAM) that combines standard SPAM methods with a series of in-sequence measurements to detect and remove errors. The protocol can be applied in any quantum system with a long-lived (metastable) level and a means to detect population outside of this level without coupling to it. We demonstrate the use of the protocol for three different qubit encodings in a single trapped $^{137}\mathrm{Ba}^+$ ion. For all three, we achieve the lowest reported SPAM infidelities of $7(4) \times 10^{-6}$ (optical qubit), $5(4) \times 10^{-6}$ (metastable-level qubit), and $8(4) \times 10^{-6}$ (ground-level qubit).

Quantum computing has the potential to reduce the computational cost required for quantum dynamics simulations. However, existing quantum algorithms for coupled electron-nuclear dynamics simulation either require fault-tolerant devices, or involve the Born-Oppenheimer (BO) approximation and pre-calculation of electronic states on classical computers. We present the first quantum simulation approach for molecular vibronic dynamics in a pre-BO framework with an analog mapping of nuclear degrees of freedom, i.e. without the separation of electrons and nuclei, by mapping the molecular Hamiltonian to a device with coupled qubits and bosonic modes. We perform a proof-of-principle emulation of our ansatz using a single-mode model system which represents vibronic dynamics of chemical systems, such as nonadiabatic charge transfer involving polarization of the medium, and propose an implementation of our approach on a trapped-ion device. We show that our approach has exponential savings in resource and computational costs compared to the equivalent classical algorithms. Furthermore, our approach has a much smaller resource and implementation scaling than the existing pre-BO quantum algorithms for chemical dynamics. The low cost of our approach will enable an exact treatment of electron-nuclear dynamics on near-term quantum devices.

Full coherent control and generation of superpositions of the quantum harmonic oscillator are not only of fundamental interest but are crucial for applications in quantum simulations, quantum-enhanced metrology and continuous-variable quantum computation. The extension of such superpositions to nonclassical states increases their power as a resource for such applications. Here, we create arbitrary superpositions of nonclassical and non-Gaussian states of a quantum harmonic oscillator using the motion of a trapped ion coupled to its internal spin states. We interleave spin-dependent nonlinear bosonic interactions and mid-circuit measurements of the spin that preserve the coherence of the oscillator. These techniques enable the creation of superpositions between squeezed, trisqueezed, and quadsqueezed states, which have never been demonstrated before, with independent control over the complex-valued squeezing parameter and the probability amplitude of each constituent, as well as their spatial separation. We directly observe the nonclassical nature of these states in the form of Wigner negativity following a full state reconstruction. Our methods apply to any system where a quantum harmonic oscillator is coupled to a spin.

We develop a hybrid oscillator-qubit processor framework for quantum simulation of strongly correlated fermions and bosons that avoids the boson-to-qubit mapping overhead encountered in qubit hardware. This framework gives exact decompositions of particle interactions such as density-density terms and gauge-invariant hopping, as well as approximate methods based on the Baker-Campbell Hausdorff formulas including the magnetic field term for the $U(1)$ quantum link model in $(2+1)$D. We use this framework to show how to simulate dynamics using Trotterisation, perform ancilla-free partial error detection using Gauss's law, measure non-local observables, estimate ground state energies using a oscillator-qubit variational quantum eigensolver as well as quantum signal processing, and we numerically study the influence of hardware errors in circuit QED experiments. To show the advantages over all-qubit hardware, we perform an end-to-end comparison of the gate complexity for the gauge-invariant hopping term and find an improvement of the asymptotic scaling with the boson number cutoff $S$ from $\mathcal{O}(\log(S)^2)$ to $\mathcal{O}(1)$ in our framework as well as, for bosonic matter, a constant factor improvement of better than $10^4$. We also find an improvement from $\mathcal{O}(\log(S))$ to $\mathcal{O}(1)$ for the $U(1)$ magnetic field term. While our work focusses on an implementation in superconducting hardware, our framework can also be used in trapped ion, and neutral atom hardware. This work establishes digital quantum simulation with hybrid oscillator-qubit hardware as a viable and advantageous method for the study of qubit-boson models in materials science, chemistry, and high-energy physics.

Trapped ions offer long coherence times and high fidelity, programmable quantum operations, making them a promising platform for quantum simulation of condensed matter systems, quantum dynamics, and problems related to high-energy physics. We review selected developments in trapped-ion qubits and architectures and discuss quantum simulation applications that utilize these emerging capabilities. This review emphasizes developments in digital (gate-based) quantum simulations that exploit trapped-ion hardware capabilities, such as flexible qubit connectivity, selective mid-circuit measurement, and classical feedback, to simulate models with long-range interactions, explore non-unitary dynamics, compress simulations of states with limited entanglement, and reduce the circuit depths required to prepare or simulate long-range entangled states.

The masses of the ground and isomeric states in $^{124,125}$Ag have been measured using the phase-imaging ion-cyclotron-resonance technique at the JYFLTRAP double Penning trap mass spectrometer. The ground states of $^{124}$Ag and $^{125}$Ag were found to be 30(250) keV and 250(430) keV less bound but 36 and 110 times more precise than in the Atomic Mass Evaluation 2020, respectively. The excitation energy of $^{124}$Ag$^{m}$, ${E_x = 188.2(25)}$ keV, was determined for the first time. The new precise mass values have been utilised to study the evolution of nuclear structure via two-neutron separation energies. The impact on the astrophysical rapid neutron capture process has been investigated via neutron-capture reaction rate calculations. The precision measurements indicate a more linear trend in two-neutron separation energies and reduce the mass-related uncertainties for the neutron-capture rate of $^{124}$Ag$(n,γ)^{125}$Ag by a factor of around 100. The new mass values also improve the mass of $^{123}$Pd, previously measured using $^{124}$Ag as a reference.

Cooling of atomic motion is a crucial tool for many branches of atomic physics, ranging from fundamental physics explorations to quantum information and sensing. For trapped ions, electromagnetically-induced-transparency (EIT) cooling has received attention for the relative speed, low laser power requirements, and broad cooling bandwidth of the technique. However, in applications where the ion used for cooling has hyperfine structure to enable long coherence times, it is difficult to find a closed three-level system in which to perform standard EIT cooling. Here, we demonstrate successful EIT cooling on 25Mg+ by the addition of an extra laser frequency; this method can be applied to any ion with non-zero nuclear spin. Furthermore, we demonstrate simultaneous EIT cooling of all axial modes in mixed-species crystals 9Be+ - 25Mg+ and 9Be+ - 25Mg+ - 9Be+ through the 25Mg+ ion.

As superconducting quantum computing continues to advance at an unprecedented pace, there is a compelling demand for the innovation of specialized electronic instruments that act as crucial conduits between quantum processors and host computers. Here, we introduce a Microwave Measurement and Control System (M2CS) dedicated for large-scale superconducting quantum processors. M2CS features a compact modular design that balances overall performance, scalability, and flexibility. Electronic tests of M2CS show key metrics comparable to commercial instruments. Benchmark tests on transmon superconducting qubits further show qubit coherence and gate fidelities comparable to state-of-the-art results, confirming M2CS's capability to meet the stringent requirements of quantum experiments run on intermediate-scale quantum processors. The system's compact and scalable design offers significant room for further enhancements that could accommodate the measurement and control requirements of over 1000 qubits, and can also be adopted to other quantum computing platforms such as trapped ions and silicon quantum dots. The M2CS architecture may also be applied to wider range of scenarios, such as microwave kinetic inductance detectors, as well as phased array radar systems.

Quantum chemical calculations are among the most promising applications for quantum computing. Implementations of dedicated quantum algorithms on available quantum hardware were so far, however, mostly limited to comparatively simple systems without strong correlations. As such, they can also be addressed by classically efficient single-reference methods. In this work, we calculate the lowest energy eigenvalue of active space Hamiltonians of industrially relevant and strongly correlated metal chelates on trapped ion quantum hardware, and integrate the results into a typical industrial quantum chemical workflow to arrive at chemically meaningful properties. We are able to achieve chemical accuracy by training a variational quantum algorithm on quantum hardware, followed by a classical diagonalization in the subspace of states measured as outputs of the quantum circuit. This approach is particularly measurement-efficient, requiring 600 single-shot measurements per cost function evaluation on a ten qubit system, and allows for efficient post-processing to handle erroneous runs.

To enhance the variational quantum eigensolver (VQE), the CAFQA method can utilize classical computational capabilities to identify a better initial state than the Hartree-Fock method. Previous research has demonstrated that the initial state provided by CAFQA recovers more correlation energy than that of the Hartree-Fock method and results in faster convergence. In the present study, we advance the investigation of CAFQA by demonstrating its advantages on a high-fidelity trapped-ion quantum computer located at the Duke Quantum Center -- this is the first experimental demonstration of CAFQA-bootstrapped VQE on a TI device and on any academic quantum device. In our VQE experiment, we use LiH and BeH$_2$ as test cases to show that CAFQA achieves faster convergence and obtains lower energy values within the specified computational budget limits. To ensure the seamless execution of VQE on this academic device, we develop a novel hardware-software interface framework that supports independent software environments for both the circuit and hardware end. This mechanism facilitates the automation of VQE-type job executions as well as mitigates the impact of random hardware interruptions. This framework is versatile and can be applied to a variety of academic quantum devices beyond the trapped-ion quantum computer platform, with support for integration with customized packages.

We report on high-precision atomic mass measurements of $^{148\text{-}153}$La and $^{151}$Ce performed with the JYFLTRAP double Penning trap using the Phase-Imaging Ion-Cyclotron-Resonance technique. The masses of $^{152,153}$La were experimentally determined for the first time. We confirm the sharp kink in the two-neutron separation energies at the neutron number ${N=93}$ in the cerium (${Z=58}$) isotopic chain. Our precision mass measurements of the most exotic neutron-rich lanthanum (${Z=57}$) isotopes reveal a sudden increase in two-neutron separation energies from ${N=92}$ to ${N=93}$. Unlike in the cerium isotopic chain, the kink is not sharp but extends to ${N=94}$ forming a prominent bump. The gain in energy is about 0.4 MeV, making it one of the strongest changes in two-neutron separation energies over the whole chart of nuclides, away from nuclear shell closures. The results call for further studies to elucidate the structure of neutron-rich lanthanum isotopes.

Any quantum computation consists of a sequence of unitary evolutions described by a finite set of Hamiltonians. When this set is taken to consist of only products of Pauli operators, we show that the minimal such set generating $\mathfrak{su}(2^{N})$ contains $2N+1$ elements. We provide a number of examples of such generating sets and furthermore provide an algorithm for producing a sequence of rotations corresponding to any given Pauli rotation, which is shown to have optimal complexity. We also observe that certain sets generate $\mathfrak{su}(2^{N})$ at a faster rate than others, and we show how this rate can be optimized by tuning the fraction of anticommuting pairs of generators. Finally, we briefly comment on implications for measurement-based and trapped ion quantum computation as well as the construction of fault-tolerant gate sets.

Simulating non-equilibrium phenomena in strongly-interacting quantum many-body systems, including thermalization, is a promising application of near-term and future quantum computation. By performing experiments on a digital quantum computer consisting of fully-connected optically-controlled trapped ions, we study the role of entanglement in the thermalization dynamics of a $Z_2$ lattice gauge theory in 2+1 spacetime dimensions. Using randomized-measurement protocols, we efficiently learn a classical approximation of non-equilibrium states that yields the gap-ratio distribution and the spectral form factor of the entanglement Hamiltonian. These observables exhibit universal early-time signals for quantum chaos, a prerequisite for thermalization. Our work, therefore, establishes quantum computers as robust tools for studying universal features of thermalization in complex many-body systems, including in gauge theories.

We measure the energy-differential cross sections for collisional excitation of the soft X-ray electric-dipole K$α$ ($x+y+w$) emission from He-like oxygen (O VII), using an electron beam ion trap. Values near their excitation thresholds were extracted from the observed emissivity by rapidly cycling the energy of the exciting electron beam. This allows us to subtract time-dependent contributions of the forbidden $z$-line emission to the multiplet. We develop a time-dependent collisional-radiative model to further demonstrate the method and predict all spectral features. We then compare the extracted $x+y+w$ cross-sections with calculations based on distorted-wave and R-matrix methods from the literature and our own predictions using the Flexible Atomic Code (FAC). All R-matrix results are validated by our measurements of direct and resonant excitation, supporting the use of such state-of-the-art codes for astrophysical and plasma physics diagnostics.

Quantum spin models with a large number of interaction partners per spin are frequently used to describe modern many-body quantum optical systems like arrays of Rydberg atoms, atom-cavity systems or trapped ion crystals. For theoretical analysis the mean-field (MF) ansatz is routinely applied. However, besides special cases of all-to-all or strong long range interactions, the MF ansatz provides only approximate results. Here we present a systematic correction to MF theory based on diagrammatic perturbation theory for quantum spin correlators in thermal equilibrium. Our analytic results are universally applicable for any lattice geometry and spin-length S. We provide pre-computed and easy-to-use building blocks for Ising, Heisenberg and transverse field Ising models in the symmetry-unbroken regime. We showcase the quality and simplicity of the method by computing magnetic phase boundaries and excitations gaps. We also treat the Dicke-Ising model of ground-state superradiance where we show that corrections to the MF phase boundary vanish.

Accurate thermometry of laser-cooled ions is crucial for the performance of the trapped-ions quantum computing platform. However, most existing methods face a computational exponential bottleneck. Recently, a thermometry method based on bichromatic driving was theoretically proposed by Ivan Vybornyi et al. to overcome this obstacle, which allows the computational complexity to remain constant with the increase of ion numbers. In this paper, we provide a detailed statistical analysis of this method and prove its robustness to several imperfect experimental conditions using Floquet theory. We then experimentally verify its good performance on a linear segmented surface-electrode ion trap platform for the first time. This method is proven to be effective from near the motional ground state to a few mean phonon numbers. Our theoretical analysis and experimental verification demonstrate that the scheme can accurately and efficiently measure the temperature in ion crystals.

Radium-225 (nuclear spin $I=1/2$) ions possess electronic hyperfine transitions that are first-order insensitive to magnetic field noise, which is advantageous for optical clocks and quantum information science. We report on laser cooling and trapping of radium-225 ions and hyperfine splitting measurements of the ion's $7s$ $^2S_{1/2}$, $7p$ $^2P_{1/2}$, and $6d$ $^2D_{3/2}$ states. We measured the ground state hyperfine constant, $A(^2S_{1/2}) = -27.684511056(9)\ \mathrm{GHz}$, and the quadratic Zeeman coefficient, $C_2 = 142.3(10)\ \mathrm{Hz\ G}^{-2}$, of the $^2S_{1/2} (F=0, m_F = 0) \leftrightarrow~^2S_{1/2} (F=1, m_{F} = 0)$ transition. We also measured the hyperfine constants of the $^2P_{1/2}$ state, $A(^2P_{1/2}) = -5.447(4)\ \mathrm{GHz}$, and the $^2D_{3/2}$ state, $A(^2D_{3/2}) = -619.7(11)\ \mathrm{MHz}$.

As an homage to Quantum Energy Teleportation, we generalize the idea to arbitrary physical observables, not limited to energy, and prove a rigorous upper bound on the activated ("teleported") quantity. The essence of this protocol is a quantum feedback control with respect to the entangled ground state of a quantum many-body system. To demonstrate the concept, we explore a (1+1)-dimensional chiral Dirac system and execute the protocol for the electric current and charge. One of the most significant results is the creation of long-range correlations across the system after applying control operations only to one local site. Consequently but surprisingly, the induced charge susceptibility fully reconstructs the phase diagram, despite the model initially having no charge. Moreover, we find an activation of novel chiral dynamics induced by feedback control operations, which can be experimentally confirmed using trapped ions and neutral atoms.

Levitated optomechanics, a rapidly expanding field that employs light to monitor and manipulate the mechanical motion of levitated objects, is increasingly relevant across physics, engineering, and other fields. This technique, which involves levitating micro- and nano-scale objects in a vacuum where they exhibit high-quality motion, provides an essential platform for precision measurements. Noted for their ultra-high sensitivity, levitated particles hold potential for a wide range of real-world applications. This perspective article briefly introduces the principle of optical levitation and the dynamics of levitated particles. It then reviews the emerging applications of levitated particles in ultrasensitive force and torque measurements, acceleration and rotation sensing, electric and magnetic field detection, scanning probe microscopy, localized vacuum pressure gauging, acoustic transduction, and chemical and biological sensing. Moreover, we discuss the present challenges and explore opportunities to minimize and integrate levitation systems for broader applications. We also briefly review optomechanics with ion traps and magnetic traps which can levitate particles in high vacuum without laser heating.

In this study, we employed a quantum computer to solve a low-energy effective Hamiltonian for spin defects in diamond (so-called NV centre) and wurtzite-type aluminium nitride, which are anticipated to be qubits. The probabilistic imaginary-time evolution (PITE) method, designed for use in a fault-tolerant quantum computer (FTQC) era, was employed to calculate the ground and excited states of the spin singlet state, as represented by the effective Hamiltonian. It is difficult to compute the spin singlet state correctly using density functional theory (DFT), which should be described by multiple Slater determinants. To mitigate the effects of quantum errors inherent in current quantum computers, we implemented a $[[ n+2,n,2 ]]$ quantum error detection (QED) code called the Iceberg code. Despite the inevitable destruction of the encoded state resulting from the measurement of the ancilla qubit at each PITE step, we were able to successfully re-encode and recover the logical success state. In the implementation of the PITE, it was observed that the effective Hamiltonian comprises large components of the diagonal part and a relatively small non-diagonal part, which is frequently the case with quantum chemistry calculations. An efficient implementation of Hamiltonian simulations, in which the diagonal components dominate, was developed on a quantum computer based on the second-order Trotter-Suzuki decomposition. This is the first instance of an encoded PITE circuit being executed on a trapped-ion quantum computer. Our results demonstrate that QED effectively reduces quantum errors and that we successfully obtained both the ground and excited states of the spin singlet state. Our demonstration clearly manifests that Zr$_{\rm Al}$V$_{\rm N}$, Ti$_{\rm Al}$V$_{\rm N}$, and Hf$_{\rm Al}$V$_{\rm N}$ defects have a high potential as spin qubits for quantum sensors.

Quantum computing with discrete variable (DV, qubit) hardware is approaching the large scales necessary for computations beyond the reach of classical computers. However, important use cases such as quantum simulations of physical models containing bosonic modes, and quantum error correction are challenging for DV-only systems. Separately, hardware containing native continuous-variable (CV, oscillator) systems has received attention as an alternative approach, yet the universal control of such systems is non-trivial. In this work, we show that hybrid CV-DV hardware offers a great advantage in meeting these challenges, offering a powerful computational paradigm that inherits the strengths of both DV and CV processors. We provide a pedagogical introduction to CV-DV systems and the multiple abstraction layers needed to produce a full software stack connecting applications to hardware. We present a variety of new hybrid CV-DV compilation techniques, algorithms, and applications, including the extension of quantum signal processing concepts to CV-DV systems and strategies to simulate systems of interacting spins, fermions, and bosons. To facilitate the development of hybrid CV-DV processor systems, we introduce formal Abstract Machine Models and Instruction Set Architectures -- essential abstractions that enable developers to formulate applications, compile algorithms, and explore the potential of current and future hardware for realizing fault-tolerant circuits, modules, and processors. Hybrid CV-DV quantum computations are beginning to be performed in superconducting, trapped ion, and neutral atom platforms, and large-scale experiments are set to be demonstrated in the near future. We present a timely and comprehensive guide to this relatively unexplored yet promising approach to quantum computation and providing an architectural backbone to guide future development.

The central challenge of quantum computing is implementing high-fidelity quantum gates at scale. However, many existing approaches to qubit control suffer from a scale-performance trade-off, impeding progress towards the creation of useful devices. Here, we present a vision for an electronically controlled trapped-ion quantum computer that alleviates this bottleneck. Our architecture utilizes shared current-carrying traces and local tuning electrodes in a microfabricated chip to perform quantum gates with low noise and crosstalk regardless of device size. To verify our approach, we experimentally demonstrate low-noise site-selective single- and two-qubit gates in a seven-zone ion trap that can control up to 10 qubits. We implement electronic single-qubit gates with 99.99916(7)% fidelity, and demonstrate consistent performance with low crosstalk across the device. We also electronically generate two-qubit maximally entangled states with 99.97(1)% fidelity and long-term stable performance over continuous system operation. These state-of-the-art results validate the path to directly scaling these techniques to large-scale quantum computers based on electronically controlled trapped-ion qubits.

Tunable scattering resonances are crucial for controlling atomic and molecular systems. However, their use has so far been limited to ultracold temperatures. These conditions remain hard to achieve for most hybrid trapped ion-atom systems -- a prospective platform for quantum technologies and fundamental research. Here we measure inelastic collision probabilities for ${\text{Sr}^++\text{Rb}}$ and use them to calibrate a comprehensive theoretical model of ion-atom collisions. Our theoretical results, compared with experimental observations, confirm that quantum interference effects persist to the multiple-partial-wave regime, leading to the pronounced state and mass dependence of the collision rates. Using our model, we go beyond interference and identify a rich spectrum of Feshbach resonances at moderate magnetic fields with the Rb atom in its lower ($f=1$) hyperfine state, which persist at temperatures as high as 1 mK. Future observation of these predicted resonances should allow precise control of the short-range dynamics in ${\text{Sr}^+}+{\text{Rb}}$ collisions under unprecedentedly warm conditions.

We propose encoding multiple qubits inside ions in existing trapped-ion quantum computers to access more qubits and to simplify circuits implementing standard algorithms. By using such `virtual' qubits, some inter-ion gates can be replaced by intra-ion gates, reducing the use of vibrational modes of the ion chain, leading to less noise. We discuss specific examples such as the Bernstein-Vazirani algorithm and random circuit sampling, using a small number of virtual qubits. Additionally, virtual qubits enable using larger number of data qubits for an error correcting code, and we consider the repetition code as an example. We also lay out practical considerations to be made when choosing states to encode virtual qubits in $^{137}\mathrm{Ba}^+$ ions, and for preparing states and performing measurements.

Quantum computers have long been anticipated to excel in simulating quantum many-body physics. While most previous work has focused on Hermitian physics, we demonstrate the power of variational quantum circuits for resource-efficient simulations of dynamical and equilibrium physics in non-Hermitian systems, revealing new phenomena beyond standard Hermitian quantum machines. Using a variational quantum compilation scheme for fermionic systems, we reduce gate count, save qubits, and eliminate the need for postselection, a major challenge in simulating non-Hermitian dynamics via standard Trotterization. Experimentally, we observed a supersonic mode in the connected density-density correlation function on an $ n = 18 $ fermionic chain after a non-Hermitian, locally interacting quench, which would otherwise be forbidden by the Lieb-Robinson bound in a Hermitian system. Additionally, we investigate sequential quantum circuits generated by tensor networks for ground state preparation, here defined as the eigenstate with the lowest real part eigenvalue, using a variance minimization scheme. Through a trapped-ion implementation on the Quantinuum H1 quantum processor, we accurately capture correlation functions and energies across an exceptional point on a dissipative spin chain up to length $ n = 20 $ using only 3 qubits. Motivated by these advancements, we provide an analytical example demonstrating that simulating single-qubit non-Hermitian dynamics for $Θ(\log(n))$ time from certain initial states is exponentially hard on a quantum computer, offering insights into the opportunities and limitations of using quantum computation for simulating non-Hermitian physics.

Quantum state preparation for trapped-ion qubits often relies on high-quality circularly-polarised light, which may be difficult to achieve with chip-based integrated optics technology. We propose and implement a hybrid optical/microwave scheme for intermediate-field hyperfine qubits which instead relies on frequency selectivity. Experimentally, we achieve $99.94\%$ fidelity for linearly-polarised ($σ^+$/$σ^-$) light, using $^{43}$Ca$^+$ at 28.8 mT. We find that the fidelity remains above $99.8\%$ for a mixture of all polarisations ($σ^+$/$σ^-$/$π$). We calculate that the method is capable of $99.99\%$ fidelity in $^{43}$Ca$^+$, and even higher fidelities in heavier ions such as $^\text{137}$Ba$^\text{+}$.

While limitations on quantum computation by Markovian environmental noise are well-understood in generality, their behavior for different quantum circuits and noise realizations can be less universal. Here we consider a canonical quantum algorithm - Grover's algorithm for unordered search on $L$ qubits - in the presence of systematic noise. This allows us to write the behavior as a random Floquet unitary, which we show is well-characterized by random matrix theory (RMT). The RMT analysis enables analytical predictions for phases and phase transitions of the many-body dynamics. We find two separate transitions. At moderate disorder $δ_{c,\mathrm{gap}}\sim L^{-1}$, there is a ergodicity breaking transition such that a finite-dimensional manifold remains non-ergodic for $δ< δ_{c,\mathrm{gap}}$. Computational power is lost at a much smaller disorder, $δ_{c,\mathrm{comp}} \sim L^{-1/2}2^{-L/2}$. We comment on relevance to non-systematic noise in realistic quantum computers, including cold atom, trapped ion, and superconducting platforms.

Hyperfine energy levels in trapped ions offer long-lived spin states. In addition, the motion of these charged particles couples strongly to external electric field perturbations. These characteristics make trapped ions attractive platforms for the quantum sensing of electric fields. However, the spin states do not exhibit a strong intrinsic coupling to electric fields. This limits the achievable sensitivities. Here, we amplify the coupling between electric field perturbations and the spin states by using a static magnetic field gradient. Displacements of the trapped ion resulting from the forces experienced by an applied external electric field perturbation are thereby mapped to an instantaneous change in the energy level splitting of the internal spin states. This gradient mediated coupling of the electric field to the spin enables the use of a range of well-established magnetometry protocols for electrometry. Using our quantum sensor, we demonstrate AC sensitivities of $\mathrm{S^{AC}_{min}=960(10)\times 10^{-6}~V m^{-1}Hz^{-\frac{1}{2}}}$ at a signal frequency of $ω_ε/2π=5.82~\mathrm{Hz}$, and DC sensitivities of $\mathrm{S^{DC}_{min}=1.97(3)\times 10^{-3} ~V m^{-1}Hz^{-\frac{1}{2}}}$ with a Hahn-echo type sensing sequence. We also employ a rotating frame relaxometry technique, with which our quantum sensor can be utilised as an electric field noise spectrum analyser. We measure electric field signals down to a noise floor of $\mathrm{S_{E}(ω)=6.2(5)\times 10^{-12}~V^2 m^{-2}Hz^{-1}}$ at a frequency of $\mathrm{30.0(3)~kHz}$. We therefore demonstrate unprecedented electric field sensitivities for the measurement of both DC signals and AC signals across a frequency range of sub-Hz to $\sim\mathrm{500~kHz}$. Finally, we describe a set of hardware modifications that are capable of achieving a further improvement in sensitivity by up to six orders of magnitude.

Quantum nuclear dynamics with wavepacket time-evolution is classically intractable and viewed as a promising avenue for quantum information processing. Here, we use an IonQ 11-qubit trapped-ion quantum computer, Harmony, to study the quantum wavepacket dynamics of a shared-proton within a short-strong hydrogen-bonded system. We also provide the first application of distributed quantum computing for chemical dynamics problems, where the distributed set of quantum processes is constructed using a tensor network formalism. For a range of initial states, we experimentally drive the ion-trap system to emulate the quantum nuclear wavepacket as it evolves along the potential surface generated from electronic structure. Following the experimental creation of the nuclear wavepacket, we extract measurement observables such as its time-dependent spatial projection and its characteristic vibrational frequencies to good agreement with classical results. Vibrational eigenenergies obtained from quantum computational are in agreement with those obtained from classical simulations to within a fraction of a kcal/mol, thus suggesting chemical accuracy. Our approach opens a new paradigm for studying the quantum chemical dynamics and vibrational spectra of molecules and also provides the first demonstration for parallel quantum computation on a distributed set of ion-trap quantum computers.

The quantum-classical hybrid variational quantum eigensolver (VQE) algorithm is among the most actively studied topics in atomic and molecular calculations on quantum computers, yet few studies address properties other than energies or account for relativistic effects. This work presents high-precision 18-qubit relativistic VQE simulations for calculating the permanent electric dipole moments (PDMs) of BeH to RaH molecules on traditional computers, and 6- and 12-qubit PDM computations for SrH on IonQ quantum devices. To achieve high precision on current noisy intermediate scale era quantum hardware, we apply various resource reduction methods, including Reinforcement Learning and causal flow preserving ZX-Calculus routines, along with error mitigation and post-selection techniques. Our approach reduces the two-qubit gate count in our 12-qubit circuit by 99.71%, with only a 2.35% trade-off in precision for PDM when evaluated classically within a suitably chosen active space. On the current generation IonQ Forte-I hardware, the error in PDM is -1.17% relative to classical calculations and only 1.21% compared to the unoptimized circuit.

Quantum error correction protects logical quantum information against environmental decoherence by encoding logical qubits into entangled states of physical qubits. One of the most important near-term challenges in building a scalable quantum computer is to reach the break-even point, where logical quantum circuits on error-corrected qubits achieve higher fidelity than equivalent circuits on uncorrected physical qubits. Using Quantinuum's H2 trapped-ion quantum processor, we encode the GHZ state in four logical qubits with fidelity $ 99.5 \pm 0.15 \% \le F \le 99.7 \pm 0.1\% $ (after postselecting on over 98% of outcomes). Using the same quantum processor, we can prepare an uncorrected GHZ state on four physical qubits with fidelity $97.8 \pm 0.2 \% \le F\le 98.7\pm 0.2\%$. The logical qubits are encoded in a $[\![ 25,4,3 ]\!]$ Tanner-transformed long-range-enhanced surface code. Logical entangling gates are implemented using simple swap operations. Our results are a first step towards realizing fault-tolerant quantum computation with logical qubits encoded in geometrically nonlocal quantum low-density parity check codes.

We study the non-equilibrium dynamics of a one-dimensional Bose gas with long-range interactions that decay as $(\frac{1}{r^α})$ $(0.5 < α<4.0$). We investigate exotic dynamics when the interactions are suddenly switched from strongly repulsive to strongly attractive, a procedure known to generate super-Tonks-Girardeau gases in systems with contact interactions. We find that relaxation is achieved through a complex intermediate dynamics demonstrated by violent fragmentation and chaotic delocalization. We establish that the relaxed state exhibits classical gaseous characteristics and an asymptotic state associated with unbounded entropy production. The phase diagram shows an exponential boundary between the coherent (quantum) gas and the chaotic (classical) gas. We show the universality of the dynamics by also presenting analogous results for spinless fermions. Weaker quench protocols give a certain degree of control over the relaxation process and induce a slower initial entropy growth. Our study showcases the complex relaxation behavior of tunable long-range interacting systems that could be engineered in state-of-the-art experiments, e.g. in trapped ions or Rydberg atoms.

We introduce a method for solving combinatorial optimization problems on digital quantum computers, where we incorporate auxiliary counterdiabatic (CD) terms into the adiabatic Hamiltonian, while integrating bias terms derived from an iterative digitized counterdiabatic quantum algorithm. We call this protocol bias-field digitized counterdiabatic quantum optimization (BF-DCQO). Designed to effectively tackle large-scale combinatorial optimization problems, BF-DCQO demonstrates resilience against the limitations posed by the restricted coherence times of current quantum processors and shows clear enhancement even in the presence of noise. Additionally, our purely quantum approach eliminates the dependency on classical optimization required in hybrid classical-quantum schemes, thereby circumventing the trainability issues often associated with variational quantum algorithms. Through the analysis of an all-to-all connected general Ising spin-glass problem, we exhibit a polynomial scaling enhancement in ground state success probability compared to traditional DCQO and finite-time adiabatic quantum optimization methods. Furthermore, it achieves scaling improvements in ground state success probabilities, increasing by up to two orders of magnitude, and offers an average 1.3x better approximation ratio than the quantum approximate optimization algorithm for the problem sizes studied. We validate these findings through experimental implementations on both trapped-ion quantum computers and superconducting processors, tackling a maximum weighted independent set problem with 36 qubits and a spin-glass on a heavy-hex lattice with 100 qubits, respectively. These results mark a significant advancement in gate-based quantum computing, employing a fully quantum algorithmic approach.

We simulate the dynamics, including laser cooling, of 3D ion crystals confined in a Penning trap using a newly developed molecular dynamics-like code. The numerical integration of the ions' equations of motion is accelerated using the fast multipole method to calculate the Coulomb interaction between ions, which allows us to efficiently study large ion crystals with thousands of ions. In particular, we show that the simulation time scales linearly with ion number, rather than with the square of the ion number. By treating the ions' absorption of photons as a Poisson process, we simulate individual photon scattering events to study laser cooling of 3D ellipsoidal ion crystals. Initial simulations suggest that these crystals can be efficiently cooled to ultracold temperatures, aided by the mixing of the easily cooled axial motional modes with the low frequency planar modes. In our simulations of a spherical crystal of 1,000 ions, the planar kinetic energy is cooled to several millikelvin in a few milliseconds while the axial kinetic energy and total potential energy are cooled even further. This suggests that 3D ion crystals could be well-suited as platforms for future quantum science experiments.

Quantum many-body scarring (QMBS) is an intriguing mechanism of weak ergodicity breaking that has recently spurred significant attention. Particularly prominent in Abelian lattice gauge theories (LGTs), an open question is whether QMBS nontrivially arises in non-Abelian LGTs. Here, we present evidence of robust QMBS in a non-Abelian SU(2) LGT with dynamical matter. Starting in product states that require little experimental overhead, we show that prominent QMBS arises for certain quenches, facilitated through meson and baryon-antibaryon excitations, highlighting its non-Abelian nature. The uncovered scarred dynamics manifests as long-lived coherent oscillations in experimentally accessible local observables as well as prominent revivals in the state fidelity. Our findings bring QMBS to the realm of non-Abelian LGTs, highlighting the intimate connection between scarring and gauge symmetry, and are amenable for observation in a recently proposed trapped-ion qudit quantum computer.

High-rate remote entanglement between photon and matter-based qubits is essential for distributed quantum information processing. A key technique to increase the modest entangling rates of existing long-distance quantum networking approaches is multiplexing. Here, we demonstrate a temporally multiplexed ion-photon interface via rapid transport of a chain of nine calcium ions across 74 $\mathrm{μm}$ within 86 $\mathrm{μs}$. The non-classical nature of the multiplexed photons is verified by measuring the second-order correlation function with an average value of $g^{(2)}(0)$ = 0.060(13), indicating negligible crosstalk between the multiplexed modes. In addition, we characterize the motional degree-of-freedom of the ion crystal after transport and find that it is coherently excited to as much as $\bar{n}_α\approx 110$ for the center-of-mass mode. Our proof-of-principle implementation paves the way for large-scale quantum networking with trapped ions, but highlights some challenges that must be overcome.

Electron transfer is at the heart of many fundamental physical, chemical, and biochemical processes essential for life. The exact simulation of these reactions is often hindered by the large number of degrees of freedom and by the essential role of quantum effects. Here, we experimentally simulate a paradigmatic model of molecular electron transfer using a multispecies trapped-ion crystal, where the donor-acceptor gap, the electronic and vibronic couplings, and the bath relaxation dynamics can all be controlled independently. By manipulating both the ground-state and optical qubits, we observe the real-time dynamics of the spin excitation, measuring the transfer rate in several regimes of adiabaticity and relaxation dynamics. Our results provide a testing ground for increasingly rich models of molecular excitation transfer processes that are relevant for molecular electronics and light-harvesting systems.

We have performed high-precision mass measurements of neutron-rich rare-earth Tb, Dy and Ho isotopes using the Phase-Imaging Ion-Cyclotron-Resonance technique at the JYFLTRAP double Penning trap. We report on the first experimentally determined mass values for $^{169}$Tb, $^{170}$Dy and $^{171}$Dy, as well as the first high-precision mass measurements of $^{169}$Dy and $^{169\text{-}171}$Ho. For $^{170}$Ho, the two long-lived ground and isomeric states were resolved and their mass measured, yielding an isomer excitation energy of $E_\text{exc}=150.8(54)$~keV. In addition, we have performed independent crosschecks of previous Penning-trap values obtained for $^{167\text{,} 168}$Tb and $^{167\text{,} 168}$Dy. We have extended the systematics of two-neutron separation energies to the neutron midshell at $N=104$ in all of the studied isotopic chains. Our updated and new mass measurements provide better mass-related constraints for the neutron-capture reaction rates relevant to the astrophysical rapid neutron capture (r) process. The r-process abundances calculated with the new mass values seem to produce a steeper minimum at A=170 and differ by around 15-30\% from the abundances computed with the Atomic Mass Evaluation 2020 values.

Photo stimulated luminescent materials are one of the most attractive alternatives for next generation optical information storage technologies. However, there are still some challenges in regulating appropriate energy levels in luminescent materials for optical information storage. Herein, a green emission nanophosphor Zn2SiO4: Cr3+, Mn2+ with the trap depth of 1.05 eV, fulfilling the requirements for optical information storage, was fabricated for the first time through the solution combustion method and subsequent heat treatment at 1000 degree centigrade for 2h. The crystal structure, micromorphology, photoluminescence (PL), photoluminescence excitation (PLE), and afterglow properties of Zn2SiO4: xCr3+, yMn2+ were studied systematically. By applying the strategy of trap depth engineering, high trap density with proper trap depth was observed when Cr3+ ions were introduced into Zn2SiO4: Mn2+. Thermoluminescence (TL) glow curve analysis through the initial rise (IR) method was conducted to gain some insight into the information of traps. As proof of application, information storage was experimentally achieved by choosing 275 nm illumination for information writing and 980 nm NIR excitation for information reading. The results indicate that Zn2SiO4: Cr3+, Mn2+ phosphor holds promise for potential applications in the field of optical information storage.

We introduce a hardware-specific, problem-dependent digital-analog quantum algorithm of a counterdiabatic quantum dynamics tailored for optimization problems. Specifically, we focus on trapped-ion architectures, taking advantage from global Mølmer-Sørensen gates as the analog interactions complemented by digital gates, both of which are available in the state-of-the-art technologies. We show an optimal configuration of analog blocks and digital steps leading to a substantial reduction in circuit depth compared to the purely digital approach. This implies that, using the proposed encoding, we can address larger optimization problem instances, requiring more qubits, while preserving the coherence time of current devices. Furthermore, we study the minimum gate fidelity required by the analog blocks to outperform the purely digital simulation, finding that it is below the best fidelity reported in the literature. To validate the performance of the digital-analog encoding, we tackle the maximum independent set problem, showing that it requires fewer resources compared to the digital case. This hybrid co-design approach paves the way towards quantum advantage for efficient solutions of quantum optimization problems.

Gauge-field configurations with nontrivial topology have profound consequences for the physics of Abelian and non-Abelian gauge theories. Over time, arguments have been gathering for the existence of gauge-field configurations with fractional topological charge, called fractons. Ground-state properties of gauge theories can drastically change in presence of fractons in the path integral. However, understanding the origin of such fractons is usually restricted to semiclassical argumentation. Here, we show that fractons persist in strongly correlated many-body systems, using the multiflavor Schwinger model of quantum electrodynamics as a paradigm example. Through detailed numerical tensor-network analysis, we find strong fracton signatures even in highly discretized lattice models, at sizes that are implementable on already existing quantum-simulation devices. Our work sheds light on how the nontrivial topology of gauge theories persists in challenging nonperturbative regimes, and it shows a path forward to probing it in tabletop experiments.

The approach of shortcuts to adiabaticity enables the effective execution of adiabatic dynamics in quantum information processing with enhanced speed. Owing to the inherent trade-off between dynamical speed and the cost associated with the transitionless driving field, executing arbitrarily fast operations becomes impractical. To understand the accurate interplay between speed and energetic cost in this process, we propose theoretically and verify experimentally a new trade-off, which is characterized by a tightly optimized bound within $s$-parameterized phase spaces. Our experiment is carried out in a single ultracold $^{40}$Ca$^{+}$ ion trapped in a harmonic potential. By exactly operating the quantum states of the ion, we execute the Landau-Zener model as an example, where the quantum speed limit as well as the cost are governed by the spectral gap. We witness that our proposed trade-off is indeed tight in scenarios involving both initially eigenstates and initially thermal equilibrium states. Our work helps understanding the fundamental constraints in shortcuts to adiabaticity and illuminates the potential of under-utilized phase spaces that have been traditionally overlooked.

Quantum friction, a quantum analog of classical friction, reduces the performance of quantum machines, such as heat engines, and makes them less energy efficient. We here report the experimental realization of an energy efficient quantum engine coupled to a quantum battery that stores the produced work, using a single ion in a linear Paul trap. We first establish the quantum nature of the device by observing nonclassical work oscillations with the number of cycles as verified by energy measurements of the battery. We moreover successfully apply shortcut-to-adiabaticity techniques to suppress quantum friction and improve work production. While the average energy cost of the shortcut protocol is only about $3\%$, the work output is enhanced by up to approximately 33$\%$, making the machine significantly more energy efficient. In addition, we show that the quantum engine consistently outperforms its classical counterpart in this regime. Our results pave the way for energy efficient machines with quantum-enhanced performance.

We experimentally study the heating of trapped atomic ions during measurement of their internal qubit states. During measurement, ions are projected into one of two basis states and discriminated by their state-dependent fluorescence. We observe that ions in the fluorescing state rapidly scatter photons and heat at a rate of \mbox{$\dot{\bar{n}}\gtrsim 2\times 10^4$ quanta/s}, which is orders of magnitude faster than typical anomalous ion heating rates. We introduce a quantum trajectory-based framework that accurately reproduces the experimental results and provides a unified description of ion heating for both continuous and discrete sources.

We explore the potential for hybrid development of quantum hardware where currently available quantum computers simulate open Cavity Quantum Electrodynamical (CQED) systems for applications in optical quantum communication, simulation and computing. Our simulations make use of a recent quantum algorithm that maps the dynamics of a singly excited open Tavis-Cummings model containing N atoms coupled to a lossy cavity. We report the results of executing this algorithm on two noisy intermediate-scale quantum computers: a superconducting processor and a trapped ion processor, to simulate the population dynamics of an open CQED system featuring N = 3 atoms. By applying technology-specific transpilation and error mitigation techniques, we minimize the impact of gate errors, noise, and decoherence in each hardware platform, obtaining results which agree closely with the exact solution of the system. These results can be used as a recipe for efficient and platform-specific quantum simulation of cavity-emitter systems on contemporary and future quantum computers.

The absolute mass of $^{84}$Sr was determined using the phase-imaging ion-cyclotron-resonance technique with the JYFLTRAP double Penning trap mass spectrometer. A more precise value for the mass of $^{84}$Sr is essential for providing potential indications of physics beyond the Standard Model through high-precision isotope shift measurements of Sr atomic transition frequencies. The mass excess of $^{84}$Sr was refined to be -80649.229(37) keV/c$^2$ from high-precision cyclotron-frequency-ratio measurements with a relative precision of 4.8$\times$10$^{-10}$. The obtained mass-excess value is in agreement with the adopted value in the Atomic Mass Evaluation 2020, but is 30 times more precise. With this new value, we confirm the previously observed nonlinearity in the study of the isotope shift of strontium. Moreover, the double-beta ($2β^{+}$) decay $Q$ value of $^{84}$Sr was directly determined to be 1790.115(37) keV, and the precision was improved by a factor of 30.

Trapped ions in a periodic potential are a paradigm of a frustrated Wigner crystal. The dynamics is captured by a long-range Frenkel-Kontorova model. The classical ground state can be mapped to the one of an antiferromagnetic spin chain with long-range interactions in a magnetic field, whose strength is determined by the mismatch between chain's and substrate lattice's periodicity. The mapping is exact when the substrate potential is a piecewise harmonic potential and holds for any two-body interaction decaying as $1/r^α$ with the distance $r$. The ground state is a devil's staircase of regular, periodic structures as a function of the mismatch, whose range of stability depends also on the coefficient $α$. While the staircase is well defined in the thermodynamic limit for $α>1$, for Coulomb interactions, $α=1$, it disappears and the sliding-to-pinned transitions becomes crossovers. However, due to the logarithmic convergence to the thermodynamic limit characteristic of the Coulomb potential, the staircase is found for any finite number of ions. We discuss the experimental parameters as well as the features that allow one to observe and reveal our predictions in experimental platforms. These dynamics are a showcase of the versatility of trapped ion platforms for exploring the interplay between frustration and interactions.

We investigate the control mechanism of trap frequencies and determine the orientation of ion trap principal axes. The application of DC voltage to the ground electrodes, commonly employed to finely tune trap frequencies in ion traps, leads to the rotation of the trap principal axes. Analyzing the ion matter-wave interference signal enables us to determine the directions of the trap principal axes. Both the experiments and simulations reveal an avoided-crossing behavior resulting from the coupling between the trap radial axes. Additionally, simulations indicate that symmetric trap structures lack this coupling, suggesting that trap structure asymmetry causes coupling between the axes. The findings of this study offer valuable insights into ion traps for diverse applications in quantum science and technology.

Solvation, the result of the complicated interplay between solvent-solute and solvent-internal interactions, is one of the most important chemical processes. Consequently, a complete theoretical understanding of solvation seems a heroic task. However, it is possible to elucidate fundamental solvation mechanisms by looking into simpler systems, such as ion solvation in atomic baths. In this work, we study ion solvation by calculating the ground state properties of a single ion in a neutral bath from the high-density regime to the low-density regime, finding common ground for these two, in principle, disparate regimes. Our results indicate that a single $^{174}$Yb$^+$ ion in a bath of $^{7}$Li atoms forms a coordination complex at high densities with a coordination number of 8, with strong electrostriction, characteristic of the snowball effect. On the contrary, treating the atomic bath as a dilute quantum gas at low densities, we find that the ion-atom interaction's short-range plays a significant role in the physics of many-body bound states and polarons. Furthermore, in this regime, we explore the role of a putative ion trap, which drastically affects the binding mechanism of the ion and atoms from a quantum gas. Therefore, our results give a novel insight into the universality of ion-neutral systems in the ultracold regime and the possibilities of observing exotic many-body effects.

Interferometers, which are built using spatially propagating light or matter waves, are commonly used to measure physical quantities. These measurements are made possible by exploiting the interference between waves traveling along different paths. This study introduces a novel approach to sensing of the Aharonov--Bohm phase, an ion matter-wave interferometer operating within a two-dimensional circular trajectory in a trap potential. The ion orbitals in the potential form Lissajous curves, causing the direction of ion rotation to reverse. This reversal results in a corresponding change in the interference phase. Our study is groundbreaking as it is the first attempt to utilize propagating matter waves of an ion in constructing an interferometer for the measurement of physical quantities. Given that the scale factor of the interferometer to the cyclotron motion and the rotation of the system is common, the sensitivity to the Aharonov--Bohm phase in this study corresponds to a rotation sensitivity of approximately 300~rad/s. Besides advancing interferometry, our work also lays the foundation for future research into the use of ion matter waves in gyroscopic applications.

Interference underpins some of the most practical and impactful properties of both the classical and quantum worlds. In this work we experimentally investigate a new formalism to describe interference effects, based on collective states which have enhanced or suppressed coupling to a two-level system. We employ a single trapped ion, whose electronic state is coupled to two of the ion's motional modes in order to simulate a multi-mode light-matter interaction. We observe the emergence of phononic bright and dark states for both a single phonon and a superposition of coherent states and demonstrate that a view of interference which is based solely on their decomposition in the collective basis is able to intuitively describe their coupling to a single atom. This work also marks the first time that multi-mode bright and dark states have been formed with the bounded motion of a single trapped ion and we highlight the potential of the methods discussed here for use in quantum information processing.

Studying high-energy collisions of composite particles, such as hadrons and nuclei, is an outstanding goal for quantum simulators. However, preparation of hadronic wave packets has posed a significant challenge, due to the complexity of hadrons and the precise structure of wave packets. This has limited demonstrations of hadron scattering on quantum simulators to date. Observations of confinement and composite excitations in quantum spin systems have opened up the possibility to explore scattering dynamics in spin models. In this article, we develop two methods to create entangled spin states corresponding to wave packets of composite particles in analog quantum simulators of Ising spin Hamiltonians. One wave-packet preparation method uses the blockade effect enabled by beyond-nearest-neighbor Ising spin interactions. The other method utilizes a quantum-bus-mediated exchange, such as the native spin-phonon coupling in trapped-ion arrays. With a focus on trapped-ion simulators, we numerically benchmark both methods and show that high-fidelity wave packets can be achieved in near-term experiments. We numerically study scattering of wave packets for experimentally realizable parameters in the Ising model and find inelastic-scattering regimes, corresponding to particle production in the scattering event, with prominent and distinct experimental signals. Our proposal, therefore, demonstrates the potential of observing inelastic scattering in near-term quantum simulators.

Quantum harmonic oscillators model a wide variety of phenomena ranging from electromagnetic fields to vibrations of atoms in molecules. Their excitations can be represented by bosons such as photons, single particles of light, or phonons, the quanta of vibrational energy. Linear interactions that only create and annihilate single bosons can generate coherent states of light or motion. Introducing nth-order nonlinear interactions, that instead involve n bosons, leads to increasingly complex quantum behaviour. For example, second-order interactions enable squeezing, used to enhance the precision of measurements beyond classical limits, while higher-order interactions create non-Gaussian states essential for continuous-variable quantum computation. However, generating nonlinear interactions is challenging, typically requiring higher-order derivatives of the driving field or specialized hardware. Hybrid systems, where linear interactions couple an oscillator to an additional spin, offer a solution and are readily available across many platforms. Here, using the spin of a single trapped ion coupled to its motion, we employ two linear interactions to demonstrate up to fourth-order bosonic interactions; we focus on generalised squeezing interactions and demonstrate squeezing, trisqueezing, and quadsqueezing. We characterise these interactions, including their spin dependence, and reconstruct the Wigner function of the resulting states. We also discuss the scaling of the interaction strength, where we drive the quadsqueezing interaction more than 100 times faster than using conventional techniques. Our method presents no fundamental limit in the interaction order n and applies to any platform supporting spin-dependent linear interactions. Strong higher-order nonlinear interactions unlock the study of fundamental quantum optics, quantum simulation, and computation in a hitherto unexplored regime.

A novel two-qubit entangling gate for trapped-ion quantum processors is proposed theoretically and demonstrated experimentally. During the gate, double-dressed quantum states are created by applying a phase-modulated continuous driving field. The speed of this quantum gate is an order of magnitude higher than that of previously demonstrated rf controlled two-qubit entangling gates in static magnetic field gradients. At the same time, the field driving the gate dynamically decouples the qubits from amplitude and frequency noise, increasing the qubits' coherence time by $3$ orders of magnitude. The gate requires only a single continuous rf field per qubit, making it well suited for scaling a quantum processor to large numbers of qubits. Implementing this entangling gate, we generate the Bell states $|Φ^+\rangle$ and $|Ψ^+\rangle$ in less than or equal to $313$ $\mathrmμ$s with fidelities up to $98^{+2}_{-3}$% in a static magnetic gradient of only $19.09$ T/m. At higher magnetic field gradients, the entangling gate speed can be further improved to match that of laser-based counterparts.

The masses of $^{84}$Br, $^{105}$Mo, $^{115,119,121}$Pd, $^{122}$Ag, $^{127,129}$In, $^{132}$Sb and their respective isomeric states have been measured with the JYFLTRAP Penning trap mass spectrometer using the phase-imaging ion-cyclotron-resonance technique. The excitation energies of the isomeric states in $^{132}$Sb and $^{119}$Pd were experimentally determined for the first time, while for $^{84}$Br, $^{115}$Pd and $^{127,129}$In, the precision of the mass values was substantially improved. In $^{105}$Mo and $^{121}$Pd there were no signs of a long-lived isomeric state. The ground-state measurements of $^{119}$Pd and $^{122}$Ag indicated that both are significantly more bound than the literature values. For $^{122}$Ag, there was no indication of a proposed third long-lived state. The results for the $N=49$ nucleus $^{84}$Br and isomers close to doubly magic $^{132}$Sn have been compared to the shell-model and the microscopic quasiparticle-phonon model calculations.

Harnessing quantum correlations can enable sensing beyond the classical limits of precision, with the realization of such sensors poised for transformative impacts across science and engineering. Real devices, however, face the accumulated impacts of noise effects, architecture constraints, and finite sampling rates, making the design and success of practical quantum sensors challenging. Numerical and theoretical frameworks that support the optimization and analysis of imperfections from one end of a sensing protocol through to the other (i.e., from probe state preparation through to parameter estimation) are thus crucial for translating quantum advantage into widespread practice. Here, we present an end-to-end variational framework for quantum sensing protocols, where parameterized quantum circuits and neural networks form trainable, adaptive models for quantum sensor dynamics and estimation, respectively. The framework is general and can be adapted towards arbitrary qubit architectures, as we demonstrate with experimentally-relevant ansätze for trapped-ion and photonic systems, and enables to directly quantify the impacts that noisy state preparation/measurement and finite data sampling have on parameter estimation. End-to-end variational frameworks can thus underpin powerful design and analysis tools for realizing quantum advantage in practical, robust sensors.

We report on a search for magnetic monopoles (MMs) produced in ultraperipheral Pb--Pb collisions during Run-1 of the LHC. The beam pipe surrounding the interaction region of the CMS experiment was exposed to 184.07 \textmu b$^{-1}$ of Pb--Pb collisions at 2.76 TeV center-of-mass energy per collision in December 2011, before being removed in 2013. It was scanned by the MoEDAL experiment using a SQUID magnetometer to search for trapped MMs. No MM signal was observed. The two distinctive features of this search are the use of a trapping volume very close to the collision point and ultra-high magnetic fields generated during the heavy-ion run that could produce MMs via the Schwinger effect. These two advantages allowed setting the first reliable, world-leading mass limits on MMs with high magnetic charge. In particular, the established limits are the strongest available in the range between 2 and 45 Dirac units, excluding MMs with masses of up to 80 GeV at 95\% confidence level.

We present an architecture for encoding two qubits within the optical "clock" transition and nuclear spin-1/2 degree of freedom of neutral ytterbium-171 atoms. Inspired by recent high-fidelity control of all pairs of states within this four-dimensional ququart space, we present a toolbox for intra-ququart (single atom) one- and two-qubit gates, inter-ququart (two atom) Rydberg-based two- and four-qubit gates, and quantum nondemolition (QND) readout. We then use this toolbox to demonstrate the advantages of the ququart encoding for entanglement distillation and quantum error correction which exhibit superior hardware efficiency and better performance in some cases since fewer two-atom (Rydberg-based) operations are required. Finally, leveraging single-state QND readout in our ququart encoding, we present a unique approach to studying interactive circuits as well as to realizing a symmetry protected topological phase of a spin-1 chain with a shallow, constant-depth circuit. These applications are all within reach of recent experiments with neutral ytterbium-171 atom arrays or with several trapped ion species.

Microwave-driven logic is a promising alternative to laser control in scaling trapped-ion based quantum processors. However, such electronic gates have yet to match the speed offered by their laser-driven counterparts. Here, we implement Mølmer-Sørensen two-qubit gates on $^{43}\text{Ca}^+$ hyperfine clock qubits in a cryogenic ($\approx25~\text{K}$) surface trap, driven by near-field microwaves. We achieve gate durations of $154~μ\text{s}$ (with $1.0(2)\%$ error) and $331~μ\text{s}$ ($0.5(1)\%$ error), which approaches the performance of typical laser-driven gates. In the $331~μ\text{s}$ gate, we demonstrate a new Walsh-modulated dynamical decoupling scheme which suppresses errors due to fluctuations in the qubit frequency as well as imperfections in the decoupling drive itself.

In this work, we present a method for measuring the motional state of a two-level system coupled to a harmonic oscillator. Our technique uses ultra-narrowband composite pulses on the blue sideband transition to scan through the populations of the different motional states. Our approach does not assume any previous knowledge of the motional state distribution and is easily implemented. It is applicable both inside and outside of the Lamb-Dicke regime. For higher phonon numbers especially, the composite pulse sequence can be used as a filter for measuring phonon number ranges. We demonstrate this measurement technique using a single trapped ion and show good detection results with the numerically evaluated pulse sequence.

We calculated cross sections for the dielectronic recombination (DR) satellite lines of Fe XVII and benchmarked our predictions with experimental cross sections of Fe XVII resonances that were mono-energetically excited in an electron beam ion trap. We extend the benchmark to all resolved DR and direct electron-impact excitation (DE) channels in the experimental dataset, specifically the $n\geq4$ DR resonances of Fe XVII, complementing earlier investigations of $n=3$ channels. Our predictions overestimate by 20-25$\%$ the DR and DE absolute cross sections for the higher $n$ complexes when using the same methods as in previous works. However, we achieve agreement within $\sim$10$\%$ of the experimental results by an approach in which we "forward fold" the predicted cross sections with the spread of the electron-beam energy and the photon-energy resolution of our experiment. We then calculated rate coefficients from the experimental and theoretical cross sections, finding departures of $10-20\%$ from the rates found in the OPEN-ADAS atomic database.

Excess "micromotion" of trapped ions due to the residual radio-frequency (rf) trapping field at their location is often undesirable and is usually carefully minimized. Here, we induce precise amounts of excess micromotion on individual ions by adjusting the local static electric field they experience. Micromotion modulates the coupling of an ion to laser fields, ideally tuning it from its maximum value to zero as the ion is moved away from the trap's rf null. We use tunable micromotion to vary the Rabi frequency of stimulated Raman transitions over two orders of magnitude, and to individually control the rates of resonant fluorescence from three ions under global laser illumination without any changes to the driving light fields. The technique is amenable to situations where addressing individual ions with focused laser beams is challenging, such as tightly packed linear ion strings or two-dimensional ion arrays illuminated from the side.

As quantum computers progress towards a larger scale, it is imperative that the "top" of the computing-technology stack is improved. This project investigates the quantum resources required to compute primitive arithmetic algorithms, particularly multiplication. By using various quantum resource estimators, like Microsoft's Azure Quantum Resource Estimator, one can determine the resources required for numerous quantum algorithms [5]. In this paper, we will provide a comprehensive resource analysis of numerous quantum multiplication algorithms such as Karatsuba, schoolbook, and windowed arithmetic for different qubit platforms (trapped ion, superconducting, and Majorana) using the new Azure Quantum Resource Estimator.

Quantum simulation holds promise of enabling a complete description of high-energy scattering processes rooted in gauge theories of the Standard Model. A first step in such simulations is preparation of interacting hadronic wave packets. To create the wave packets, one typically resorts to adiabatic evolution to bridge between wave packets in the free theory and those in the interacting theory, rendering the simulation resource intensive. In this work, we construct a wave-packet creation operator directly in the interacting theory to circumvent adiabatic evolution, taking advantage of resource-efficient schemes for ground-state preparation, such as variational quantum eigensolvers. By means of an ansatz for bound mesonic excitations in confining gauge theories, which is subsequently optimized using classical or quantum methods, we show that interacting mesonic wave packets can be created efficiently and accurately using digital quantum algorithms that we develop. Specifically, we obtain high-fidelity mesonic wave packets in the $Z_2$ and $U(1)$ lattice gauge theories coupled to fermionic matter in 1+1 dimensions. Our method is applicable to both perturbative and non-perturbative regimes of couplings. The wave-packet creation circuit for the case of the $Z_2$ lattice gauge theory is built and implemented on the Quantinuum H1-1 trapped-ion quantum computer using 13 qubits and up to 308 entangling gates. The fidelities agree well with classical benchmark calculations after employing a simple symmetry-based noise-mitigation technique. This work serves as a step toward quantum computing scattering processes in quantum chromodynamics.

Probing electrical and magnetic properties in aqueous environments remains a frontier challenge in nanoscale sensing. Our inability to do so with quantitative accuracy imposes severe limitations, for example, on our understanding of the ionic environments in a diverse array of systems, ranging from novel materials to the living cell. The Nitrogen-Vacancy (NV) center in fluorescent nanodiamonds (FNDs) has emerged as a good candidate to sense temperature, pH, and the concentration of paramagnetic species at the nanoscale, but comes with several hurdles such as particle-to-particle variation which render calibrated measurements difficult, and the challenge to tightly confine and precisely position sensors in aqueous environment. To address this, we demonstrate relaxometry with NV centers within optically-trapped FNDs. In a proof of principle experiment, we show that optically-trapped FNDs enable highly reproducible nanomolar sensitivity to the paramagnetic ion, (\mathrm{Gd}^{3+}). We capture the three distinct phases of our experimental data by devising a model analogous to nanoscale Langmuir adsorption combined with spin coherence dynamics. Our work provides a basis for routes to sense free paramagnetic ions and molecules in biologically relevant conditions.

An ancient and counterintuitive phenomenon know as the Mpemba effect (water can cool faster when initially heated up) showcases the critical role of initial conditions in relaxation processes. How to realize and utilize this effect for speeding up relaxation is an important but challenging task in purely quantum system till now. Here, we report the first experiment, as far as we know,about the strong Mpemba effect in a single trapped ion system in which an exponentially expedited relaxation in time is observed by preparing an optimal initial state with no excitation of the slowest decaying mode. Also, we find that the condition of realizing such effect coincides with the Liouvillian exceptional point, featuring the coalescence of both the eigenvalues and the eigenmodes of the system. Our work provides an efficient strategy to exponentially accelerate relaxations of quantum system to their stationary state, and suggests a link unexplored yet between the Mpemba effect and the non-Hermitian physics. It could open up the door to engineer a wide range of dissipative quantum systems by utilizing the anomalous Mpemba effect, for applications in quantum simulation and quantum information processing.

The detailed design and operation of the Smithsonian Astrophysical Observatory's EBIT are described for the first time, including recent design upgrades that have led to improved system stability and greater user control, increasing the scope of possible experiments. Measurements of emission from highly charged Ar were taken to determine the spatial distribution of the ion cloud and electron beam. An optical setup consisting of two lenses, a narrow band filter, and a CCD camera was used to image visible light, while an X-ray pinhole and CCD camera were used to image X-rays. Measurements were used to estimate an effective electron density of 1.77 x 10$^{10}$ cm$^{-3}$. Additionally, observations of X-ray emission from background EBIT gases were measured with a Silicon Lithium detector. Measurements indicate the presence of Ba and Si, which are both easily removed by dumping the trap every 2 s or less.

The ability for real-time control of topological defects can open up prospects for dynamical manipulation of macroscopic properties of solids. A sub-category of these defects, formed by particle dislocations, can be effectively described using the Frenkel-Kontorova chain, which characterizes the dynamics of these particles in a periodic lattice potential. This model is known to host solitons, which are the topological defects of the system and are linked to structural transitions in the chain. This work addresses three key questions: Firstly, we investigate how imperfections present in concrete implementations of the model affect the properties of topological defects. Secondly, we explore how solitons can be injected after the rapid change in lattice potential or nucleated due to quantum fluctuations. Finally, we analyze the propagation and scattering of solitons, examining the role of quantum fluctuations and imperfections in influencing these processes. Furthermore, we address the experimental implementation of the Frenkel-Kontorova model. Focusing on the trapped ion quantum simulator, we set the stage for controllable dynamics of topological excitations and their observation in this platform.

We improve by a factor of 4-20 the energy accuracy of the strongest soft X-ray transitions of Fe XVII ions by resonantly exciting them in an electron beam ion trap with a monochromatic beam at the P04 beamline of the PETRA III synchrotron facility. By simultaneously tracking instantaneous photon-energy fluctuations with a high-resolution photoelectron spectrometer, we minimize systematic uncertainties down to 10-15 meV, or velocity equivalent $\pm\sim$5 km s$^{-1}$ in their rest energies, substantially improving our knowledge of this key astrophysical ion. Our large-scale configuration-interaction computations include more than four million relativistic configurations and agree with the experiment at a level without precedent for a 10-electron system. Thereby, theoretical uncertainties for interelectronic correlations become far smaller than those of quantum electrodynamics (QED) corrections. The present QED benchmark strengthens our trust in future calculations of many other complex atomic ions of interest to astrophysics, plasma physics, and for the development of optical clocks with highly charged ions.

Trapped ions for quantum information processing has been an area of intense study due to the extraordinarily high fidelity operations that have been reported experimentally. Specifically, barium trapped ions have been shown to have exceptional state-preparation and measurement (SPAM) fidelities. The $^{133}\mathrm{Ba}^+$ ($I = 1/2$) isotope in particular is a promising candidate for large-scale quantum computing experiments. However, a major pitfall with this isotope is that it is radioactive and is thus generally used in microgram quantities to satisfy safety regulations. We describe a new method for creating microgram barium chloride ($\mathrm{BaCl}_2$) ablation targets for use in trapped ion experiments and compare our procedure to previous methods. We outline two recipes for fabrication of ablation targets that increase the production of neutral atoms for isotope-selective loading of barium ions. We show that heat-treatment of the ablation targets greatly increases the consistency at which neutral atoms can be produced and we characterize the uniformity of these targets using trap-independent techniques such as energy dispersive x-ray spectroscopy (EDS) and neutral fluorescence collection. Our comparison between fabrication techniques and demonstration of consistent neutral fluorescence paves a path towards reliable loading of $^{133}\mathrm{Ba}^+$ in surface traps and opens opportunities for scalable quantum computing with this isotope.

High-precision mass measurements of exotic $^{95-97}$Ag isotopes close to the $N = Z$ line have been conducted with the JYFLTRAP double Penning trap mass spectrometer, with the silver ions produced using the recently commissioned inductively-heated hot cavity catcher laser ion source at the Ion Guide Isotope Separator On-Line facility. The atomic mass of $^{95}$Ag was directly determined for the first time. In addition, the atomic masses of $β$-decaying 2$^+$ and 8$^+$ states in $^{96}$Ag have been identified and measured for the first time, and the precision of the $^{97}$Ag mass has been improved. The newly measured masses, with a precision of $\approx$ 1 keV/c$^2$, have been used to investigate the $N =$ 50 neutron shell closure confirming it to be robust. Empirical shell-gap and pairing energies determined with the new ground-state mass data are compared with the state-of-the-art \textit{ab initio} calculations with various chiral effective field theory Hamiltonians. The precise determination of the excitation energy of the $^{96m}$Ag isomer in particular serves as a benchmark for \textit{ab initio} predictions of nuclear properties beyond the ground state, specifically for odd-odd nuclei situated in proximity to the proton dripline below $^{100}$Sn. In addition, density functional theory (DFT) calculations and configuration-interaction shell-model (CISM) calculations are compared with the experimental results. All theoretical approaches face challenges to reproduce the trend of nuclear ground-state properties in the silver isotopic chain across the $N =$50 neutron shell and toward the proton drip-line.

Helium nanodroplets ("HNDs") are widely used for forming tailor-made clusters and molecular complexes in a cold, transparent, and weakly-interacting matrix. Characterization of embedded species by mass spectrometry is often complicated by fragmentation and trapping of ions in the HNDs. Here, we systematically study fragment ion mass spectra of HND-aggregated water and oxygen clusters following their ionization by charge transfer ionization ("CTI") and Penning ionization ("PEI"). While the efficiency of PEI of embedded clusters is lower than for CTI by about factor 10, both the mean sizes of detected water clusters and the relative yields of unprotonated cluster ions are significantly larger, making PEI a ``soft ionization'' scheme. However, the tendency of ions to remain bound to HNDs leads to a reduced detection efficiency for large HNDs containing $>10^4$ helium atoms. These results are instrumental for determining optimal conditions for mass spectrometry and photoionization spectroscopy of molecular complexes and clusters aggregated in HNDs.

The non-equilibrium physics of many-body quantum systems harbors various unconventional phenomena. In this study, we experimentally investigate one of the most puzzling of these phenomena -- the quantum Mpemba effect, where a tilted ferromagnet restores its symmetry more rapidly when it is farther from the symmetric state compared to when it is closer. We present the first experimental evidence of the occurrence of this effect in a trapped-ion quantum simulator. The symmetry breaking and restoration are monitored through entanglement asymmetry, probed via randomized measurements, and postprocessed using the classical shadows technique. Our findings are further substantiated by measuring the Frobenius distance between the experimental state and the stationary thermal symmetric theoretical state, offering direct evidence of subsystem thermalization.

Comformally flat spacetime converts the Anti-de Sitter (AdS) spacetime into a z-dependent metric. We take advantage of this metric to solve Dirac equations in the AdS geometry analytically, including Dirac, Majorana, Dirac tachyon and Majorana tachyon. Constraints on Majorana wavefunctions limit the mass. Besides, there gives rise flatlands and Majorana particles hop in between, just mimicking the D-brane stack and open strings. Furthermore, a plausible way of ion-trapped experiment is suggested.

Hybridizing different degrees of freedom or physical platforms potentially offers various advantages in building scalable quantum architectures. We here introduce a fault-tolerant hybrid quantum computation by taking the advantages of both discrete variable (DV) and continuous variable (CV) systems. Particularly, we define a CV-DV hybrid qubit with bosonic cat-code and single photon, which is implementable in current photonic platforms. By the cat-code encoded in the CV part, the dominant loss errors are readily correctable without multi-qubit encoding, while the logical basis is inherently orthogonal due to the DV part. We design fault-tolerant architectures by concatenating hybrid qubits and an outer DV quantum error correction code such as topological codes, exploring their potential merits in developing scalable quantum computation. We demonstrate by numerical simulations that our scheme is at least an order of magnitude more resource-efficient over all previous proposals in photonic platforms, allowing to achieve a record-high loss threshold among existing CV and hybrid approaches. We discuss its realization not only in all-photonic platforms but also in other hybrid platforms including superconduting and trapped-ion systems, which allows us to find various efficient routes towards fault-tolerant quantum computing.

Randomized benchmarking (RB) is a widely used strategy to assess the quality of available quantum gates in a computational context. RB involves applying known random sequences of gates to an initial state and using the statistics of a final measurement step to determine an effective depolarizing error per step of the sequence, which is a metric of gate quality. Here we investigate the advantages of fully randomized benchmarking, where a new random sequence is drawn for each experimental trial. The advantages of full randomization include smaller confidence intervals on the inferred step error, the ability to use maximum likelihood analysis without heuristics, straightforward optimization of the sequence lengths, and the ability to model and measure behaviors that go beyond the typical assumption of time-independent error rates. We discuss models of time-dependent or non-Markovian errors that generalize the basic RB model of a single exponential decay of the success probability. For any of these models, we implement a concrete protocol to minimize the uncertainty of the estimated parameters given a fixed time constraint on the complete experiment, and we implement a maximum likelihood analysis. We consider several previously published experiments and determine the potential for improvements with optimized full randomization. We experimentally observe such improvements in Clifford randomized benchmarking experiments on a single trapped ion qubit at the National Institute of Standards and Technology (NIST). For an experiment with uniform lengths and intentionally repeated sequences the step error was $2.42^{+0.30}_{-0.22}\times 10^{-5}$, and for an optimized fully randomized experiment of the same total duration the step error was $2.57^{+0.07}_{-0.06}\times 10^{-5}$. We find a substantial decrease in the uncertainty of the step error as a result of optimized fully randomized benchmarking.

Trapped ion systems are a leading platform for quantum information processing, but they are currently limited to 1D and 2D arrays, which imposes restrictions on both their scalability and their range of applications. Here, we propose a path to overcome this limitation by demonstrating that Penning traps can be used to realize remarkably clean bilayer crystals, wherein hundreds of ions self-organize into two well-defined layers. These bilayer crystals are made possible by the inclusion of an anharmonic trapping potential, which is readily implementable with current technology. We study the normal modes of this system and discover salient differences compared to the modes of single-plane crystals. The bilayer geometry and the unique properties of the normal modes open new opportunities, in particular in quantum sensing and quantum simulation, that are not straightforward in single-plane crystals. Furthermore, we illustrate that it may be possible to extend the ideas presented here to realize multilayer crystals with more than two layers. Our work increases the dimensionality of trapped ion systems by efficiently utilizing all three spatial dimensions and lays the foundation for a new generation of quantum information processing experiments with multilayer 3D crystals of trapped ions.

We experimentally implement circuits of one and two mode operations on two motional modes of a single trapped ion. This is achieved by implementing the required displacement, squeezing, two-mode squeezing, and beamsplitter operations using oscillating electric potentials applied to the trap electrodes. The resulting electric fields drive the modes resonantly or parametrically without the need for optical forces. As a demonstration, we implement SU(2) and SU(1,1) interferometers with phase sensitivities near the Cramér-Rao bound. We report a maximum sensitivity of a SU(2) interferometer within $0.67(5)\,$dB of the standard quantum limit (SQL) as well as a single and two-mode SU(1,1) sensitivity of $5.9(2)\,$dB and $4.5(2)\,$dB below the SQL respectively.

Electromagnetically induced transparency (EIT) can be used to cool an atom in a harmonic potential close to the ground state by addressing several vibrational modes simultaneously. Previous experimental efforts focus on trapped ions and neutral atoms in a standing wave trap. In this work, we demonstrate EIT cooling of an optically trapped single neutral atom, where the trap frequencies are an order of magnitude smaller than in an ion trap and a standing wave trap. We resolve the Fano resonance feature in fluorescence excitation spectra and the corresponding cooling profile in temperature measurements. A final temperature of around 6 $μ$K is achieved with EIT cooling, a factor of two lower than the previous value obtained using olarization gradient cooling.

Cold ions in traps are well-established, highly controllable quantum systems with a wide variety of applications in quantum information, precision spectroscopy, clocks and chemistry. Nanomechanical oscillators are used in advanced sensing applications and for exploring the border between classical and quantum physics. Here, we report on the implementation of a hybrid system combining a metallic nanowire with laser-cooled ions in a miniaturised ion trap. We demonstrate resonant and off-resonant coupling of the two systems and the coherent motional excitation of the ion by the mechanical drive of the nanowire. The present results open up avenues for mechanically manipulating the quantum motion of trapped ions, for the development of ion-mechanical hybrid quantum systems and for the sympathetic cooling of mechanical systems by trapped ions and vice versa.

We report a precise measurement of the isotope shifts in the $4^2$S$_{1/2} \rightarrow 3^2$D$_{3/2}$ electric quadrupole transition at 732~nm in $^{40 - 42,44,48}$Ca$^+$ via high-resolution laser spectroscopy of co-trapped ions, finding measured shifts of 2,775,392,374.8(6.0), 5,347,679,835.1(5.9), and 10,003,129,115.1(5.7)\,Hz between $^{42,44,48}$Ca$^+$and $^{40}$Ca$^+$, respectively. When combined with prior measurements on the $4^2$S$_{1/2} \rightarrow 3^2$D$_{5/2}$ transition [Phys. Rev. A 100, 022514 (2019), https://journals.aps.org/pra/abstract/10.1103/PhysRevA.100.022514] a King Plot analysis shows the data to be consistent with linearity below the level of parts per billion. This observed linearity, which is free of nuclear systematics, improves the previous isotope-shift based limits of Ca$^+$ for couplings of a scalar boson beyond the Standard Model to electrons and neutrons by a factor of 3. Our new limit excludes part of the coupling range remaining for a new physics interpretation after accounting for one higher-order nuclear term in the nonlinear King plot of Yb/Yb$^+$.

We theoretically investigate prospects for the creation of nonclassical spin states in trapped ion arrays by coupling to a squeezed state of the collective motion of the ions. The correlations of the generated spin states can be tailored for quantum-enhanced sensing of global or differential rotations of sub-ensembles of the spins by working with specific vibrational modes of the ion array. We propose a pair of protocols to utilize the generated states and determine the impact of finite size effects, inhomogeneous couplings between the spin and motional degrees of freedom and technical noise. Our work suggests new opportunities for the preparation of many-body states with tailored correlations for quantum-enhanced metrology in spin-boson systems.

A Wigner chain in a periodic potential is a paradigmatic example of geometric frustration with long-range interactions. The dynamics emulates the Frenkel-Kontorova model with Coulomb interactions. In the continuum approximation, dislocations are sine-Gordon solitons with power-law decaying tails. We show that their action is mapped into a massive, long-range (1+1) Thirring model, where the solitons are charged fermionic excitations over an effective Dirac sea. We identify the corresponding mean field theory and show that the Coulomb interactions destabilize structures commensurate with the periodic substrate, suppressing their onset and giving rise to {\it interaction-induced} lubrication. Our study identifies the role of long-range interactions on determining nanofriction. Our predictions can be probed in state-of-the-art trapped ion experiments.

Zeros of partition functions, in particular Lee-Yang zeros, in a complex plane provide important information for understanding phase transitions. A recent discovery on the equivalence between the coherence of a central quantum system and the partition function of the environment in the complex plane enabled the experimental study of Lee-Yang zeros, with several pioneering experiments on spin systems. Lee-Yang zeros have not been observed in Bosonic systems. Here we propose an experimental scheme to demonstrate Lee-Yang zeros in Bosonic systems associated with a single trapped ion by introducing strong coupling between the spin and motion degrees of freedom, i.e. beyond the weak coupling Lamb-Dicke regime. Our scheme provides new possibilities for quantum simulation of the thermodynamics of Bosonic systems in the complex plane.

In the last decade, a growing interest has been devoted to models of spontaneous collapse of the wavefunction, known also as collapse models. They coherently solve the well-known quantum measurement problem by suitably modifying the Schrödinger evolution. Quantum experiments are now finally within the reach of testing such models (and thus testing the limits of quantum theory). Here, we propose a method based on a two-ions confined in a linear Paul trap to possibly enhance the testing capabilities of such experiments. The combination of an atomic and a macromolecular ion provide a good match for the cooling of the motional degrees of freedom and a non-negligible insight in the collapse mechanism, respectively.

Ultrasensitive detection of the frequency, phase, and amplitude of radio frequency (RF) electric fields is central to a variety of important applications, including radio communication, cosmology, dark matter searches, and high-fidelity qubit control. Quantum harmonic oscillator (QHO) systems, especially trapped ions, have been used with several quantum sensing techniques to achieve electric field sensing with state-of-the-art sensitivity and nanometer spatial resolution. However, these systems are limited to a narrow frequency range centered around either the motional frequency of the trapped ion oscillator or the frequency of an optical transition in the ion; often these techniques are not sensitive to the RF phase. Here, we propose and demonstrate a procedure that unlocks the extreme sensitivity of a QHO to allow high precision wideband detection of the frequency, phase, and amplitude of an unknown electric field. Specifically, we use motional Raman transitions in a single trapped ion, cooled near its motional ground state to realize state of the art sensitivities to frequency, phase, and amplitude, and show the technique works over a frequency range that is >800x larger than previous techniques. Further, this technique is shown to be compatible with both quantum amplification via squeezing and measurement in the Fock basis, allowing performance 3.4(20) dB below the standard quantum limit and the potential for several orders of magnitude improvement in sensitivity with moderate upgrades. In addition to providing an attractive platform for quantum sensing of small fields, this technique allows in situ calibration of qubit control lines in QHO systems, as well as transduction of external, non-resonant drives into oscillator excitation. Additionally, this approach can be extended to other QHO systems, such as a superconducting qubit-resonator system.

We propose a highly feasible technique with no experimental overhead to rapidly cool the in-plane degrees of freedom of large two-dimensional ion crystals in Penning traps. Through simulations, we demonstrate that our approach enables the in-plane modes to cool down to a temperature of around 1 mK in less than 10 ms. Our technique relies on near-resonant coupling of the poorly cooled in-plane motions and the efficiently cooled out-of-plane motions, and is achieved without introducing additional potentials. The rapid cooling enabled by our approach is in contrast to typical operating conditions, where our simulations of the laser cooling dynamics suggest that the ion crystal's in-plane motion cools very slowly on a timescale of several hundreds of milliseconds, a rate likely slower than experimental heating rates. Our work sets the stage for sub-Doppler laser cooling of the planar motion, and more robust and versatile quantum simulation and quantum sensing experiments with two-dimensional crystals in Penning traps.

We report the direct measurement of isotope shifts of the barium 6s$^2$ $^1$S$_0$ --5d6p $^3$D$^\text{o}_1$ 413-nm electric quadrupole transition, which is utilized for efficient barium ion trapping via photoionization using a single coherent light source. The measured isotope shifts relative to $^{138}$Ba are $392.9\pm0.9$ MHz, $178.1\pm0.8$ MHz, $401.4\pm1.2$ MHz, and $124.3\pm1.3$ MHz for isotopes with atomic numbers 137, 136, 135, and 134, respectively. We verify the measured isotopes with King plot analysis and compare the result with the formerly known shifts inferred from previous studies on neighboring transitions. The results can be used for efficient isotope selective loading of low-abundant barium ions, while careful suppression of line broadening is required for successful isotopic selectivity.

The electromagnetic trapping of ion chains can be regarded as a process of non-trivial entangled quantum state preparation within Hilbert spaces of the local axial motional modes. To begin uncovering properties of this entanglement resource produced as a byproduct of conventional ion-trap quantum information processing, the quantum continuous-variable formalism is herein utilized to focus on the leading-order entangled ground state of local motional modes in the presence of a quadratic trapping potential. The decay of entanglement between disjoint subsets of local modes is found to exhibit features of entanglement structure and responses to partial measurement reminiscent of the free massless scalar field vacuum. With significant fidelities between the two, even for large system sizes, a framework is established for initializing quantum field simulations via "imaging" extended entangled states from natural sources, rather than building correlations through deep circuits of few-body entangling operators. By calculating probabilities in discrete Fock subspaces of the local motional modes, considerations are presented for locally transferring these pre-distributed entanglement resources to the qudits of ion internal energy levels, improving this procedure's anticipated experimental viability.

Open quantum many-body systems with controllable dissipation can exhibit novel features in their dynamics and steady states. A paradigmatic example is the dissipative transverse field Ising model. It has been shown recently that the steady state of this model with all-to-all interactions is genuinely non-equilibrium near criticality, exhibiting a modified time-reversal symmetry and violating the fluctuation-dissipation theorem. Experimental study of such non-equilibrium steady-state phase transitions is however lacking. Here we propose realistic experimental setups and measurement schemes for current trapped-ion quantum simulators to demonstrate this phase transition, where controllable dissipation is engineered via a continuous weak optical pumping laser. With extensive numerical calculations, we show that strong signatures of this dissipative phase transition and its non-equilibrium properties can be observed with a small system size across a wide range of system parameters. In addition, we show that the same signatures can also be seen if the dissipation is instead achieved via Floquet dynamics with periodic and probabilistic resetting of the spins. Dissipation engineered in this way may allow the simulation of more general types of driven-dissipative systems or facilitate the dissipative preparation of useful many-body entangled states.

A variational quantum algorithm for numerically solving partial differential equations (PDEs) on a quantum computer was proposed by Lubasch et al. In this paper, we generalize the method introduced by Lubasch et al. to cover a broader class of nonlinear PDEs as well as multidimensional PDEs, and study the performance of the variational quantum algorithm on several example equations. Specifically, we show via numerical simulations that the algorithm can solve instances of the Single-Asset Black-Scholes equation with a nontrivial nonlinear volatility model, the Double-Asset Black-Scholes equation, the Buckmaster equation, and the deterministic Kardar-Parisi-Zhang equation. Our simulations used up to $n=12$ ansatz qubits, computing PDE solutions with $2^n$ grid points. We also performed proof-of-concept experiments with a trapped-ion quantum processor from IonQ, showing accurate computation of two representative expectation values needed for the calculation of a single timestep of the nonlinear Black--Scholes equation. Through our classical simulations and experiments on quantum hardware, we have identified -- and we discuss -- several open challenges for using quantum variational methods to solve PDEs in a regime with a large number ($\gg 2^{20}$) of grid points, but also a practical number of gates per circuit and circuit shots.

Qubits based on ions trapped in linear radio-frequency traps form a successful platform for quantum computing, due to their high fidelity of operations, all-to-all connectivity and degree of local control. In principle there is no fundamental limit to the number of ion-based qubits that can be confined in a single 1D register. However, in practice there are two main issues associated with long trapped-ion crystals, that stem from the 'softening' of their modes of motion, upon scaling up: high heating rates of the ions' motion, and a dense motional spectrum; both impede the performance of high-fidelity qubit operations. Here we propose a holistic, scalable architecture for quantum computing with large ion-crystals that overcomes these issues. Our method relies on dynamically-operated optical potentials, that instantaneously segment the ion-crystal into cells of a manageable size. We show that these cells behave as nearly independent quantum registers, allowing for parallel entangling gates on all cells. The ability to reconfigure the optical potentials guarantees connectivity across the full ion-crystal, and also enables efficient mid-circuit measurements. We study the implementation of large-scale parallel multi-qubit entangling gates that operate simultaneously on all cells, and present a protocol to compensate for crosstalk errors, enabling full-scale usage of an extensively large register. We illustrate that this architecture is advantageous both for fault-tolerant digital quantum computation and for analog quantum simulations.

The mechanism by which an effective macroscopic description of quantum measurement in terms of discrete, probabilistic collapse events emerges from the reversible microscopic dynamics remains an enduring open question. Emerging quantum computers offer a promising platform to explore how measurement processes evolve across a range of system sizes while retaining coherence. Here, we report the experimental observation of evidence for an observable-sharpening measurement-induced phase transition in a chain of trapped ions in Quantinuum H1-1 system model quantum processor. This transition manifests as a sharp, concomitant change in both the quantum uncertainty of an observable and the amount of information an observer can (in principle) learn from the measurement record, upon increasing the strength of measurements. We leverage insights from statistical mechanical models and machine learning to design efficiently-computable algorithms to observe this transition (without non-scalable post-selection on measurement outcomes) and to mitigate the effects on errors in noisy hardware.

Highly charged ions (HCIs) offer many opportunities for next-generation clock research due to the vast landscape of available electronic transitions in different charge states. The development of XUV frequency combs has enabled the search for clock transitions based on shorter wavelengths in HCIs. However, without initial knowledge of the energy of the clock states, these narrow transitions are difficult to be probed by lasers. In this Letter, we provide experimental observation and theoretical calculation of a long-lived electronic state in Nb-like Pb$^{41+}$ which could be used as a clock state. With the mass spectrometer Pentatrap, the excitation energy of this metastable state is directly determined as a mass difference at an energy of 31.2(8) eV, corresponding to one of the most precise relative mass determinations to date with a fractional uncertainty of $4\times10^{-12}$. This experimental result agrees within 1 $σ$ with two partially different \textit{ab initio} multi-configuration Dirac-Hartree-Fock calculations of 31.68(13) eV and 31.76(35) eV, respectively. With a calculated lifetime of 26.5(5.3) days, the transition from this metastable state to the ground state bears a quality factor of $1.1\times10^{23}$ and allows for the construction of a HCI clock with a fractional frequency instability of $<10^{-19}/\sqrtτ$.

Individual optical addressing in chains of trapped atomic ions requires generation of many small, closely spaced beams with low cross-talk. Furthermore, implementing parallel operations necessitates phase, frequency, and amplitude control of each individual beam. Here we present a scalable method for achieving all of these capabilities using a novel integrated photonic chip coupled to a network of optical fibre components. The chip design results in very low cross-talk between neighbouring channels even at the micrometre-scale spacing by implementing a very high refractive index contrast between the channel core and cladding. Furthermore, the photonic chip manufacturing procedure is highly flexible, allowing for the creation of devices with an arbitrary number of channels as well as non-uniform channel spacing at the chip output. We present the system used to integrate the chip within our ion trap apparatus and characterise the performance of the full individual addressing setup using a single trapped ion as a light-field sensor. Our measurements showed intensity cross-talk below $10^{-3}$ across the chip, with minimum observed cross-talk as low as $O\left(10^{-5}\right)$.

The quantum rotor is one of the simplest model systems in quantum mechanics, but only in recent years has theoretical work revealed general fundamental scaling laws for its decoherence. For example, a superposition of orientations decoheres at a rate proportional to the sine squared of the angle between them. Here we observe scaling laws for rotational decoherence dynamics for the first time, using a 4-micrometer diameter planar rotor composed of two Paul-trapped ions. We prepare the rotational motion of the ion crystal into superpositions of angular momentum with well-defined differences ranging from 1-3 $\hbar$, and measure the rate of decoherence. We also tune the system-environment interaction strength by introducing resonant electric field noise. The observed scaling relationships for decoherence are in excellent agreement with recent theoretical work, and are directly relevant to the growing development of rotor-based quantum applications.

Confinement is an intriguing phenomenon prevalent in condensed matter and high-energy physics. Exploring its effect on the far-from-equilibrium criticality of quantum many-body systems is of great interest both from a fundamental and technological point of view. Here, we employ large-scale uniform matrix product state calculations to show that a qualitative change in the type of dynamical quantum phase transitions (DQPTs) accompanies the confinement-deconfinement transition in three paradigmatic models -- the power-law interacting quantum Ising chain, the two-dimensional quantum Ising model, and the spin-$S$ $\mathrm{U}(1)$ quantum link model. By tuning a confining parameter in these models, it is found that \textit{branch} (\textit{manifold}) DQPTs arise as a signature of (de)confinement. Whereas manifold DQPTs are associated with a sign change of the order parameter, their branch counterparts are not, but rather occur even when the order parameter exhibits considerably constrained dynamics. Our conclusions can be tested in modern quantum-simulation platforms, such as ion-trap setups and cold-atom experiments of gauge theories.

Particle physics underpins our understanding of the world at a fundamental level by describing the interplay of matter and forces through gauge theories. Yet, despite their unmatched success, the intrinsic quantum mechanical nature of gauge theories makes important problem classes notoriously difficult to address with classical computational techniques. A promising way to overcome these roadblocks is offered by quantum computers, which are based on the same laws that make the classical computations so difficult. Here, we present a quantum computation of the properties of the basic building block of two-dimensional lattice quantum electrodynamics, involving both gauge fields and matter. This computation is made possible by the use of a trapped-ion qudit quantum processor, where quantum information is encoded in $d$ different states per ion, rather than in two states as in qubits. Qudits are ideally suited for describing gauge fields, which are naturally high-dimensional, leading to a dramatic reduction in the quantum register size and circuit complexity. Using a variational quantum eigensolver, we find the ground state of the model and observe the interplay between virtual pair creation and quantized magnetic field effects. The qudit approach further allows us to seamlessly observe the effect of different gauge field truncations by controlling the qudit dimension. Our results open the door for hardware-efficient quantum simulations with qudits in near-term quantum devices.

We present a novel technique to probe electroweak nuclear properties by measuring parity violation (PV) in single molecular ions in a Penning trap. The trap's strong magnetic field Zeeman shifts opposite-parity rotational and hyperfine molecular states into near degeneracy. The weak interaction-induced mixing between these degenerate states can be larger than in atoms by more than twelve orders of magnitude, thereby vastly amplifying PV effects. The single molecule sensitivity would be suitable for applications to nuclei across the nuclear chart, including rare and unstable nuclei.

Trapped-ion quantum simulators have demonstrated a long history of studying the physics of interacting spin-lattice systems using globally addressed entangling operations. Here, we seek to broaden and delimit the classes of effective spin-spin interactions achievable using exclusively global driving fields. We find that new categories of interaction graphs become achievable with perfect or near-perfect theoretical fidelity by tailoring the coupling to each vibrational mode of the ion crystal, or by shaping the trapping potential to include specific anharmonic terms. We also derive a rigorous test to determine whether a desired interaction graph is accessible using only globally driven fields. These tools broaden the reach of trapped-ion quantum simulators so that they may more easily address open questions in materials science and quantum chemistry.

Photonic interconnects between quantum systems will play a central role in both scalable quantum computing and quantum networking. Entanglement of remote qubits via photons has been demonstrated in many platforms; however, improving the rate of entanglement generation will be instrumental for integrating photonic links into modular quantum computers. We present an ion trap system that has the highest reported free-space photon collection efficiency for quantum networking. We use a pair of in-vacuum aspheric lenses, each with a numerical aperture of 0.8, to couple 10% of the 493 nm photons emitted from a $^{138}$Ba$^+$ ion into single-mode fibers. We also demonstrate that proximal effects of the lenses on the ion position and motion can be mitigated.

Squeezed spin states and squeezed light are both key resources for quantum metrology and quantum information science, but have been separately investigated in experiments so far. Simultaneous generation of these two types of quantum states in one experiment setup is intriguing but remains a challenging goal. Here we propose a novel protocol based on judiciously engineered symmetric atom-light interaction, and report proof-of-principle experimental results of concurrent spin squeezing of $0.61\pm0.09~\mathrm{dB}$ and light squeezing of $0.65^{+0.11}_{-0.10}~\mathrm{dB}$ in a hot atomic ensemble. The squeezing process is deterministic, yielding fixed squeezing directions for both the light field and the collective atomic spin. Furthermore, the squeezed light modes lie in the multiple frequency sidebands of a single spatial mode. This new type of dual squeezed state is applicable for quantum enhanced metrology and quantum networks. Our method can be extended to other quantum platforms such as optomechanics, cold atom and trapped ions.

Trapped-ion applications, such as in quantum information, precision measurements, optical clocks, and mass spectrometry, rely on specialized high-performance ion traps. The latter applications typically employ traditional machining to customize macroscopic 3D Paul traps, while quantum information processing experiments usually rely on photo-lithographic techniques to miniaturize the traps and meet scalability requirements. Using photolithography, however, it is challenging to fabricate the complex three-dimensional electrode structures required for optimal confinement. Here we address these limitations by adopting a high-resolution 3D printing technology based on two-photon polymerization supporting fabrication of large arrays of high-performance miniaturized 3D traps. We show that 3D-printed ion traps combine the advantages of traditionally machined 3D traps with the miniaturization provided by photolithography by confining single calcium ions in a small 3D-printed ion trap with radial trap frequencies ranging from 2 MHz to 24 MHz. The tight confinement eases ion cooling requirements and allows us to demonstrate high-fidelity coherent operations on an optical qubit after only Doppler cooling. With 3D printing technology, the design freedom is drastically expanded without sacrificing scalability and precision so that ion trap geometries can be optimized for higher performance and better functionality.

Electron cyclotron waves (whistlers), are commonly observed in plasmas near Earth and the solar wind. In the presence of nonlinear mirror modes, bursts of whistlers, usually called lion roars, have been observed within low magnetic field regions associated to these modes. In the intracluster medium (ICM) of galaxy clusters, the excitation of the mirror instability is expected, but it is not yet clear whether electron and ion cyclotron waves can also be present under conditions where gas pressure dominates over magnetic pressure (high $β$). In this work, we perform fully kinetic particle-in-cell (PIC) simulations of a plasma subject to a continuous amplification of the mean magnetic field $\textbf{B}(t)$ to study the nonlinear stages of the mirror instability and the ensuing excitation of whistler and ion cyclotron (IC) waves under ICM conditions. Once mirror modes reach nonlinear amplitudes, both whistler and IC waves start to emerge simultaneously, with sub-dominant amplitudes, propagating in low-$\textbf{B}$ regions, and quasi-parallel to $\textbf{B}(t)$. We show that the underlying source of excitation is the pressure anisotropy of electrons and ions trapped in mirror modes with loss-cone type distributions. We also observe that IC waves play an essential role in regulating the ion pressure anisotropy at nonlinear stages. We argue that whistler and IC waves are a concomitant feature at late stages of the mirror instability even at high-$β$, and therefore expected to be present in astrophysical environments like the ICM. We discuss the implications of our results for collisionless heating and dissipation of turbulence in the ICM.

Reducing errors in quantum gates is critical to the development of quantum computers. To do so, any distortions in the control signals should be identified, however, conventional tools are not always applicable when part of the system is under high vacuum, cryogenic, or microscopic. Here, we demonstrate a method to detect and compensate for amplitude-dependent phase changes, using the qubit itself as a probe. The technique is implemented using a microwave-driven trapped ion qubit, where correcting phase distortions leads to a three-fold improvement in single-qubit gate error, to attain state-of-the-art performance benchmarked at $1.6(4)\times 10^{-6}$ error per Clifford gate.

The surface code is a quantum error-correcting code for one logical qubit, protected by spatially localized parity checks in two dimensions. Due to fundamental constraints from spatial locality, storing more logical qubits requires either sacrificing the robustness of the surface code against errors or increasing the number of physical qubits. We bound the minimal number of spatially nonlocal parity checks necessary to add logical qubits to a surface code while maintaining, or improving, robustness to errors. We saturate the lower limit of this bound, when the number of added logical qubits is a constant, using a family of hypergraph product codes, interpolating between the surface code and constant-rate low-density parity-check codes. Fault-tolerant protocols for logical gates in the quantum code can be inherited from its classical parent codes. We provide near-term practical implementations of this code for hardware based on trapped ions or neutral atoms in mobile optical tweezers. Long-range-enhanced surface codes outperform conventional surface codes using hundreds of physical qubits, and represent a practical strategy to enhance the robustness of logical qubits to errors in near-term devices.

We present a practical scheme for the efficient preparation of laser-cooled $^{43}$Ca$^+$ ions in an ion trap. Our approach integrates two well-established methods: isotope-selective photoionization and isotope-specific parametric excitation. Drawing inspiration from the individual merits of each method, we have successfully integrated these techniques to prepare extended chains of $^{43}$Ca$^+$ ions, overcoming the challenge posed by their low natural abundance of 0.135\% in a natural source. Furthermore, we explore the subtleties of our scheme, focusing on the influence of different factors on the purification process. Our investigation contributes to a broader understanding of the technique and highlights the adaptability of established methods in addressing specific isotopic challenges.

Universality and scaling laws are hallmarks of equilibrium phase transitions and critical phenomena. However, extending these concepts to non-equilibrium systems is an outstanding challenge. Despite recent progress in the study of dynamical phases, the universality classes and scaling laws for non-equilibrium phenomena are far less understood than those in equilibrium. In this work, using a trapped-ion quantum simulator with single-spin resolution, we investigate the non-equilibrium nature of critical fluctuations following a quantum quench to the critical point. We probe the scaling of spin fluctuations after a series of quenches to the critical Hamiltonian of a long-range Ising model. With systems of up to 50 spins, we show that the amplitude and timescale of the post-quench fluctuations scale with system size with distinct universal critical exponents, depending on the quench protocol. While a generic quench can lead to thermal critical behavior, we find that a second quench from one critical state to another (i.e.~a double quench) results in a new universal non-equilibrium behavior, identified by a set of critical exponents distinct from their equilibrium counterparts. Our results demonstrate the ability of quantum simulators to explore universal scaling beyond equilibrium.

Quantum computers promise to solve problems that are intractable for classical computers, but qubits are vulnerable to many sources of error, limiting the depth of the circuits that can be reliably executed on today's quantum hardware. Quantum error correction has been proposed as a solution to this problem, whereby quantum information is protected by encoding it into a quantum error-correcting code. But protecting quantum information is not enough, we must also process the information using logic gates that are robust to faults that occur during their execution. One method for processing information fault-tolerantly is to use quantum error-correcting codes that have logical gates with a tensor product structure (transversal gates), making them naturally fault-tolerant. Here, we test the performance of a code with such transversal gates, the [[8,3,2]] color code, using trapped-ion and superconducting hardware. We observe improved performance (compared to no encoding) for encoded circuits implementing non-Clifford gates, a class of gates that are essential for achieving universal quantum computing. In particular, we find improved performance for an encoded circuit implementing the control-control $Z$ gate, a key gate in Shor's algorithm. Our results illustrate the potential of using codes with transversal gates to implement non-trivial algorithms on near-term quantum hardware.

Levitated diamond particles in high vacuum with internal spin qubits have been proposed for exploring macroscopic quantum mechanics, quantum gravity, and precision measurements. The coupling between spins and particle rotation can be utilized to study quantum geometric phase, create gyroscopes and rotational matter-wave interferometers. However, previous efforts in levitated diamonds struggled with vacuum level or spin state readouts. To address these gaps, we fabricate an integrated surface ion trap with multiple stabilization electrodes. This facilitates on-chip levitation and, for the first time, optically detected magnetic resonance measurements of a nanodiamond levitated in high vacuum. The internal temperature of our levitated nanodiamond remains moderate below $10^{-5}$ Torr. Impressively, we have driven a nanodiamond to rotate up to 20 MHz ($1.2 \times 10^{9}$ rpm), surpassing typical nitrogen-vacancy (NV) center electron spin dephasing rates. Using these NV spins, we observe the effect of the Berry phase arising from particle rotation. In addition, we demonstrate quantum control of spins in a rotating nanodiamond. These results mark an important development in interfacing mechanical rotation with spin qubits, expanding our capacity to study quantum phenomena.

A leading approach to implementing small-scale quantum computers has been to use laser beams, focused to micron spot sizes, to address and entangle trapped ions in a linear crystal. Here we propose a method to implement individually-addressed entangling gate interactions, but driven by microwave fields, with a spatial-resolution of a few microns, corresponding to $10^{-5}$ microwave wavelengths. We experimentally demonstrate the ability to suppress the effect of the state-dependent force using a single ion, and find the required interaction introduces $3.7(4)\times 10^{-4}$ error per emulated gate in a single-qubit benchmarking sequence. We model the scheme for a 17-qubit ion crystal, and find that any pair of ions should be addressable with an average crosstalk error of $\sim 10^{-5}$.

Simulation of quantum systems is notoriously challenging for classical computers, while quantum hardware is naturally well-suited for this task. However, the imperfections of contemporary quantum systems poses a considerable challenge in carrying out accurate simulations over long evolution times. Here we experimentally demonstrate a method for quantum simulations on a small-scale trapped ions-based quantum simulator. Our method enables quantum simulations of programmable spin-Hamiltonians, using only simple global fields, driving all qubits homogeneously and simultaneously. We measure the evolution of a quantum Ising ring and accurately reconstruct the Hamiltonian parameters, showcasing an accurate and high-fidelity simulation. Our method enables a significant reduction in the required control and depth of quantum simulations, thus generating longer evolution times with higher accuracy.

We propose a faster digital quantum algorithm for portfolio optimization using the digitized-counterdiabatic quantum optimization (DCQO) paradigm in the impulse regime, that is, where the counterdiabatic terms are dominant. Our approach notably reduces the circuit depth requirement of the algorithm and enhances the solution accuracy, making it suitable for current quantum processors. We apply this protocol to a real-case scenario of portfolio optimization with 20 assets, using purely quantum and hybrid classical-quantum paradigms. We experimentally demonstrate the advantages of our protocol using up to 20 qubits on an IonQ trapped-ion quantum computer. By benchmarking our method against the standard quantum approximate optimization algorithm and finite-time digitized-adiabatic algorithms, we obtain a significant reduction in the circuit depth by factors of 2.5 to 40, while minimizing the dependence on the classical optimization subroutine. Besides portfolio optimization, the proposed method is applicable to a large class of combinatorial optimization problems.

We report on the first direct mass measurements of the $^{118,119}$Cd and $^{117-119}$In isotopes performed at the Ion Guide Isotope Separator On-Line facility using the JYFLTRAP double Penning trap mass spectrometer. The masses of $^{117}$In and $^{118}$Cd isotopes are in agreement with the literature, while $^{118,119}$In and $^{119}$Cd differ from literature by 49, 13 and 85 keV (6.1, 1.9 and 2.1 standard deviations), respectively. The excitation energy of the $^{118}$In first isomeric state, $E_x = 40.3(25)$ keV, was determined for the first time. The updated mass values removed the fluctuations observed in the two-neutron separation energies and lead to a smoother linear decrease of both isotopic chains. The $\log(ft)$ value for the $^{118}$Cd decay is also found to increase from 3.93(6) to 4.089(8). The reported results indicate an absence of significant structural changes around $N=70$.

We report on a certain class of three-dimensional topological insulators and semimetals protected by spinless $\mathcal{P}\mathcal{T}$ symmetry, hosting an integer-valued bulk invariant. We show using homotopy arguments that these phases host multi-gap topology, providing a realization of a single $\mathbb{Z}$ invariant in three spatial dimensions that is distinct from the Hopf index. We identify this invariant with the Pontryagin index, which describes BPST instantons in particle physics contexts and corresponds to a 3-sphere winding number. We study naturally arising multi-gap linked nodal rings, topologically characterized by split-biquaternion charges, which can be removed by non-Abelian braiding of nodal rings, even without closing a gap. We additionally connect the describing winding number in terms of gauge-invariant combinations of non-Abelian Berry connection elements, indicating relations to Pontryagin characteristic class in four dimensions. These topological configurations are furthermore related to fully non-degenerate multi-gap phases that are characterized by a pair of winding numbers relating to two isoclinic rotations in the case of four bands and can be generalized to an arbitrary number of bands. From a physical perspective, we also analyze the edge states corresponding to this Pontryagin index as well as their dissolution subject to the gap-closing disorder. Finally, we elaborate on the realization of these novel non-Abelian phases, their edge states and linked nodal structures in acoustic metamaterials and trapped-ion experiments.

We report on a cycling scheme for Doppler cooling of trapped OH$^+$ ions using transitions between the electronic ground state $X^3Σ^-$ and the first excited triplet state $A^3Π$. We have identified relevant transitions for photon cycling and repumping, have found that coupling into other electronic states is strongly suppressed, and have calculated the number of photon scatterings required to cool OH$^+$ to a temperature where Raman sideband cooling can take over. In contrast to the standard approach, where molecular ions are sympathetically cooled, our scheme does not require co-trapping of another species and opens the door to the creation of pure samples of cold molecular ions with potential applications in quantum information, quantum chemistry, and astrochemistry. The laser cooling scheme identified for OH$^+$ is efficient despite the absence of near-diagonal Franck-Condon factors, suggesting that broader classes of molecules and molecular ions are amenable to laser cooling than commonly assumed.

We report the first direct measurement of the nuclear electron capture (EC) decay $Q$-value of $^{7}$Be $\rightarrow$ $^{7}$Li via high-precision Penning trap mass spectrometry (PTMS). This was performed using the LEBIT Penning trap located at the National Superconducting Cyclotron Laboratory/Facility for Rare Isotope Beams (NSCL/FRIB) using the newly commissioned Batch-Mode Ion-Source (BMIS) to deliver the unstable $^{7}$Be$^{+}$ samples. With a measured value of $Q_{EC}$ = 861.963(23) keV this result is also three times more precise than any previous determination of this quantity. This improved precision, and accuracy of the $^7$Be EC decay $Q$-value is critical for ongoing experiments that measure the recoiling nucleus in this system as a signature to search for beyond Standard Model (BSM) neutrino physics using $^7$Be-doped superconducting sensors.

Precision laser spectroscopy in the extreme ultraviolet of the 1S-2S two-photon transition in singly-ionized helium is a promising route for tests of fundamental physics. We demonstrate laser excitation of this transition in an atomic beam of $^3$He, based on an amplified frequency comb pulse at 790 nm combined with its 25$^{\text{th}}$ harmonic at 32 nm. A clear resonance is observed with a maximum excitation probability of close to 10$^{-4}$ per pulse, and the results are well described by our simulations. This paves the way for high-precision Ramsey-comb spectroscopy of a single helium ion in a Paul trap.

Geometry and dimensionality have played crucial roles in our understanding of the fundamental laws of nature, with examples ranging from curved space-time in general relativity to modern theories of quantum gravity. In quantum many-body systems, the entanglement structure can change if the constituents are connected differently, leading to altered bounds for correlation growth and difficulties for classical computers to simulate large systems. While a universal quantum computer can perform digital simulations, an analog-digital hybrid quantum processor offers advantages such as parallelism. Here, we engineer a class of high-dimensional Ising interactions using a linear one-dimensional (1D) ion chain with up to 8 qubits through stroboscopic sequences of commuting Hamiltonians. %with a thorough understanding of the error sources and deviation from the target Hamiltonian. In addition, we extend this method to non-commuting circuits and demonstrate the quantum XY and Heisenberg models using Floquet periodic drives with tunable symmetries. The realization of higher dimensional spin models offers new opportunities ranging from studying topological phases of matter or quantum spin glasses to future fault-tolerant quantum computation.

We numerically investigate a hybrid trapping architecture for 2D ion crystals using static electrode voltages and optical cavity fields for in-plane and out-of-plane confinements, respectively. By studying the stability of 2D crystals against 2D-3D structural phase transitions, we identify the necessary trapping parameters for ytterbium ions. Multiple equilibrium configurations for 2D crystals are possible, and we analyze their stability by estimating potential barriers between them. We find that scattering to anti-trapping states limits the trapping lifetime, which is consistent with recent experiments employing other optical trapping architectures. These 2D ion crystals offer an excellent platform for quantum simulation of frustrated spin systems, benefiting from their 2D triangular lattice structure and phonon-mediated spin-spin interactions. Quantum information processing with tens of ions is feasible in this scheme with current technologies.

We report on the precise mass measurement of the $^{173}$Hf isotope performed at the Ion Guide Isotope Separator On-Line facility using the JYFLTRAP double Penning trap mass spectrometer. The new mass-excess value, ${\mathrm{ME} = -55390.8(30)}$ keV, is in agreement with the literature while being nine times more precise. The newly determined $^{173}$Hf electron-capture $Q$ value, $Q_{EC} = 1490.2(34)$ keV, allows us to firmly reject the population of an excited state at 1578 keV in $^{173}$Lu and 11 transitions tentatively assigned to the decay of $^{173}$Hf. Our refined mass value of $^{173}$Hf reduces mass-related uncertainties in the reaction rate of $^{174}$Hf$(γ,n)^{173}$Hf. Thus, the rate for the main photodisintegration destruction channel of the $p$ nuclide $^{174}$Hf in the relevant temperature region for the $γ$ process is better constrained.

Trapped ions in radio-frequency traps are among the leading approaches for realizing quantum computers, due to high-fidelity quantum gates and long coherence times. However, the use of radio-frequencies presents a number of challenges to scaling, including requiring compatibility of chips with high voltages, managing power dissipation and restricting transport and placement of ions. By replacing the radio-frequency field with a 3 T magnetic field, we here realize a micro-fabricated Penning ion trap which removes these restrictions. We demonstrate full quantum control of an ion in this setting, as well as the ability to transport the ion arbitrarily in the trapping plane above the chip. This unique feature of the Penning micro-trap approach opens up a modification of the Quantum CCD architecture with improved connectivity and flexibility, facilitating the realization of large-scale trapped-ion quantum computing, quantum simulation and quantum sensing.

Cooling the motion of trapped ions to near the quantum ground state is crucial for many applications in quantum information processing and quantum metrology. However, certain motional modes of trapped-ion crystals can be difficult to cool due to weak or zero interaction between the modes and the cooling radiation, typically laser beams. We overcome this challenge by coupling a mode with weak cooling radiation interaction to one with strong cooling radiation interaction using parametric modulation of the trapping potential, thereby enabling indirect cooling of the former. In this way, we demonstrate near-ground-state cooling of motional modes with weak or zero cooling radiation interaction in multi-ion crystals of the same and mixed ion species, specifically $^9$Be$^+$-$^9$Be$^+$, $^9$Be$^+$-$^{25}$Mg$^+$, and $^9$Be$^+$-$^{25}$Mg$^+$-$^9$Be$^+$ crystals. This approach can be generally applied to any Coulomb crystal where certain motional modes cannot be directly cooled efficiently, including crystals containing molecular ions, highly-charged ions, charged fundamental particles, or charged macroscopic objects.

We report laser cooling and trapping of $^{224}$Ra$^+$ ions. This was realized via two-step photoionization loading of radium into an ion trap. A robust source for $^{224}$Ra atoms, which have a 3.6-day half-life, was realized with an effusive oven containing $^{228}$Th, which has a 1.9-yr half-life, which continuously generates $^{224}$Ra via its $α$-decay. We characterized the efficacy of this source and found that after depleting built-up radium the thorium decay provides a continuous source of radium atoms suitable for ion trapping. The vacuum system has been sealed for more than 6 months and continues to trap ions on demand. We also report a measurement of the $^{224}$Ra $7s^2\ ^1$S$_0 \rightarrow 7s7p\ ^1$P$_1$ transition frequency: 621 043 830(60) MHz, which is helpful for efficient photoionization. With this measurement and previous isotope shift measurements we find that the frequency of the same transition in $^{226}$Ra is 621 037 830(60) MHz, which disagrees with the most precise measurement, 621 038 489(15) MHz, which is used for the recommended value in the National Institute of Standards and Technology Atomic Spectra Database.

High-fidelity operation of quantum computers requires precise knowledge of the physical system through characterization. For motion-mediated entanglement generation in trapped ions, it is crucial to have precise knowledge of the motional-mode parameters such as the mode frequencies and the Lamb-Dicke parameters. Unfortunately, the state-of-the-art mode-characterization schemes do not easily render the mode parameters in a sufficiently scalable and accurate fashion, due to the unwanted excitation of adjacent modes in the frequency space when targeting a single mode, an effect known as the \textit{cross-mode coupling}. Here, we develop an alternative scheme that leverages the degrees of freedom in pulse design for the characterization experiment such that the effects of the cross-mode coupling is actively silenced. Further, we devise stabilization methods to accurately characterize the Lamb-Dicke parameters even when the mode frequencies are not precisely known due to experimental drifts or characterization inaccuracies. We extensively benchmark our scheme in simulations of a three-ion chain and discuss the parameter regimes in which the shaped pulses significantly outperform the traditional square pulses.

We perform entanglement of spin and motional degrees of freedom of a single, ground-state trapped ion through the application of a $16$ ps laser pulse. The duration of the interaction is significantly shorter than both the motional timescale ($30$ $μ$s) and spin precession timescale ($1$ ns) , demonstrating that neither sets a fundamental speed limit on this operation for quantum information processing. Entanglement is demonstrated through the collapse and revival of spin coherence as the spin components of the wavefunction separate and recombine in phase space. We infer the fidelity of these single qubit operations to be $(97^{+3}_{-4})\%$.

Quantum computers based on crystals of trapped ions are a prominent technology for quantum computation. A unique feature of trapped ions is their long-range Coulomb interactions, which can be exploited to realize large-scale multiqubit entanglement gates. However, scaling up the number of qubits, $N$, in these systems, while retaining high-fidelity and high-speed operations, is challenging. Specifically, designing multiqubit entanglement gates in long ion crystals of hundreds of ions involves an NP-hard optimization problem, rendering scale-up not only a technological challenge, but also a conceptual challenge. Here we introduce a method that mitigates this challenge, effectively allowing for a polynomial-time design of fast, robust, and programmable entanglement gates, acting on the entire ion-crystal. We show that while the number of simultaneous entanglement operations scales as $N^2$, the gate duration scales as $N$, leading to a scaling advantage. We use our methods to investigate the drive-power requirements and susceptibility to noise and errors of these multiqubit gates. Our method delineates a path towards scaling up quantum computers based on ion-crystals with hundreds of qubits.

Trapped ions have emerged as a front runner in quantum information processing due to their identical nature, all-to-all connectivity, and high fidelity quantum operations. As current trapped ion technologies are scaled, it will be important to improve the efficiency of loading ions, which is currently the slowest process in operating a trapped ion quantum computer. Here, we compare two isotope-selective photoionization schemes for loading $^{138}\mathrm{Ba}^+$ ions. We show that a two-step photoionization scheme ending in an autoionizing transition increases the ion loading rate nearly an order of magnitude compared to an established technique which does not excite an autoionizing state. The only additional technology required to implement the autoionizing transition is a commercial diode laser. Our technique can be extended to all isotopes of barium, and autoionizing resonances exist in every species currently used for trapped ion quantum processing, making this a promising technique to drastically increase the loading rates for all trapped ion computers.

Current noisy intermediate-scale quantum (NISQ) trapped-ion devices are subject to errors which can significantly impact the accuracy of calculations if left unchecked. A form of error mitigation called zero noise extrapolation (ZNE) can decrease an algorithm's sensitivity to these errors without increasing the number of required qubits. Here, we explore different methods for integrating this error mitigation technique into the Variational Quantum Eigensolver (VQE) algorithm for calculating the ground state of the HeH+ molecule at 0.8 Angstrom in the presence of realistic noise. Using the Quantum Scientific Computing Open User Testbed (QSCOUT) trapped-ion device, we test three methods of scaling noise for extrapolation: time-stretching the two-qubit gates, scaling the sideband amplitude parameter, and inserting two-qubit gate identity operations into the ansatz circuit. We find time-stretching and sideband amplitude scaling fail to scale the noise on our particular hardware in a way that can be directly extrapolated to zero noise. Scaling our noise with global gate identity insertions and extrapolating after variational optimization, we achieve an estimate of the ground state energy within -0.004 +- 0.04 Hartree; outside chemical accuracy, but greatly improved over our non-error-mitigated estimate with error 0.127 +- 0.008 Hartree. Our results show that the efficacy of this error mitigation technique depends on choosing the correct implementation for a given device architecture.

We propose and experimentally demonstrate an analog scheme for generating XY-type ($J_{ij}^x σ_x^i σ_x^j \;$ + $J_{ij}^y σ_y^i σ_y^j \;$) Hamiltonians on trapped ion spins with independent control over the $J_{ij}^x$ and $J_{ij}^y$ terms. The Ising-type interactions $σ_x^i σ_x^j \;$ and $σ_y^i σ_y^j \;$ are simultaneously generated by employing two spin-dependent forces operating in parallel on the same set of normal modes. We analytically calculate the region of validity of this scheme, and provide numerical and experimental validation with $^{171}\rm{Yb}^+\;$ ions. This scheme inherits the programmability and scalability of the Ising-type interactions with trapped ions that have been explored in numerous quantum simulation experiments. Our approach extends the capabilities of existing trapped ion quantum simulators to access a large class of spin Hamiltonians relevant for exploring exotic quantum phases such as superfluidity and spin liquids.

Fascinating in art and science, the ability to float is also captivating and relevant in practical applications, such as Penning and ion traps that are fundamental to quantum computing. In this work, we first reproduce the classic water bridge by glycerol and, as it breaks down due to thermal agitation, observe that a lump of glycerol with mass~2.5 g can float and exhibit near-periodic oscillations. Through experiments, finite element analysis, and simulations, we discover that the stability of the floating droplet is made possible by the interaction between three mechanisms: Deformation, Plasma, and Kelvin force. Note that glycerol cluster (GC) falls in the class of adaptive materials that can change their properties or behavior in response to varying environmental conditions, i.e., stimuli-responsive. Furthermore, the stimuli, modified by the deformation of GC, collaborate with it to create this unique simple, yet stable, floating system. Backed up by simulations, this process, operated by only a single pair of electrodes, holds the potential to develop a simple yet powerful railgun.

Coulomb crystals of cold trapped ions are a leading platform for the realisation of quantum processors and quantum simulations and, in quantum metrology, for the construction of optical atomic clocks and for fundamental tests of the Standard Model. For these applications, it is not only essential to cool the ion crystal in all its degrees of freedom down to the quantum ground state, but also to be able to determine its temperature with a high accuracy. However, when a large ground-state cooled crystal is interrogated for thermometry, complex many-body interactions take place, making it challenging to accurately estimate the temperature with established techniques. In this work we present a new thermometry method tailored for ion crystals. The method is applicable to all normal modes of motion and does not suffer from a computational bottleneck when applied to large ion crystals. We test the temperature estimate with two experiments, namely with a 1D linear chain of 4 ions and a 2D crystal of 19 ions and verify the results, where possible, using other methods. The results show that the new method is an accurate and efficient tool for thermometry of ion crystals.

In the noisy intermediate-scale quantum era, variational algorithms have become a standard approach to solving quantum many-body problems. Here, we present variational quantum eigensolver (VQE) results of selected oxygen isotopes within the shell model description. The aim of the present work is to locate the neutron drip line of the oxygen chain using unitary coupled cluster (UCC) type ansatze with different microscopic interactions (DJ16, JISP16, and N3LO), in addition to a phenomenological USDB interaction. While initially infeasible to execute on contemporary quantum hardware, the size of the problem is reduced significantly using qubit tapering techniques in conjunction with custom circuit design and optimization. The optimal values of ansatz parameters from classical simulation are taken for the DJ16 interaction, and the tapered circuits are run on IonQ's Aria, a trapped-ion quantum computer. After applying gate error mitigation for three isotopes, we reproduced exact ground state energies within a few percent error. The post-processed results from hardware also clearly show $^{24}$O as the drip line nucleus of the oxygen chain. Future improvements in quantum hardware could make it possible to locate drip lines of heavier nuclei.

The $β^-$ decay $Q$-value of $^{136}$Cs ($J^π= 5^+$, $t_{1/2} \approx 13$~days) was measured with the JYFLTRAP Penning trap setup at the Ion Guide Isotope Separator On-Line (IGISOL) facility of the University of Jyväskylä, Finland. The mono-isotopic samples required in the measurements were prepared with a new scheme utilised for the cleaning, based on the coupling of dipolar excitation with Ramsey's method of time-separated oscillatory fields and the phase-imaging ion-cyclotron-resonance (PI-ICR) technique. The $Q$ value is determined to be 2536.83(45) keV, which is $\sim$4 times more precise and 11.4(20) keV ($\sim$ 6$σ$) smaller than the adopted value in the most recent Atomic Mass Evaluation AME2020. The daughter, $^{136}$Ba, has a 4$^+$ state at 2544.481(24) keV and a $3^-$ state at 2532.653(23) keV, both of which can potentially be ultralow $Q$-value end-states for the $^{136}$Cs decay. With our new ground-to-ground state $Q$ value, the decay energies to these two states become -7.65(45) keV and 4.18(45) keV, respectively. The former is confirmed to be negative at the level of $\sim$ 17$σ$, which verifies that this transition is not a suitable candidate for neutrino mass determination. On the other hand, the slightly negative $Q$ value makes this transition an interesting candidate for the study of virtual $β$-$γ$ transitions. The decay to the 3$^{-}$ state is validated to have a positive low $Q$ value which makes it a viable candidate for neutrino mass determination. For this transition, we obtained a shell-model-based half-life estimate of $2.1_{-0.8}^{+1.6}\times10^{12}$ yr.

Ultracold molecules, because of their rich internal structures and interactions, have been proposed as a promising platform for quantum science and precision measurement. Direct laser-cooling promises to be a rapid and efficient way to bring molecules to ultracold temperatures. For trapped molecules, laser-cooling to the quantum motional ground state remains an outstanding challenge. A technique capable of reaching the motional ground state is Raman sideband cooling, first demonstrated in trapped ions and atoms. In this work, we demonstrate for the first time Raman sideband cooling of molecules. Specifically, we demonstrate 3D Raman cooling for single CaF molecules trapped in an optical tweezer array, achieving average radial (axial) motional occupation as low as $\bar{n}_r=0.27(7)$ ($\bar{n}_z=7.0(10)$). Notably, we measure a 1D ground state fraction as high as 0.79(4), and a motional entropy per particle of $s = 4.9(3)$, the lowest reported for laser-cooled molecules to date. These lower temperatures could enable longer coherence times and higher fidelity molecular qubit gates desirable for quantum information processing and quantum simulation. With further improvements, Raman cooling could also be a new route towards molecular quantum degeneracy applicable to many laser-coolable molecular species including polyatomic ones.

We implement sympathetic cooling of highly charged ions (HCI) by fully enclosing a linear Paul trap within a superconducting radio-frequency resonator. A quantization magnetic field applied while cooling down into the superconducting state remains present in the trap for centuries and external electromagnetic fluctuations are greatly suppressed. A magnetic field decay rate at the 10$^{-10}$ s$^{-1}$ level is found using trapped Doppler-cooled Be$^+$ ions as hyperfine-structure (hfs) qubits. Ramsey interferometry and spin-echo measurements on magnetically-sensitive hfs transitions yield coherence times of >400 ms, showing excellent passive shielding at frequencies down to DC. For sympathetic cooling of HCI, we extract them from an electron beam ion trap (EBIT) and co-crystallize one together with Doppler-cooled Be$^+$ ions. By subsequently ejecting all but one Be$^+$ ions, we prepare single HCI for quantum logic spectroscopy towards frequency metrology and qubit operations with a great variety of HCI species.

The quantum approximate optimization algorithm (QAOA) has the potential to approximately solve complex combinatorial optimization problems in polynomial time. However, current noisy quantum devices cannot solve large problems due to hardware constraints. In this work, we develop an algorithm that decomposes the QAOA input problem graph into a smaller problem and solves MaxCut using QAOA on the reduced graph. The algorithm requires a subroutine that can be classical or quantum--in this work, we implement the algorithm twice on each graph. One implementation uses the classical solver Gurobi in the subroutine and the other uses QAOA. We solve these reduced problems with QAOA. On average, the reduced problems require only approximately 1/10 of the number of vertices than the original MaxCut instances. Furthermore, the average approximation ratio of the original MaxCut problems is 0.75, while the approximation ratios of the decomposed graphs are on average of 0.96 for both Gurobi and QAOA. With this decomposition, we are able to measure optimal solutions for ten 100-vertex graphs by running single-layer QAOA circuits on the Quantinuum trapped-ion quantum computer H1-1, sampling each circuit only 500 times. This approach is best suited for sparse, particularly $k$-regular graphs, as $k$-regular graphs on $n$ vertices can be decomposed into a graph with at most $\frac{nk}{k+1}$ vertices in polynomial time. Further reductions can be obtained with a potential trade-off in computational time. While this paper applies the decomposition method to the MaxCut problem, it can be applied to more general classes of combinatorial optimization problems.

We present experimental demonstrations of accurate and unambiguous single-shot discrimination between three quantum channels using a single trapped $^{40}\text{Ca}^{+}$ ion. The three channels cannot be distinguished unambiguously using repeated single channel queries, the natural classical analogue. We develop techniques for using the 6-dimensional $\text{D}_{5/2}$ state space for quantum information processing, and we implement protocols to discriminate quantum channel analogues of phase shift keying and amplitude shift keying data encodings used in classical radio communication. The demonstrations achieve discrimination accuracy exceeding $99\%$ in each case, limited entirely by known experimental imperfections.

We investigate speeding up of relaxation of Markovian open quantum systems with the Liouvillian exceptional point (LEP), where the slowest decay mode degenerate with a faster decay mode. The degeneracy significantly increases the gap of the Liouvillian operator, which determines the timescale of such systems in converging to stationarity, and hence accelerates the relaxation process. We explore an experimentally relevant three level atomic system, whose eigenmatrices and eigenspectra are obtained completely analytically. This allows us to gain insights in the LEP and examine respective dynamics with details. We illustrate that the gap can be further widened through Floquet engineering, which further accelerates the relaxation process. Finally, we extend this approach to analyze laser cooling of trapped ions, where vibrations (phonons) couple to the electronic states. An optimal cooling condition is obtained analytically, which agrees with both existing experiments and numerical simulations. Our study provides analytical insights in understanding LEP, as well as in controlling and optimizing dissipative dynamics of atoms and trapped ions.

One of the most formidable challenges of scaling up quantum computers is that of control signal delivery. Today's small-scale quantum computers typically connect each qubit to one or more separate external signal sources. This approach is not scalable due to the I/O limitations of the qubit chip, necessitating the integration of control electronics. However, it is no small feat to shrink control electronics into a small package that is compatible with qubit chip fabrication and operation constraints without sacrificing performance. This so-called "wiring challenge" is likely to impact the development of more powerful quantum computers even in the near term. In this paper, we address the wiring challenge of trapped-ion quantum computers. We describe a control architecture called WISE (Wiring using Integrated Switching Electronics), which significantly reduces the I/O requirements of ion trap quantum computing chips without compromising performance. Our method relies on judiciously integrating simple switching electronics into the ion trap chip - in a way that is compatible with its fabrication and operation constraints - while complex electronics remain external. To demonstrate its power, we describe how the WISE architecture can be used to operate a fully connected 1000-qubit trapped ion quantum computer using ~ 200 signal sources at a speed of ~ 40 - 2600 quantum gate layers per second.

Cooling of systems to sub-kelvin temperatures is usually done using either a cold bath of particles or spontaneous photon scattering from a laser field; in either case, cooling is driven by interaction with a well-ordered, cold (i.e. low entropy) system. However, there have recently been several schemes proposed for ``cooling by heating,'' in which raising the temperature of some mode drives the cooling of the desired system faster. We discuss how to cool a trapped ion to its motional ground state using unfiltered sunlight at $5800\,\mathrm{K}$ to drive the cooling. We show how to treat the statistics of thermal light in a single-mode fiber for delivery to the ion, and show experimentally how the black-body spectrum is strongly modified by being embedded in quasi-one-dimension. Quantitative estimates for the achievable cooling rate with our measured fiber-coupled, low-dimensional sunlight show promise for demonstrating this implementation of cooling by heating.

The spontaneous breaking of time translation symmetry has led to the discovery of a new phase of matter - the discrete time crystal. Discrete time crystals exhibit rigid subharmonic oscillations, which result from a combination of many-body interactions, collective synchronization, and ergodicity breaking. This Colloquium reviews recent theoretical and experimental advances in the study of quantum and classical discrete time crystals. We focus on the breaking of ergodicity as the key to discrete time crystals and the delaying of ergodicity as the source of numerous phenomena that share many of the properties of discrete time crystals, including the AC Josephson effect, coupled map lattices, and Faraday waves. Theoretically, there exists a diverse array of strategies to stabilize time crystalline order in both closed and open systems, ranging from localization and prethermalization to dissipation and error correction. Experimentally, many-body quantum simulators provide a natural platform for investigating signatures of time crystalline order; recent work utilizing trapped ions, solid-state spin systems, and superconducting qubits will be reviewed. Finally, this Colloquium concludes by describing outstanding challenges in the field and a vision for new directions on both the experimental and theoretical fronts.

We present a detailed scheme for the analog quantum simulation of $\mathbb{Z}_2$ gauge theories in crystals of trapped ions, which exploits a more efficient hybrid encoding of the gauge and matter fields using the native internal and motional degrees of freedom. We introduce a versatile toolbox based on parametric excitations corresponding to different spin-motion-coupling schemes that induce a tunneling of the ions vibrational excitations conditioned to their internal qubit state. This building block, when implemented with a single trapped ion, corresponds to a minimal $\mathbb{Z}_2$ gauge theory, where the qubit plays the role of the gauge field on a synthetic link, and the vibrational excitations along different trap axes mimic the dynamical matter fields two synthetic sites, each carrying a $\mathbb{Z}_2$ charge. To evaluate their feasibility, we perform numerical simulations of the state-dependent tunneling using realistic parameters, and identify the leading sources of error in future experiments. We discuss how to generalise this minimal case to more complex settings by increasing the number of ions, moving from a single link to a $\mathbb{Z}_2$ plaquette, and to an entire $\mathbb{Z}_2$ chain. We present analytical expressions for the gauge-invariant dynamics and the corresponding confinement, which are benchmarked using matrix product state simulations.

We use electronic microwave control methods to implement addressed single-qubit gates with high speed and fidelity, for $^{43}\text{Ca}^{+}$ hyperfine "atomic clock" qubits in a cryogenic (100K) surface trap. For a single qubit, we benchmark an error of $1.5$ $\times$ $10^{-6}$ per Clifford gate (implemented using $600~\text{ns}$ $π/2$-pulses). For two qubits in the same trap zone (ion separation $5~μ\text{m}$), we use a spatial microwave field gradient, combined with an efficient 4-pulse scheme, to implement independent addressed gates. Parallel randomized benchmarking on both qubits yields an average error $3.4$ $\times$ $10^{-5}$ per addressed $π/2$-gate. The scheme scales theoretically to larger numbers of qubits in a single register.

The reaction of the acetylene cation (C2H2+) with acetonitrile (CH3CN) is measured in a linear Paul ion trap coupled to a time-of-flight mass spectrometer. C2H2+ and CH3CN are both noted for their astrochemical abundance and predicted relevance for understanding prebiotic chemistry. The observed primary products are c-C3H3+, C3H4+ and C2NH3+. The latter two products react with excess CH3CN to form the secondary product C2NH4+, protonated acetonitrile. The molecular formula of these ionic products can be verified with the aid of isotope substitution via deuteration of the reactants. Primary product reaction pathways and thermodynamics are investigated with quantum chemical calculations and demonstrate exothermic pathways to two isomers of C2NH3+, two isomers of C3H4+, and the cyclopropenyl cation c-C3H3+. This study deepens our understanding of the dynamics and products of a pertinent ion-molecule reaction between two astrochemically abundant molecules in conditions that mimic those of the interstellar medium.

All laser-driven entangling operations for trapped-ion qubits have hitherto been performed without control of the optical phase of the light field, which precludes independent tuning of the carrier and motional coupling. By placing $^{88}$Sr$^+$ ions in a $λ=674$ nm standing wave, whose relative position is controlled to $\approxλ/100$, we suppress the carrier coupling by a factor of $18$, while coherently enhancing the spin-motion coupling. We experimentally demonstrate that the off-resonant carrier coupling imposes a speed limit for conventional traveling-wave Mølmer-Sørensen gates; we use the standing wave to surpass this limit and achieve a gate duration of $15\ μ$s, restricted by the available laser power.

Non-Abelian topological order (TO) is a coveted state of matter with remarkable properties, including quasiparticles that can remember the sequence in which they are exchanged. These anyonic excitations are promising building blocks of fault-tolerant quantum computers. However, despite extensive efforts, non-Abelian TO and its excitations have remained elusive, unlike the simpler quasiparticles or defects in Abelian TO. In this work, we present the first unambiguous realization of non-Abelian TO and demonstrate control of its anyons. Using an adaptive circuit on Quantinuum's H2 trapped-ion quantum processor, we create the ground state wavefunction of $D_4$ TO on a kagome lattice of 27 qubits, with fidelity per site exceeding $98.4\%$. By creating and moving anyons along Borromean rings in spacetime, anyon interferometry detects an intrinsically non-Abelian braiding process. Furthermore, tunneling non-Abelions around a torus creates all 22 ground states, as well as an excited state with a single anyon -- a peculiar feature of non-Abelian TO. This work illustrates the counterintuitive nature of non-Abelions and enables their study in quantum devices.

We report the first hybrid matter-photon implementation of verifiable blind quantum computing. We use a trapped-ion quantum server and a client-side photonic detection system networked via a fibre-optic quantum link. The availability of memory qubits and deterministic entangling gates enables interactive protocols without post-selection - key requirements for any scalable blind server, which previous realisations could not provide. We quantify the privacy at <~0.03 leaked classical bits per qubit. This experiment demonstrates a path to fully verified quantum computing in the cloud.

Trapped ions are one of the leading candidates for scalable and long-distance quantum networks because of their long qubit coherence time, high fidelity single- and two-qubit gates, and their ability to generate photons entangled with the qubit state of the ion. One method for creating ion-photon entanglement is to exploit optically transitions from the P_(1/2) to S_(1/2) levels, which naturally emit spin-photon entangled states. But these optical transitions typically lie in the ultra-violet and visible wavelength regimes. These wavelengths exhibit significant fiber-optic propagation loss, thereby limiting the transfer of quantum information to tens of meters. Quantum frequency conversion is essential to convert these photons to telecom wavelengths so that they can propagate over long distances in fiber-based networks, as well as for compatibility with the vast number of telecom-based opto-electronic components. Here, we generate O-band telecom photons via a low noise quantum frequency conversion scheme from photons emitted from the P_(1/2) to S_(1/2) dipole transition of a trapped barium ion. We use a two-stage quantum frequency conversion scheme to achieve a frequency shift of 375.4 THz between the input visible photon and the output telecom photon achieving a conversion efficiency of 11%. We attain a signal-to-background ratio of over 100 for the converted O-band telecom photon with background noise less than 15 counts/sec. These results are an important step toward achieving trapped ion quantum networks over long distances for distributed quantum computing and quantum communication.

Entangled coherent states play pivotal roles in various fields such as quantum computation, quantum communication, and quantum sensing. We experimentally demonstrate the generation of entangled coherent states with the two-dimensional motion of a trapped ion system. Using Raman transitions with appropriate detunings, we simultaneously drive the red and blue sidebands of the two transverse axes of a single trapped ion and observe multi-periodic entanglement and disentanglement of its spin and two-dimensional motion. Then, by measuring the spin state, we herald entangled coherent states of the transverse motions of the trapped ion and observe the corresponding modulation in the parity of the phonon distribution of one of the harmonic oscillators. Lastly, we trap two ions in a linear chain and realize Molmer-Sorensen gate using two-dimensional motion.

The spin-boson model, describing a two-level system strongly coupled to a bosonic bath, is extensively studied as a paradigmatic dissipative quantum system, exhibiting rich dynamical behavior and even a localization transition in the strong coupling regime. Here, we additionally consider dephasing as a source of Markovian dissipation on top of the non-Markovian dynamics due to an Ohmic bath, and investigate the dynamics of the spin. We show that the characteristic frequency of the spin dynamics, while strongly renormalized by the bosonic bath, changes in a simple fashion (or doesn't change at all) with dephasing. To obtain these results, we develop an exact non-perturbative method known as the stochastic Schrödinger equation, mimicking the Ohmic bath via a stochastic magnetic field combined with the Lindblad quantum master equation due to dephasing, which allows us to numerically compute the dynamics. Furthermore, we derive weak-coupling analytic results utilizing the well-known non-interacting blip approximation. Our findings are relevant to quantum simulation of the spin-boson model in the regime of strong coupling in trapped ions and circuit QED architectures among others.

In cross-beam energy transfer (CBET), the interference of two laser beams ponderomotively drives an ion-acoustic wave that coherently scatters light from one beam into the other. This redirection of laser beam energy can severely inhibit the performance of direct-drive inertial confinement fusion (ICF) implosions. To assess the role of nonlinear and kinetic processes in direct-drive-relevant CBET, the energy transfer between two laser beams in the plasma conditions of an ICF implosion at the OMEGA laser facility was modeled using particle-in-cell simulations. For typical laser beam intensities, the simulations are in excellent agreement with linear kinetic theory, indicating that nonlinear processes do not play a role in direct-drive implosions. At higher intensities, CBET can be modified by pump depletion, backward stimulated Raman scattering, or ion trapping, depending on the plasma density.

The phenomenon of confinement is well known in high-energy physics and can also be realized for low-energy domain-wall excitations in one-dimensional quantum spin chains. A bound state consisting of two domain-walls can behave like a meson, and in a recent work of Vovrosh et al. [PRX Quantum 3, 040309 (2022)] , it was demonstrated that a pair of mesons could dynamically form a meta-stable confinement-induced bound state (consisting of four domain-walls) akin to a hadronic state. However, the protocol discussed in Vovrosh et al. [PRX Quantum 3, 040309 (2022)] involving the use of interactions with characteristically non-monotonic distance dependence is not easy to come by in nature, thus, posing a challenge for its experimental realization. In this regard, Rydberg atoms can provide the required platform for simulating confinement-related physics. We exploit the flexibility offered by interacting Rydberg-dressed atoms to engineering modified spin-spin interactions for the one-dimensional transverse field Ising model. Our numerical simulations show how Rydberg-dressed interactions can give rise to a variety of effective potentials that are suitable for hadron formation, which opens the possibility of simulating confinement physics with Rydberg platforms as a viable alternative to current trapped-ion experiments.

This work investigates the out-of-equilibrium dynamics of dipole and higher-moment conserving systems with long-range interactions, drawing inspiration from trapped ion experiments in strongly tilted potentials. We introduce a hierarchical sequence of multipole-conserving models characterized by power-law decaying couplings. Although the moments are always globally conserved, adjusting the power-law exponents of the couplings induces various regimes in which only a subset of multipole moments are effectively locally conserved. We examine the late-time hydrodynamics analytically and numerically using an effective classical framework, uncovering a rich dynamical phase diagram that includes subdiffusion, conventional diffusion, and Lévy flights. Our results are unified in an analytic reciprocal relationship that captures the nested hierarchy of hydrodynamics in multipole conserving systems where only a subset of the moments are locally conserved. Moreover, we extend our findings to higher dimensions and explore the emergence of long-time scales, reminiscent of pre-thermal regimes, in systems with low charge density. Lastly, we corroborate our results through state-of-the-art numerical simulations of a fully quantum long-range dipole-conserving system and discuss their relevance to trapped-ion experimental setups.

Quantum theory provides rules governing much of the microscopic world, and among its counter-intuitive consequences are correlations that exceed the bounds from local, classical theories. In two-level quantum systems - qubits - unitary dynamics theoretically limit these spatiotemporal quantum correlations, called Bell/Clauser-Horn-Shimony-Holt or Leggett-Garg inequalities, to $2\sqrt{2}$ or 1.5 respectively. Experiments with state-of-the-art qubits have approached the spatial, Bell and temporal, Leggett-Garg quantum correlation bounds. Here, using a dissipative, trapped $^{40}$Ca$^+$ ion governed by a two-level, non-Hermitian Hamiltonian, we observe temporal correlation values up to 1.703(4) for the Leggett-Garg parameter $K_3$, clearly exceeding the hitherto inviolable Lüder's bound of 1.5. These excesses occur across the exceptional point of the parity-time symmetric Hamiltonian responsible for the qubit's non-unitary, coherent dynamics. Distinct evolution speeds for antipodal qubit states, which violate the unified (Mendelstam-Tamm or Margolus-Levitin) bound $τ_{\textrm{QSL}}$ for the transit time based on quantum speed limit, result in the super-quantum $K_3$ values observed over a wide parameter range. Our results demonstrate that post-selected, coherent dynamics of non-Hermitian Hamiltonians pave the way for enhanced quantum correlations that exceed protocols based on unitary or dissipative dynamics.

Quantum correlations, both spatial and temporal, are the central pillars of quantum mechanics. Over the last two decades, a big breakthrough in quantum physics is its complex extension to the non-Hermitian realm, and dizzying varieties of novel phenomena and applications beyond the Hermitian framework have been uncovered. However, unique features of non-Hermitian quantum correlations, especially in the time domain, still remain to be explored. Here, for the first time, we experimentally achieve this goal by using a parity-time (PT)-symmetric trapped-ion system. The upper limit of temporal quantum correlations, known as the algebraic bound, which has so far not been achieved in the standard measurement scenario, is reached here by approaching the exceptional point (EP), thus showing the unexpected ability of EPs in tuning temporal quantum correlation effects. Our study, unveiling the fundamental interplay of non-Hermiticity, nonlinearity, and temporal quantum correlations, provides the first step towards exploring and utilizing various non-Hermitian temporal quantum effects by operating a wide range of EP devices, which are important for both fundamental studies and applications of quantum EP systems.

We show experimentally that a broad class of interactions involving quantum harmonic oscillators can be made stronger (amplified) using a unitary squeezing protocol. While our demonstration uses the motional and spin states of a single trapped $^{25}$Mg$^{+}$ ion, the scheme applies generally to Hamiltonians involving just a single harmonic oscillator as well as Hamiltonians coupling the oscillator to another quantum degree of freedom such as a qubit, covering a large range of systems of interest in quantum information and metrology applications. Importantly, the protocol does not require knowledge of the parameters of the Hamiltonian to be amplified, nor does it require a well-defined phase relationship between the squeezing interaction and the rest of the system dynamics, making it potentially useful in instances where certain aspects of a signal or interaction may be unknown or uncontrolled.

In this paper, we develop a one-dimensional (1-D), quasineutral, hybrid Vlasov-Maxwell equilibrium model with kinetic ions and massless fluid electrons and derive associated solutions. The model allows for an electrostatic potential that is expressed in terms of the vector potential components through the quasineutrality condition. The equilibrium states are calculated upon solving an inhomogeneous Beltrami equation that determines the magnetic field, where the inhomogeneous term is the current density of the kinetic ions and the homogeneous term represents the electron current density. We show that the corresponding 1-D system is Hamiltonian, with position playing the role of time, and its trajectories have a regular, periodic behavior for ion distribution functions that are symmetric in the two conserved particle canonical momenta. For asymmetric distribution functions, the system is nonintegrable, resulting in irregular and chaotic behavior of the fields. The electron current density can modify the magnetic field phase space structure, inducing orbit trapping and the organization of orbits into large islands of stability. Thus the electron contribution can be responsible for the emergence of localized electric field structures that induce ion trapping. We also provide a paradigm for the analytical construction of hybrid equilibria using a rotating two-dimensional harmonic oscillator Hamiltonian, enabling the calculation of analytic magnetic fields and the construction of the corresponding distribution functions in terms of Hermite polynomials.

This pedagogical article elucidates the fundamentals of trapped-ion quantum computing, which is one of the potential platforms for constructing a scalable quantum computer. The evaluation of a trapped-ion system's viability for quantum computing is conducted in accordance with DiVincenzo's criteria.

Recent advances in experimental methodology enabled studies of the quantum-state and conformational dependence of chemical reactions under precisely controlled conditions in the gas phase. Here, we generated samples of selected gauche and s-trans 2,3-dibromobutadiene (DBB) by electrostatic deflection in a molecular beam and studied their reaction with Coulomb crystals of laser-cooled $\mathrm{Ca^{+}}$ ions in an ion trap. The rate coefficients for the total reaction were found to strongly depend on both the conformation of DBB and the electronic state of $\mathrm{Ca^{+}}$. In the $\mathrm{(4p)~^{2}P_{1/2}}$ and $\mathrm{(3d)~^{2}D_{3/2}}$ excited states of $\mathrm{Ca^{+}}$, the reaction is capture-limited and faster for the gauche conformer due to long-range ion-dipole interactions. In the $\mathrm{(4s)~^{2}S_{1/2}}$ ground state of $\mathrm{Ca^{+}}$, the reaction rate for s-trans DBB still conforms with the capture limit, while that for gauche DBB is strongly suppressed. The experimental observations were analysed with the help of adiabatic capture theory, ab-initio calculations and reactive molecular dynamics simulations on a machine-learned full-dimensional potential energy surface of the system. The theory yields near-quantitative agreement for s-trans-DBB, but overestimates the reactivity of the gauche-conformer compared to the experiment. The present study points to the important role of molecular geometry even in strongly reactive exothermic systems and illustrates striking differences in the reactivity of individual conformers in gas-phase ion-molecule reactions.

Based on the Rb$^+$-Rb hybrid trap, we investigate the effect of ion-atom elastic collisions on the number and temperature of the remaining atoms. We measured the remaining atomic number and temperature as a function of the wavelength and intensity of the ionization laser, and whether the ion trap was turned on. Fittings with a single exponential decay function plus an offset to the number and radius of the remaining atoms are found to be in good agreement. We found a difference in the exponential factor of different wavelengths of ionization laser with the ion trap on or off. We suppose that the presence of electrons affects ion-atom collisions through disorder-induced heating. Our research contributes to a better understanding of how ultracold neutral plasma evolves, particularly the subsequent kinetics of atomic processes, which also serves as a useful reference for high-energy-density plasma.

We analyze electric fields in ion sources generated by quasi-continuous photo-ionization of cold Rb atoms trapped in the focal spot of a near-concentric, in-vacuum cavity for 1064-nm laser light. Ion streams are extracted with an external electric field, ${\bf{F}}$. Stark effects of Rb 57$F$ and of nearby high-angular-momentum Rydberg levels, which exhibit large, linear Stark shifts, are employed to study the net electric-field probability distribution within the ion-source region over an extraction-field range of $0<F<0.35$ V/cm. For $F=0$, we also investigate ion-field-induced Stark spectra of the 60$P_{1/2}$-state, which exhibits a (lesser) quadratic electric-field response that affords a simplified electric-field analysis. Experimental Rydberg spectra are compared with theoretical Stark spectra, which are weighed with net electric-field distributions obtained from classical ion-trajectory simulations that include Coulomb interactions. Experiments and models agree well. At small $F$ and high ion source rates, the field approximately follows a Holtsmark distribution, and the ion streams are degraded by the Coulomb micro-fields. With increasing $F$ and at lower ion source rates, the fields become narrowly distributed around ${\bf{F}}$, resulting in directional ion streams that are less degraded by micro-fields. Our results are of interest for monitoring cold-ion sources for focused-ion-beam applications, where Coulomb interactions are of concern, and for studies of electric fields in cold plasmas.

Recently we developed a local and constructive algorithm based on Lie algebraic methods for compressing Trotterized evolution under Hamiltonians that can be mapped to free fermions. The compression algorithm yields a circuit which scales linearly in the number of qubits, has a depth independent of evolution time and compresses time-dependent Hamiltonians. The algorithm is limited to simple nearest-neighbor spin interactions and fermionic hopping. In this work, we extend our methods to compress evolution with long-range fermionic hopping, thereby enabling the embedding of arbitrary lattices onto a chain of qubits for fermion models. Moreover, we show that controlled time evolution, as well as fermion creation and annihilation operators can also be compressed. We demonstrate our results by adiabatically preparing the ground state for a half-filled fermionic chain, simulating a $4 \times 4$ tight binding model on ibmq washington, and calculating the topological Zak phase on a Quantinuum H1-1 trapped-ion quantum computer. With these new developments, our results enable the simulation of a wider range of models of interest and the efficient compression of subcircuits.

We propose a laser-free method for creation of a phonon two-mode squeezed state and a beam-splitter transformation, using time-varying electric fields and non-linear couplings between the normal modes in a linear ion crystal. Such non-linear Coulomb-mediated interactions between the collective vibrational modes arise under specific trap-frequency conditions in an ion trap. We study the quantum metrological capability for parameter estimation of the two quantum states and show that a Heisenberg limit of precision can be achieved when the initial state with $n$ phonons evolves under the action of the beam-splitter transformation. Furthermore, we show that the phonon non-linearity and the spin-dependent force can be used for creation of a three-qubit Fredkin gate.

Folding of ribozymes into well-defined tertiary structures usually requires divalent cations. How Mg$^{2+}$ ions direct the folding kinetics has been a long-standing unsolved problem because experiments cannot detect the positions and dynamics of ions. To address this problem, we used molecular simulations to dissect the folding kinetics of the Azoarcus ribozyme by monitoring the path each molecule takes to reach the folded state. We quantitatively establish that Mg$^{2+}$ binding to specific sites, coupled with counter-ion release of monovalent cations, stimulate the formation of secondary and tertiary structures, leading to diverse pathways that include direct rapid folding and trapping in misfolded structures. In some molecules, key tertiary structural elements form when Mg$^{2+}$ ions bind to specific RNA sites at the earliest stages of the folding, leading to specific collapse and rapid folding. In others, the formation of non-native base pairs, whose rearrangement is needed to reach the folded state, is the rate-limiting step. Escape from energetic traps, driven by thermal fluctuations, occurs readily. In contrast, the transition to the native state from long-lived topologically trapped native-like metastable states is extremely slow. Specific collapse and formation of energetically or topologically frustrated states occur early in the assembly process.

Periodically driven quantum systems exhibit a diverse set of phenomena but are more challenging to simulate than their equilibrium counterparts. Here, we introduce the Quantum High-Frequency Floquet Simulation (QHiFFS) algorithm as a method to simulate fast-driven quantum systems on quantum hardware. Central to QHiFFS is the concept of a kick operator which transforms the system into a basis where the dynamics is governed by a time-independent effective Hamiltonian. This allows prior methods for time-independent simulation to be lifted to simulate Floquet systems. We use the periodically driven biaxial next-nearest neighbor Ising (BNNNI) model, a natural test bed for quantum frustrated magnetism and criticality, as a case study to illustrate our algorithm. We implemented a 20-qubit simulation of the driven two-dimensional BNNNI model on Quantinuum's trapped ion quantum computer. Our error analysis shows that QHiFFS exhibits not only a cubic advantage in driving frequency $ω$ but also a linear advantage in simulation time $t$ compared to~Trotterization.

Achieving fast, sensitive, and parallel measurement of a large number of quantum particles is an essential task in building large-scale quantum platforms for different quantum information processing applications such as sensing, computation, simulation, and communication. Current quantum platforms in experimental atomic and optical physics based on CMOS sensors and CCD cameras are limited by either low sensitivity or slow operational speed. Here we integrate an array of single-photon avalanche diodes with solid-state spin defects in diamond to build a fast wide-field quantum sensor, achieving a frame rate up to 100~kHz. We present the design of the experimental setup to perform spatially resolved imaging of quantum systems. A few exemplary applications, including sensing DC and AC magnetic fields, temperature, strain, local spin density, and charge dynamics, are experimentally demonstrated using an NV ensemble diamond sample. The developed photon detection array is broadly applicable to other platforms such as atom arrays trapped in optical tweezers, optical lattices, donors in silicon, and rare earth ions in solids.

Quantum error mitigation has been extensively explored to increase the accuracy of the quantum circuits in noisy-intermediate-scale-quantum (NISQ) computation, where quantum error correction requiring additional quantum resources is not adopted. Among various error-mitigation schemes, probabilistic error cancellation (PEC) has been proposed as a general and systematic protocol that can be applied to numerous hardware platforms and quantum algorithms. However, PEC has only been tested in two-qubit systems and a superconducting multi-qubit system by learning a sparse error model. Here, we benchmark PEC using up to four trapped-ion qubits. For the benchmark, we simulate the dynamics of interacting fermions with or without spins by applying multiple Trotter steps. By tomographically reconstructing the error model and incorporating other mitigation methods such as positive probability and symmetry constraints, we are able to increase the fidelity of simulation and faithfully observe the dynamics of the Fermi-Hubbard model, including the different behavior of charge and spin of fermions. Our demonstrations can be an essential step for further extending systematic error-mitigation schemes toward practical quantum advantages.

Parallel operations are important for both near-term quantum computers and larger-scale fault-tolerant machines because they reduce execution time and qubit idling. We propose and implement a pairwise-parallel gate scheme on a trapped-ion quantum computer. The gates are driven simultaneously on different sets of orthogonal motional modes of a trapped-ion chain. We demonstrate the utility of this scheme by creating a GHZ state in one step using parallel gates with one overlapping qubit. We also show its advantage for circuits by implementing a digital quantum simulation of the dynamics of an interacting spin system, the transverse-field Ising model. This method effectively extends the available gate depth by up to two times with no overhead apart from additional initial cooling when no overlapping qubit is involved. This is because using a set of extra modes as additional quantum degrees of freedom is nearly equivalent to halving the trap heating rate, doubling the laser and qubit coherence time, and extending the controller memory depth by up to a factor of two. This scheme can be easily applied to different trapped-ion qubits and gate schemes, broadly enhancing the capabilities of trapped-ion quantum computers.

The ability to efficiently load functions on quantum computers with high fidelity is essential for many quantum algorithms. We introduce the Fourier Series Loader (FSL) method for preparing quantum states that exactly encode multi-dimensional Fourier series using linear-depth quantum circuits. The FSL method prepares a ($Dn$)-qubit state encoding the $2^{Dn}$-point uniform discretization of a $D$-dimensional function specified by a $D$-dimensional Fourier series. A free parameter $m < n$ determines the number of Fourier coefficients, $2^{D(m+1)}$, used to represent the function. The FSL method uses a quantum circuit of depth at most $2(n-2)+\lceil \log_{2}(n-m) \rceil + 2^{D(m+1)+2} -2D(m+1)$, which is linear in the number of Fourier coefficients, and linear in the number of qubits ($Dn$) despite the fact that the loaded function's discretization is over exponentially many ($2^{Dn}$) points. We present a classical compilation algorithm with runtime $O(2^{3D(m+1)})$ to determine the FSL circuit for a given Fourier series. The FSL method allows for the highly accurate loading of complex-valued functions that are well-approximated by a Fourier series with finitely many terms. We report results from noiseless quantum circuit simulations, illustrating the capability of the FSL method to load various continuous 1D functions, and a discontinuous 1D function, on 20 qubits with infidelities of less than $10^{-6}$ and $10^{-3}$, respectively. We also demonstrate the practicality of the FSL method for near-term quantum computers by presenting experiments performed on the Quantinuum H$1$-$1$ and H$1$-$2$ trapped-ion quantum computers: we loaded a complex-valued function on 3 qubits with a fidelity of over $95\%$, as well as various 1D real-valued functions on up to 6 qubits with classical fidelities $\approx 99\%$, and a 2D function on 10 qubits with a classical fidelity $\approx 94\%$.

Laser cooling of single atoms in optical tweezers is a prerequisite for neutral atom quantum computing and simulation. Resolved sideband cooling comprises a well-established method for efficient motional ground-state preparation, but typically requires careful cancellation of light shifts in so-called magic traps. Here, we study a novel laser cooling scheme which overcomes such constraints, and applies when the ground-state of a narrow cooling transition is trapped stronger than the excited state. We demonstrate our scheme, which exploits sequential addressing of red sideband transitions via frequency chirping of the cooling light, at the example of $^{88}$Sr atoms, and report ground-state populations compatible with recent experiments in magic tweezers. The scheme also induces light-assisted collisions, which are key to the assembly of large atom arrays. Our work enriches the toolbox for tweezer-based quantum technology, also enabling applications for tweezer-trapped molecules and ions that are incompatible with resolved sideband cooling conditions.

We present a single-shot method to measure motional states in the number basis. The technique can be applied to systems with at least three non-degenerate energy levels which can be coupled to a linear quantum harmonic oscillator, such as in trapped ion experiments. The method relies on probing an Autler-Townes splitting that arises when two levels are strongly coupled via a phonon-number changing transition. We demonstrate the method using a single trapped ion and show that it may be used in a non-demolition fashion to prepare phonon number states. We also show how the Autler-Townes splitting can be used to measure phonon number distributions.

Quantum systems evolve in time in one of two ways: through the Schrödinger equation or wavefunction collapse. So far, deterministic control of quantum many-body systems in the lab has focused on the former, due to the probabilistic nature of measurements. This imposes serious limitations: preparing long-range entangled states, for example, requires extensive circuit depth if restricted to unitary dynamics. In this work, we use mid-circuit measurement and feed-forward to implement deterministic non-unitary dynamics on Quantinuum's H1 programmable ion-trap quantum computer. Enabled by these capabilities, we demonstrate for the first time a constant-depth procedure for creating a toric code ground state in real-time. In addition to reaching high stabilizer fidelities, we create a non-Abelian defect whose presence is confirmed by transmuting anyons via braiding. This work clears the way towards creating complex topological orders in the lab and exploring deterministic non-unitary dynamics via measurement and feed-forward.

State readout of trapped-ion qubits with trap-integrated detectors can address important challenges for scalable quantum computing, but the strong rf electric fields used for trapping can impact detector performance. Here, we report on NbTiN superconducting nanowire single-photon detectors (SNSPDs) employing grounded aluminum mirrors as electrical shielding that are integrated into linear surface-electrode rf ion traps. The shielded SNSPDs can be successfully operated at applied rf trapping potentials of up to $\mathrm{54\,V_{peak}}$ at $\mathrm{70\,MHz}$ and temperatures of up to $\mathrm{6\,K}$, with a maximum system detection efficiency of $\mathrm{68\,\%}$. This performance should be sufficient to enable parallel high-fidelity state readout of a wide range of trapped ion species in typical cryogenic apparatus.

We show that coupling of ultralight dark matter (UDM) to quarks and gluons would lead to an oscillation of the nuclear charge radius for both the quantum chromodynamics (QCD) axion and scalar dark matter. Consequently, the resulting oscillation of electronic energy levels could be resolved with optical atomic clocks, and their comparisons can be used to investigate UDM-nuclear couplings, which were previously only accessible with other platforms. We demonstrate this idea using the ${}^2S_{1/2} (F=0)\leftrightarrow {}^2F_{7/2} (F=3)$ electric octupole and ${}^2S_{1/2} (F=0)\leftrightarrow \,{}^2D_{3/2} (F=2)$ electric quadrupole transitions in ${}^{171}Yb^+$. Based on the derived sensitivity coefficients for these two transitions and a long-term comparison of their frequencies using a single trapped ${}^{171}Yb^+$ ion, we find bounds on the scalar UDM-nuclear couplings and the QCD axion decay constant. These results are at a similar level compared to the tightest spectroscopic limits, and future investigations, also with other optical clocks, promise significant improvements.

Improving coherence is a fundamental challenge in quantum simulation and sensing experiments with trapped ions. Here we discuss, experimentally demonstrate, and estimate the potential impacts of two different protocols that enhance, through motional parametric excitation, the coherent spin-motion coupling of ions obtained with a spin-dependent force. The experiments are performed on 2D crystal arrays of approximately one hundred $^9$Be$^+$ ions confined in a Penning trap. By modulating the trapping potential at close to twice the center-of-mass mode frequency, we squeeze the motional mode and enhance the spin-motion coupling while maintaining spin coherence. With a stroboscopic protocol, we measure $5.4 \pm 0.9$ dB of motional squeezing below the ground-state motion, from which theory predicts a $10$ dB enhancement in the sensitivity for measuring small displacements using a recently demonstrated protocol [Science $\textbf{373}$, 673 (2021)]. With a continuous squeezing protocol, we measure and accurately calibrate the parametric coupling strength. Theory suggests this protocol can be used to improve quantum spin squeezing, limited in our system by off-resonant light scatter. We illustrate numerically the trade-offs between strong parametric amplification and motional dephasing in the form of center-of-mass frequency fluctuations for improving quantum spin squeezing in our set-up.

Large quantum computers promise to solve some critical problems not solvable otherwise. However, modern quantum technologies suffer various imperfections such as control errors and qubit decoherence, inhibiting their potential utility. The overheads of quantum error correction are too great for near-term quantum computers, whereas error-mitigation strategies that address specific device imperfections may lose relevance as devices improve. To enhance the performance of quantum computers with high-quality qubits, we introduce a strategy based on symmetrization and nonlinear aggregation. On a commercial trapped-ion quantum computer, it improves performance of multiple practical algorithms by 100x with no qubit or gate overhead.

We study the parametric decay instability of parallel propagating Alfvén wave in a low-beta plasma using one-dimensional fully kinetic simulations. We focus for the first time on the conversion of the energy stored in the initial Alfvén wave into particle internal energy, and on its partition between particle species. We show that compressible fluctuations generated by the decay of the pump wave into a secondary ion-acoustic mode and a reflected Alfvén wave contribute to the gain of internal energy via two distinct mechanisms. First, the ion-acoustic mode leads nonlinearly to proton trapping and proton phase space mixing, in agreement with previous work based on hybrid simulations. Second, during the nonlinear stage, a compressible front of the fast type develops at the steepened edge of the backward Alfvén wave leading to a field-aligned proton beam propagating backwards at the Alfvén speed. We find that parametric decay heats preferentially protons, which gain about 50% of the pump wave energy in the form of internal energy. However, we find that electrons are also energized and that they contribute to the total energy balance by gaining 10% of the pump wave energy. By investigating energy partition and particle heating during parametric decay, our results contribute to determine the role of compressible and kinetic effects in wave-driven models of the solar wind.

The accurate characterization of the spatial potential generated by a planar electrode in a surface-type Paul trap is of great interest. To achieve this, we employ a simple yet highly precise parametric expression to describe the spatial field of a rectangular-shaped electrode. Based on this, an optimization method is introduced to precisely characterize the axial electric field intensity created by the powered electrode and the stray field. In contrast to existing methods, various types of experimental data, such as the equilibrium position of ions in a linear string, equilibrium positions of single trapped ions and trap frequencies, are utilized for potential estimation in order to mitigate systematic errors. This approach offers significant flexibility in voltage settings for data collection, making it particularly well-suited for surface electrode traps where ion probe trapping height may vary with casual voltage settings. In our demonstration, we successfully minimized the discrepancy between experimental observations and model predictions to an impressive extent. The relative errors of secular frequencies were suppressed within $\pm$ 0.5$\%$, and the positional error of ions was limited to less than 1.2 $μ$m, all surpassing those achieved by existing methodologies.

We propose a hybrid classical-quantum digitized-counterdiabatic algorithm to tackle the protein folding problem on a tetrahedral lattice. Digitized-counterdiabatic quantum computing is a paradigm developed to compress quantum algorithms via the digitization of the counterdiabatic acceleration of a given adiabatic quantum computation. Finding the lowest energy configuration of the amino acid sequence is an NP-hard optimization problem that plays a prominent role in chemistry, biology, and drug design. We outperform state-of-the-art quantum algorithms using problem-inspired and hardware-efficient variational quantum circuits. We apply our method to proteins with up to 9 amino acids, using up to 17 qubits on quantum hardware. Specifically, we benchmark our quantum algorithm with Quantinuum's trapped ions, Google's and IBM's superconducting circuits, obtaining high success probabilities with low-depth circuits as required in the NISQ era.

In quantum gas microscopy experiments, reconstructing the site-resolved lattice occupation with high fidelity is essential for the accurate extraction of physical observables. For short interatomic separations and limited signal-to-noise ratio, this task becomes increasingly challenging. Common methods rapidly decline in performance as the lattice spacing is decreased below half the imaging resolution. Here, we present a novel algorithm based on deep convolutional neural networks to reconstruct the site-resolved lattice occupation with high fidelity. The algorithm can be directly trained in an unsupervised fashion with experimental fluorescence images and allows for a fast reconstruction of large images containing several thousand lattice sites. We benchmark its performance using a quantum gas microscope with cesium atoms that utilizes short-spaced optical lattices with lattice constant $383.5\,$nm and a typical Rayleigh resolution of $850\,$nm. We obtain promising reconstruction fidelities~$\gtrsim 96\%$ across all fillings based on a statistical analysis. We anticipate this algorithm to enable novel experiments with shorter lattice spacing, boost the readout fidelity and speed of lower-resolution imaging systems, and furthermore find application in related experiments such as trapped ions.

As quantum computers and simulators begin to produce results that cannot be verified classically, it becomes imperative to develop a variety of tools to detect and diagnose experimental errors on these devices. While state or process tomography is a natural way to characterize sources of experimental error, the intense measurement requirements make these strategies infeasible in all but the smallest of quantum systems. In this work, we formulate signatures of unitary evolution based on specific properties of periodically driven quantum systems. The absence of these signatures indicates a break either in the unitarity or periodicity condition on the evolution. We experimentally detect incoherent error on a trapped-ion quantum computer using these signatures. Our method is based on repeated measurements of a single observable, making this a low-cost evaluation of error with measurement requirements that scales according to the character of the dynamics, rather than the system size.

Spatiotemporal quenches are efficient at preparing ground states of critical Hamiltonians that have emergent low-energy descriptions with Lorentz invariance. The critical transverse field Ising model with nearest neighbor interactions, for instance, maps to free fermions with a relativistic low energy dispersion. However, spin models realized in artificial quantum simulators based on neutral Rydberg atoms, or trapped ions, generically exhibit long range power-law decay of interactions with $J(r) \sim 1/r^α$ for a wide range of $α$. In this work, we study the fate of spatiotemporal quenches in these models with a fixed velocity $v$ for the propagation of the quench front, using the numerical time-dependent variational principle. For $α\gtrsim 3$, where the critical theory is suggested to have a dynamical critical exponent $z = 1$, our simulations show that optimal cooling is achieved when the front velocity $v$ approaches $c$, the effective speed of excitations in the critical model. The energy density is inhomogeneously distributed in space, with prominent hot regions populated by excitations co-propagating with the quench front, and cold regions populated by counter-propagating excitations. Lowering $α$ largely blurs the boundaries between these regions. For $α< 3$, we find that the Doppler cooling effect disappears, as expected from renormalization group results for the critical model which suggest a dispersion $ω\sim q^z$ with $z < 1$. Instead, we show that excitations are controlled by two relevant length scales whose ratio is related to that of the front velocity to a threshold velocity that ultimately determines the adiabaticity of the quench.

Over the recent years coherent, time-periodic modulation has been established as a versatile tool for realizing novel Hamiltonians. Using this approach, known as Floquet engineering, we experimentally realize a long-ranged, anisotropic Heisenberg model with tunable interactions in a trapped ion quantum simulator. We demonstrate that the spectrum of the model contains not only single magnon excitations but also composite magnon bound states. For the long-range interactions with the experimentally realized power-law exponent, the group velocity of magnons is unbounded. Nonetheless, for sufficiently strong interactions we observe bound states of these unconventional magnons which possess a non-diverging group velocity. By measuring the configurational mutual information between two disjoint intervals, we demonstrate the implications of the bound state formation on the entanglement dynamics of the system. Our observations provide key insights into the peculiar role of composite excitations in the non-equilibrium dynamics of quantum many-body systems.

Penning traps have been used for performing quantum simulations and sensing with hundreds of ions and provide a promising route toward scaling up trapped ion quantum platforms because of the ability to trap and control up to thousands of ions in 2D and 3D crystals. A leading source of decoherence in laser-based multiqubit operations on trapped ions is off-resonant spontaneous emission. While many trapped ion quantum computers or simulators utilize clock qubits, other systems rely on Zeeman qubits, which require a more complex calculation of this decoherence. We examine theoretically the impacts of spontaneous emission on quantum gates performed with trapped ions in a high magnetic field. We consider two types of gates -- light-shift and Molmer-Sorensen gates -- and compare the decoherence errors in each. We also compare different detunings, polarizations, and required intensities of the laser beams used to drive the gates. We show that both gates can have similar performance at their optimal operating conditions and examine the experimental feasibility of various operating points. By examining the magnetic field dependence of each gate, we demonstrate that when the $P$ state fine structure splitting is large compared to the Zeeman splittings, the theoretical performance of the Molmer-Sorensen gate is significantly better than that of the light-shift gate. Additionally, for the light-shift gate, we make an approximate comparison between the fidelities that can be achieved at high fields with the fidelities of state-of-the-art two-qubit trapped ion quantum gates. We show that, with regard to spontaneous emission, the achievable infidelity of our current configuration is about an order of magnitude larger than that of the best low-field gates, but we also discuss alternative configurations with potential error rates that are comparable with state-of-the-art trapped ion gates.

Two-qubit gate performance is vital for scaling up ion-trap quantum computing. Optimized quantum control is needed to achieve reductions in gate-time and gate error-rate. We describe two-qubit gates with addressed Raman beams within a linear trapped-ion chain by a quantum master equation (QME). The QME incorporates the single-ion two-photon effective Rabi frequency, Autler-Townes and vibrational Bloch-Siegert energy shifts, off-resonant transitions, Raman and Rayleigh scattering, laser-power fluctuations, motional heating, cross-Kerr phonon coupling, laser spillover, asymmetric addressing beams and an imperfect initial motional ground state, with no fitting parameters. Whereas state-of-the-art methods are oblivious to these effects in the gate design procedure. We employ global optimization to design pulse sequences for achieving a robust rapid two-qubit gate for seven trapped $^{171}$Yb$^{+}$ ions by optimizing over numerically integrated QME solutions. Here, robust means resilient against slow drift of motional frequencies, and rapid means gate execution where the effective Rabi frequency is comparable to the detuning of the laser from the ion's bare electronic transition. Our robust quantum control delivers rapid high-quality two-qubit gates in long ion chains, enabling scalable quantum computing with trapped ions.

We study the non-equilibrium dynamics of dipoles confined in multiple stacked two-dimensional layers realising a long-range interacting quantum spin 1/2 XXZ model. We demonstrate that strong in-plane XXX interactions can protect a manifold of collective layer dynamics. This then allows us to map the many-body spin dynamics to bosonic models. In a bilayer configuration we show how to engineer the paradigmatic two-mode squeezing Hamiltonian known from quantum optics, resulting in exponential production of entangled pairs and generation of metrologically useful entanglement from initially prepared product states. In multi-layer configurations we engineer a bosonic variant of the Kitaev model displaying chiral propagation along the layer direction. Our study illustrates how the control over interactions, lattice geometry and state preparation in interacting dipolar systems uniquely afforded by AMO platforms such as Rydberg and magnetic atoms, polar molecules or trapped ions allow for the control over the temporal and spatial propagation of correlations for applications in quantum sensing and quantum simulation.

Conventional theoretical studies on the ground-state laser cooling of a trapped ion have mostly focused on the weak sideband coupling (WSC) regime, where the cooling rate is inverse proportional to the linewidth of the excited state. In a recent work~[New J. Phys. 23, 023018 (2021)], we proposed a theoretical framework to study the ground state cooling of a trapped ion in the strong sideband coupling (SSC) regime, under the assumption of a vanishing carrier transition. Here we extend this analysis to more general situations with nonvanishing carrier transitions, where we show that by properly tuning the coupling lasers a cooling rate proportional to the linewidth can be achieved. Our theoretical predictions closely agree with the corresponding exact solutions in the SSC regime, which provide an important theoretical guidance for sideband cooling experiments.

The omnipresence of dust particulates in space and astrophysical plasmas has been attracting numerous researchers to study the collective excitation and propagation dynamics of different eigen-mode structures in diversifed astrocosmic circumstances for years. It includes planetary rings, interplanetary space, cometary tails, asteroid zones, planetary atmospheres, etc. The ubiquitous charged dust particulates possess collective degrees of dynamic freedom resulting in the excitation of relatively low-frequency modes, such as dust-ion-acoustic waves (DIAWs), dust-acoustic waves (DAWs), dust-Coulomb waves (DCWs), and so forth. An interesting prevalency of dusty plasma stability research lies in the Jovian magnetosphere (i.e., Jovian plasmas), embedded inside the supersonic solar wind. A brief review of the updated research works on dust-acoustic waves and related collective instability dynamics in the presence of trapped plasma particles is presented herein. The key aim of the proposed explorative meta-analysis is rooted in outlining concisely the main up-to-date investigations on such collective instability processes chronologically. An especial attention is given primarily to the thermostatistical distribution laws of the constitutive lighter electrons and ions against the heavier positively charged dust grains (microspheres). The trapping mechanism of both the lighter species (electrons+ions) is another additive feature revisited here properly. Finally, we clearly extrapolate a number of futuristic directions in light of sensible novelties with a wider scope, both horizontally as well as vertically.

Optical clocks are the apotheosis of precision measurement, but they require frequent maintenance by scientists. The supporting laser systems are a particularly demanding component of these instruments. To reduce complexity and increase robustness we propose an optical clock with trapped alkali-like ions that use the $S_{1/2}\rightarrow D_{3/2}$ electric quadrupole transition. Compared to traditional group-II ion clocks this reduces the number of laser wavelengths required, and uses hyperfine state preparation and readout techniques enabled by the nuclear spin $I=1/2$. We consider $^{225}$Ra$^{+}$ as a candidate system for a clock with three electronic states, and discuss the potential to help realize a transportable optical clock.

One-dimensional systems exhibiting a continuous symmetry can host quantum phases of matter with true long-range order only in the presence of sufficiently long-range interactions. In most physical systems, however, the interactions are short-ranged, hindering the emergence of such phases in one dimension. Here we use a one-dimensional trapped-ion quantum simulator to prepare states with long-range spin order that extends over the system size of up to $23$ spins and is characteristic of the continuous symmetry-breaking phase of matter. Our preparation relies on simultaneous control over an array of tightly focused individual-addressing laser beams, generating long-range spin-spin interactions. We also observe a disordered phase with frustrated correlations. We further study the phases at different ranges of interaction and the out-of-equilibrium response to symmetry-breaking perturbations. This work opens an avenue to study new quantum phases and out-of-equilibrium dynamics in low-dimensional systems.

We study photon scattering errors in stimulated Raman driven quantum logic gates. For certain parameter regimes, we find that previous, simplified models of the process significantly overestimate the gate error rate due to photon scattering. This overestimate is shown to be due to previous models neglecting the detuning dependence of the scattered photon frequency and Lamb-Dicke parameter, a second scattering process, interference effects on scattering rates to metastable manifolds, and the counter-rotating contribution to the Raman transition rate. The resulting improved model shows that there is no fundamental limit on gate error due to photon scattering for electronic ground state qubits in commonly-used trapped-ion species when the Raman laser beams are red detuned from the main optical transition. Additionally, photon scattering errors are studied for qubits encoded in metastable $D_{5/2}$ manifold, showing that gate errors below $10^{-4}$ are achievable for all commonly-used trapped ions.

We present a new method for coherent control of trapped ion qubits in separate interaction regions of a multi-zone trap by simultaneously applying an electric field and a spin-dependent gradient. Both the phase and amplitude of the effective single-qubit rotation depend on the electric field, which can be localised to each zone. We demonstrate this interaction on a single ion using both laser-based and magnetic field gradients in a surface-electrode ion trap, and measure the localisation of the electric field.

Erasures, or errors with known locations, are a more favorable type of error for quantum error-correcting codes than Pauli errors. Converting physical noise into erasures can significantly improve the performance of quantum error correction. Here we apply the idea of performing erasure conversion by encoding qubits into metastable atomic states, proposed by Wu, Kolkowitz, Puri, and Thompson [Nat. Comm. 13, 4657 (2022)], to trapped ions. We suggest an erasure-conversion scheme for metastable trapped-ion qubits and develop a detailed model of various types of errors. We then compare the logical performance of ground and metastable qubits on the surface code under various physical constraints, and conclude that metastable qubits may outperform ground qubits when the achievable laser power is higher for metastable qubits.

An array of ions in a linear radio-frequency (RF) Paul trap is a good candidate for investigating structural phase transitions, such as the linear-to-zigzag (LZ) transition, due to the convenient control provided by modification of the trap confinement strength. In such studies, the trap secular frequencies are a key factor that limits the stability of the critical point (CP). In this paper, we implement secular-frequency stabilization, including active feedback stabilization of the RF voltage near the trap electrodes, and achieve a stability of better than 5~ppm over 200~s for both transverse and axial potentials. To evaluate the combined long-term stability of the trap potential in both directions, we measure the zigzag (ZZ) mode frequency near the CP, where the effect of instability in both trap directions is substantially amplified. The short-term noise within a limited spectral window is also suppressed by this scheme, as inferred from decoherence rates of the ZZ mode measured at different frequencies with Ramsey fringes. We also identify that the limitation of the secular frequency stability is mainly from the imperfect temperature insensitivity of voltage dividers and RF detectors, and as a result improvement of lab temperature stability is of great help for stabilizing the trap frequency.

The AKLT state is the ground state of an isotropic quantum Heisenberg spin-$1$ model. It exhibits an excitation gap and an exponentially decaying correlation function, with fractionalized excitations at its boundaries. So far, the one-dimensional AKLT model has only been experimentally realized with trapped-ions as well as photonic systems. In this work, we successfully prepared the AKLT state on a noisy intermediate-scale quantum (NISQ) era quantum device for the first time. In particular, we developed a non-deterministic algorithm on the IBM quantum processor, where the non-unitary operator necessary for the AKLT state preparation is embedded in a unitary operator with an additional ancilla qubit for each pair of auxiliary spin-1/2's. Such a unitary operator is effectively represented by a parametrized circuit composed of single-qubit and nearest-neighbor $CX$ gates. Compared with the conventional operator decomposition method from Qiskit, our approach results in a much shallower circuit depth with only nearest-neighbor gates, while maintaining a fidelity in excess of $99.99\%$ with the original operator. By simultaneously post-selecting each ancilla qubit such that it belongs to the subspace of spin-up $|\uparrow \rangle$, an AKLT state can be systematically obtained by evolving from an initial trivial product state of singlets plus ancilla qubits in spin-up on a quantum computer, and it is subsequently recorded by performing measurements on all the other physical qubits. We show how the accuracy of our implementation can be further improved on the IBM quantum processor with readout error mitigation.

We present a new platform facilitating quantum logic control of polar molecular ions in a segmented ring ion trap, paving the way for precision measurements. This approach focuses on achieving near-unity state preparation and detection, as well as long spin coherence. A distinctive aspect lies in separating state preparation and detection conducted in a static frame, from parity-selective spin-precession in a rotating frame. This method can be applied to a wide range of ion species and will be used to search for the electron's electric dipole moment and the nuclear magnetic quadrupole moment.

Reversible computation has been proposed as a future paradigm for energy efficient computation, but so far few implementations have been realised in practice. Quantum circuits, running on quantum computers, are one construct known to be reversible. In this work, we provide a proof-of-principle of classical logical gates running on quantum technologies. In particular, we propose, and realise experimentally, Toffoli and Half-Adder circuits suitable for classical computation, using radiofrequency-controlled $^{171}$Yb$^+$ ions in a macroscopic linear Paul-trap as qubits. We analyse the energy required to operate the logic gates, both theoretically and experimentally, with a focus on the control energy. We identify bottlenecks and possible improvements in future platforms for energetically-efficient computation, e.g., trap chips with integrated antennas and cavity QED. Our experimentally verified energetic model also fills a gap in the literature of the energetics of quantum information, and outlines the path for its detailed study, as well as its potential applications to classical computing.

Precision mass measurements of neutron-rich rhodium isotopes have been performed at the JYFLTRAP Penning trap mass spectrometer at the Ion Guide Isotope Separator On-Line (IGISOL) facility. We report results on ground- and isomeric-state masses in $^{110,112,114,116,118}$Rh and the very first mass measurement of $^{120}$Rh. The isomeric states were separated and measured for the first time using the phase-imaging ion-cyclotron-resonance (PI-ICR) technique. For $^{112}$Rh, we also report new half-lives for both the ground state and the isomer. The results are compared to theoretical predictions using the BSkG1 mass model and discussed in terms of triaxial deformation.

We report an experimental demonstration of optical 2DCS in cold atoms. The experiment integrates a collinear 2DCS setup with a magneto-optical trap (MOT), in which cold rubidium (Rb) atoms are prepared at a temperature of about 200 $μ$K and a number density of $10^{10}$ cm$^{-3}$. With a sequence of femtosecond laser pulses, we first obtained one-dimensional second- and fourth-order nonlinear signals and then acquired both one-quantum and zero-quantum 2D spectra of cold Rb atoms. The capability of performing optical 2DCS in cold atoms is an important step toward optical 2DCS study of many-body physics in cold atoms and ultimately in atom arrays and trapped ions. Optical 2DCS in cold atoms/molecules can also be a new avenue to probe chemical reaction dynamics in cold molecules.

The time-evolution of multi-neutrino entanglement and correlations are studied in two-flavor collective neutrino oscillations, relevant for dense neutrino environments, building upon previous works. Specifically, simulations performed of systems with up to 12 neutrinos using Quantinuum's H1-1 20 qubit trapped-ion quantum computer are used to compute n-tangles, and two- and three-body correlations, probing beyond mean-field descriptions. n-tangle re-scalings are found to converge for large system sizes, signaling the presence of genuine multi-neutrino entanglement.

Transmon qubits are the predominant element in circuit-based quantum information processing, such as existing quantum computers, due to their controllability and ease of engineering implementation. But more than qubits, transmons are multilevel nonlinear oscillators that can be used to investigate fundamental physics questions. Here, they are explored as simulators of excited state quantum phase transitions (ESQPTs), which are generalizations of quantum phase transitions to excited states. We show that the spectral kissing (coalescence of pairs of energy levels) experimentally observed in the effective Hamiltonian of a driven SNAIL-transmon is an ESQPT precursor. We explore the dynamical consequences of the ESQPT, which include the exponential growth of out-of-time-ordered correlators, followed by periodic revivals, and the slow evolution of the survival probability due to localization. These signatures of ESQPT are within reach for current superconducting circuits platforms and are of interest to experiments with cold atoms and ion traps.

We consider a multi-qubit system of atoms or ions with two computational ground states and an interacting excited state in the so-called blockade regime, such that only one qubit can be excited at any one time. Examples of such systems are rare-earth-ion-doped crystals and neutral atoms trapped in tweezer arrays. We present a simple laser excitation protocol that yields a complex phase factor on any desired multi-qubit product state, and which can be used to implement multi-qubit gates such as the n-bit Toffoli gates. The operation is performed using only two pulses, where each pulse simultaneously address all qubits. By the use of complex hyperbolic secant pulses our scheme is robust and permits complete transfers to and from the excited states despite the variability of interaction parameters. A detailed analysis of the multi-qubit gate performance is provided.

We propose and demonstrate a new method for Doppler cooling trapped-ion crystals where the distribution of micromotion amplitudes may be large and uneven. The technique uses pulses of Doppler cooling light synchronized with the trap RF that selectively target ions when their velocity is near a node, leading to more uniform cooling across a crystal by a single tone of cooling light. We lay out a theoretical framework that describes where this technique is practical, and provide a simple experimental demonstration.