Alejandro Bermudez

Modularization promises to break down the design and implementation complexity of large scale quantum processors into smaller manageable subtasks. In this approach, quantum channels, realized for instance through physical rerouting of qubits or quantum teleportation, connect multiple modules. Each of those modules hosts a subset of qubits, e.g. multiple logical qubits, and provides quantum operations on them. In this work, we implement for the first time all logical operations required for modular fault-tolerant universal quantum computing with a non-Calderbank-Shor-Steane (CSS) code, the perfect $[[5, 1, 3]]$ code, on a trapped-ion quantum computer. This code is the smallest quantum error-correcting (QEC) code capable of correcting any single-qubit error, making it a compact alternative to larger CSS codes. We demonstrate logical state teleportation and a full suite of fault-tolerant operations required for universal logical control, including logical state preparation, QEC with real-time feedback, logical measurements, magic-state preparation, logical entangling operations, and magic-state injection. Moreover, we characterize the logical spectator error picked up by idling logical qubits during quantum operations on distinct qubit registers and demonstrate a logical Pauli quantum process tomography that minimizes required sampling resources for logical tomography.

Spectral crowding of collective motional modes limits the fidelity of entangling interactions in trapped-ion quantum processors by inducing off-resonant coupling to spectator modes. We introduce a geometric-phase entangling interaction driven by a transverse, time-dependent structured-light force. By applying the force in a plane orthogonal to the optical propagation direction, we reduce the effects of spectral crowding while preserving single-ion addressing. The scheme is compatible with arbitrary qubit encodings, provided that the qubit states experience a differential AC Stark shift. We experimentally realise high-fidelity two-qubit gates with error rates below $5\times10^{-3}$ in ion crystals containing up to 12 ions confined within a single potential well. These results establish gradient-field light-shift gates as a scalable approach to high-fidelity entangling generation in spectrally crowded trapped-ion systems.

We present a footprint study for the scaling of modular quantum error correction (QEC) protocols designed for triangular color codes, including a lattice-surgery-based logical teleportation gadget, and compare the performance of various possible architectures based on trapped ions. The differences in these architectures arise from the technology that enables the connectivity between physical qubits and the modularity required for the QEC gadgets, which is either based on laser-beam deflectors focused to independent modules hosting mid-size ion crystals, or integrated photonics guided to segmented modules of the trap and allowing for the manipulation of smaller ion crystals. Our approach integrates the transpilation of the QEC gadgets into native trapped-ion primitives and a detailed account of the specific laser addressing and ion transport leading to different amounts of crosstalk errors, motional excitation and idle qubit errors. Combining a microscopically-informed noise model with an efficient Pauli-frame simulator and different scalable decoders, we assess the near-term performance of the color-code memory and teleportation protocols on these architectures. Our analysis demonstrates that modular color-code teleportation is achievable in these near-term trapped-ion architectures, and identifies the integrated-photonics connectivity as the most promising route for longer-term scaling.

We propose and analyze a trapped-ion quantum simulator of the Jackiw-Rebbi model, a paradigmatic quantum field theory in (1+1) dimensions where solitonic excitations of a scalar field can bind fermionic zero modes leading to fractionally-charged excitations. In our approach, the scalar field is a coarse-grained description of the planar zigzag ion displacements in the vicinity of a structural phase transition. The internal electronic states of the ions encode spins with interactions mediated by the transverse phonons and in-plane spin-phonon couplings with a zigzag pattern, which together correspond to a Yukawa-coupled Dirac field. Instead of assuming a fixed soliton background, we study the effect of back-reaction and quantum fluctuations on the coupled dynamics of the full fermion-boson system. We start by applying a Born-Oppenheimer approximation to obtain an effective Peierls-Nabarro potential for the topological kink, unveiling how the fermionic back-reaction can lead to localization of the kink. Beyond this limit, a truncated Wigner approximation combined with fermionic Gaussian states captures the quantum spreading and localization of a kink and kink-antikink scattering. Our results reveal how back-reaction and quantum fluctuations modify the stability and real-time evolution of fractionalized fermions, predicting experimentally accessible signatures in current trapped-ion architectures.

To progress in the characterization of noise for current quantum computers, gate set tomography (GST) has emerged as a self-consistent tomographic protocol that can accurately estimate the complete set of noisy quantum gates, state preparations, and measurements. In its original incarnation, GST improves the estimation precision by applying the gates sequentially, provided that the noise makes them a set of fixed completely-positive and trace preserving (CPTP) maps independent of the history of previous gates in the sequence. This 'Markovian' assumption is sometimes in conflict with experimental evidence, as there might be time-correlated noise leading to non-Markovian dynamics or, alternatively, slow drifts and cumulative calibration errors that lead to context dependence, such that the CP-divisible maps composed during a sequence actually change with the circuit depth. In this work, we address this issue for trapped-ion devices with phonon-mediated two-qubit gates. By a detailed microscopic modeling of high-fidelity light-shift gates, we tailor GST to capture the main source of context dependence: motional degrees of freedom. Rather than invalidating GST, we show that context dependence can be incorporated in the parametrization of the gate set, allowing us to reduce the sampling cost of GST. Our results identify a promising research avenue that might be applicable to other platforms where microscopic modeling can be incorporated: the development of a context-aware GST.

We study the finite-density phases of a $\mathbb{Z}_2$ lattice gauge theory (LGT) of interconnected loops and dynamical $\mathbb{Z}_2$ charges. The gauge-invariant Wilson terms, accounting for the magnetic flux threading each loop, correspond to simple two-body Ising interactions in this setting. Such terms control the interference of charges tunneling around the loops, leading to dynamical Aharonov-Bohm (AB) cages that are delimited by loops threaded by a $π$-flux. The latter can be understood as $\mathbb{Z}_2$ vortices, the analog of visons in two dimensional LGTs, which become mobile by adding quantum fluctuations through an external electric field. In contrast to a semi-classical regime of static and homogeneous AB cages, the mobile visons can self-assemble leading to AB cages of different lengths depending on the density of $\mathbb{Z}_2$ charges and the interplay of magnetic and electric terms. Inside these cages, the individual charges get confined into tightly-bound charge-neutral pairs, the $\mathbb{Z}_2$ analogue of mesons. Depending on the region of parameter space, these tightly-bound mesons can propagate within dilute AB-dimers that virtually expand and contract, or else move by virtually stretching and compressing an electric field string. Both limits lead to a Luttinger liquid described by a constrained integrable model. This phase is separated from an incompressible Mott insulator where mesons belong to closely-packed AB-trimers. In light of recent trapped-ion experiments for a single $\mathbb{Z}_2$ loop, these phases could be explored in future experiments.

A major hurdle for building a large-scale quantum computer is increasing the number of qubits while maintaining connectivity between them. In trapped-ion devices, this connectivity can be achieved by moving subregisters consisting of a few ions across the processor. Here, we focus on an architecture, which we refer to as the Quantum Spring Array (QSA), that is based on a rectangular two-dimensional lattice of linear strings of ions. Connectivity between adjacent ion strings can be controlled by adjusting their separation. This requires control of trapping potentials along two directions, one along the axis of the ion string and one radial to it. In this work, we investigate key elements of the QSA architecture along both directions: We show that the coupling rate between neighboring lattice sites increases with the number of ions per site and the motion of the coupled system can be resilient to electrical noise, both being key requisites for fast and high-fidelity quantum gate operations. The coherence of the coupling is assessed and an entangling gate between qubits stored in radially separated trapping regions is demonstrated. Moreover, we demonstrate control over radio-frequency signals to adjust the radial separation, and thus the coupling rate, between strings. We further present constructions for the implementation of parallelized, transversal gate operations, and map the QSA architecture to code primitives for fault-tolerant quantum error correction, providing a step towards a quantum processor architecture that is optimized for large-scale operation.

We introduce Lindblad-like quantum tomography (L$\ell$QT) as a quantum characterization technique of time-correlated noise in quantum information processors. This approach enables the estimation of time-local master equations, including their possible negative decay rates, by maximizing a likelihood function subject to dynamical constraints. We discuss L$\ell$QT for the dephasing dynamics of single qubits in detail, which allows for a neat understanding of the importance of including multiple snapshots of the quantum evolution in the likelihood function, and how these need to be distributed in time depending on the noise characteristics. By a detailed comparative study employing both frequentist and Bayesian approaches, we assess the accuracy and precision of L$\ell$QT of a dephasing quantum dynamical map that goes beyond the Lindblad limit, focusing on two different microscopic noise models that can be realised in either trapped-ion or superconducting-circuit architectures. We explore the optimization of the distribution of measurement times to minimize the estimation errors, assessing the superiority of each learning scheme conditioned on the degree of non-Markovinity of the noise, and setting the stage for future experimental designs of non-Markovian quantum tomography.

Characterizing the dynamics of quantum systems is a central task for the development of quantum information processors (QIPs). It serves to benchmark different devices, learn about their specific noise, and plan the next hardware upgrades. However, this task is also very challenging, for it requires a large number of measurements and time-consuming classical processing. Moreover, when interested in the time dependence of the noise, there is an additional overhead since the characterization must be performed repeatedly within the time interval of interest. To overcome this limitation while, at the same time, ordering the learned sources of noise by their relevance, we focus on the inference of the dynamical generators of the noisy dynamics using Lindbladian quantum tomography (LQT). We propose two different improvements of LQT that alleviate previous shortcomings. In the weak-noise regime of current QIPs, we manage to linearize the maximum likelihood estimation of LQT, turning the constrained optimization into a convex problem to reduce the classical computation cost and to improve its robustness. Moreover, by introducing compressed sensing techniques, we reduce the number of required measurements without sacrificing accuracy. To illustrate these improvements, we apply our LQT tools to trapped-ion experiments of single- and two-qubit gates, advancing in this way the previous state of the art.

The quantum simulation of magnetism in trapped-ion systems makes use of the crystal vibrations to mediate pairwise interactions between spins, which are encoded in the internal electronic states of the ions, and measured in experiments that probe the real-time dynamics. These interactions can be accounted for by a long-wavelength relativistic theory, where the phonons are described by a coarse-grained Klein-Gordon field $φ(x)$ locally coupled to the spins that acts as a carrier, leading to an analogue of pion-mediated Yukawa interactions. In the vicinity of a structural transition of the ion crystal, one must go beyond the Klein-Gordon fields, and include additional $λφ^4$ terms responsible for phonon-phonon scattering. This leads to quantum effects that can be expressed by Feynman loop integrals that modify the range of the Yukawa-type spin interactions; an effect that could be used to probe the underlying fixed point of this quantum field theory (QFT). Unfortunately, the rigidity of the trapped-ion crystal makes it challenging to observe genuine quantum effects, such as the flow of the critical point with the quartic coupling $λ$. We hereby show that thermal effects, which can be controlled by laser cooling, can unveil this flow through the appearance of thermal masses in interacting QFTs. We perform self-consistent calculations that resum certain Feynman diagrams and, additionally, go beyond mean-field theory to predict how measurements on the trapped-ion spin system can probe key properties of the $λφ^4$ QFT.

Quantum Error Correction (QEC) exploits redundancy by encoding logical information into multiple physical qubits. In current implementations of QEC, sequences of non-perfect two-qubit entangling gates are used to codify the information redundantly into multipartite entangled states. Also, to extract the error syndrome, a series of two-qubit gates are used to build parity-check readout circuits. In the case of noisy gates, both steps cannot be performed perfectly, and an error model needs to be provided to assess the performance of QEC. We present a detailed microscopic error model to estimate the average gate infidelity of two-qubit light-shift gates used in trapped-ion platforms. We analytically derive leading-error contributions in terms of microscopic parameters and present effective error models that connect the error rates typically used in phenomenological accounts to the microscopic gate infidelities hereby derived. We then apply this realistic error model to quantify the multipartite entanglement generated by circuits that act as QEC building blocks. We do so by using entanglement witnesses, complementing in this way the recent studies by exploring the effects of a more realistic microscopic noise.

The idea of exploiting maximally-entangled states as a resource lies at the core of several modalities of quantum information processing, including secure quantum communication, quantum computation, and quantum sensing. However, due to imperfections during or after the entangling gates used to prepare such states, the amount of entanglement decreases and their quality as a resource gets degraded. We introduce a low-overhead protocol to reverse this degradation by partially filtering out a specific type of noise relevant to many quantum technologies. We present two trapped-ion schemes for the implementation of a non-unitary probabilistic filter against amplitude damping noise, which can protect any maximally-entangled pair from spontaneous photon scattering during or after the two-qubit trapped-ion entangling gates. This filter can be understood as a protocol for single-copy quasi-distillation, as it uses only local operations to realise a reversal operation that can be understood in terms of weak measurements.

Physical qubits in experimental quantum information processors are inevitably exposed to different sources of noise and imperfections, which lead to errors that typically accumulate hindering our ability to perform long computations reliably. Progress towards scalable and robust quantum computation relies on exploiting quantum error correction (QEC) to actively battle these undesired effects. In this work, we present a comprehensive study of crosstalk errors in a quantum-computing architecture based on a single string of ions confined by a radio-frequency trap, and manipulated by individually-addressed laser beams. This type of errors affects spectator qubits that, ideally, should remain unaltered during the application of single- and two-qubit quantum gates addressed at a different set of active qubits. We microscopically model crosstalk errors from first principles and present a detailed study showing the importance of using a coherent vs incoherent error modelling and, moreover, discuss strategies to actively suppress this crosstalk at the gate level. Finally, we study the impact of residual crosstalk errors on the performance of fault-tolerant QEC numerically, identifying the experimental target values that need to be achieved in near-term trapped-ion experiments to reach the break-even point for beneficial QEC with low-distance topological codes.

Ensuring the correct functioning of quantum error correction (QEC) circuits is crucial to achieve fault tolerance in realistic quantum processors subjected to noise. The first checkpoint for a fully operational QEC circuit is to create genuine multipartite entanglement across all subsystems of physical qubits. We introduce a conditional witnessing technique to certify genuine multipartite entanglement (GME) that is efficient in the number of subsystems and, importantly, robust against experimental noise and imperfections. Specifically, we prove that the detection of entanglement in a linear number of bipartitions by a number of measurements that also scales linearly, suffices to certify GME. Moreover, our method goes beyond the standard procedure of separating the state from the convex hull of biseparable states, yielding an improved finesse and robustness compared to previous techniques. We apply our method to the noisy readout of stabilizer operators of the distance-three topological color code and its flag-based fault-tolerant version. In particular, we subject the circuits to combinations of three types of noise, namely, uniform depolarizing noise, two-qubit gate depolarizing noise, and bit-flip measurement noise. We numerically compare our method with the standard, yet generally inefficient, fidelity test and to a pair of efficient witnesses, verifying the increased robustness of our method. Last but not least, we provide the full translation of our analysis to a trapped-ion native gate set that makes it suitable for experimental applications.

The micromotion of ion crystals confined in Paul traps is usually considered an inconvenient nuisance, and is thus typically minimised in high-precision experiments such as high-fidelity quantum gates for quantum information processing. In this work, we introduce a particular scheme where this behavior can be reversed, making micromotion beneficial for quantum information processing. We show that using laser-driven micromotion sidebands, it is possible to engineer state-dependent dipole forces with a reduced effect of off-resonant couplings to the carrier transition. This allows one, in a certain parameter regime, to devise entangling gate schemes based on geometric phase gates with both a higher speed and a lower error, which is attractive in light of current efforts towards fault-tolerant quantum information processing. We discuss the prospects of reaching the parameters required to observe this micromotion-enabled improvement in experiments with current and future trap designs.

We introduce a scheme that exploits laser cooling and phonon-mediated spin-spin interactions in crystals of trapped atomic ions to explore the transport of energy through a quantum magnet. We show how to implement an effective transport window to control the flow of energy through the magnet even in the absence of fermionic statistics for the carriers. This is achieved by shaping the density of states of the effective thermal reservoirs that arise from the interaction with the external bath of the modes of the electromagnetic field, and can be experimentally controlled by tuning the laser frequencies and intensities appropriately. The interplay of this transport window with the spin-spin interactions is exploited to build an analogue of the Coulomb-blockade effect in nano-scale electronic devices, and opens new possibilities to study quantum effects in energy transport.

We present a route towards the quantum simulation of exotic quantum magnetism in ion traps by exploiting dual relations between different spin models. Our strategy allows one to start from Hamiltonians that can be realized with current technology, while properties of an exotic dual model are inferred from measurements of non-local, string-order-like, operators. The latter can be achieved from fluorescence, or from certain spectroscopic measurements, both of which can be combined with finite-size scaling by controlling the number of ions in the dual quantum simulator. We apply this concept to propose quantum simulators of frustrated quantum magnets, and Ising models with multi-spin interactions. We test the validity of the idea by showing numerically that the predictions of an ideal dual quantum simulator are not qualitatively modified by relevant perturbations that occur naturally in the trapped-ion scenario.

We introduce a lattice model of interacting spins and bosons that leads to Luttinger-liquid physics, and allows for quantitative tests of the theory of bosonization by means of trapped-ion or superconducting-circuit experiments. By using a variational bosonization ansatz, we calculate the power-law decay of spin and boson correlation functions, and study their dependence on a single tunable parameter, namely a bosonic driving. For small drivings, Matrix-Product-States (MPS) numerical methods are shown to be efficient and validate our ansatz. Conversely, even static MPS become inefficient for large-driving regimes, such that the experiment can potentially outperform classical numerics, achieving one of the goals of quantum simulations.

We propose a dissipative method to prepare the ground state of the isotropic XY spin Hamiltonian in a transverse field. Our model consists of a spin chain with nearest-neighbour interactions and an additional collective coupling of the spins to a damped harmonic oscillator. The latter provides an effective environment with a Lorentzian spectral density and can be used to drive the chain asymptotically towards its multipartite-entangled ground state at a rate that depends on the degree of non-Markovianity of the evolution. We also present a detailed proposal for the experimental implementation with a chain of trapped ions. The protocol does not require individual addressing, concatenated pulses, or multi-particle jump operators, and is capable of generating the desired target state in small ion chains with very high fidelities.

We describe a versatile toolbox for the quantum simulation of many-body lattice models, capable of exploring the combined effects of background Abelian and non-Abelian gauge fields, bond and site disorder, and strong on-site interactions. We show how to control the quantum dynamics of particles trapped in lattice potentials by the photon-assisted tunneling induced by periodic drivings. This scheme is general enough to be applied to either bosons or fermions with the additional advantage of being non-perturbative. It finds an ideal application in microfabricated ion trap arrays, where the quantized vibrational modes of the ions can be described by a quantum lattice model. We present a detailed theoretical proposal for a quantum simulator in that experimental setup, and show that it is possible to explore phases of matter that range from the fractional quantum Hall effect, to exotic strongly-correlated glasses, or flux-lattice models decorated with arbitrary patterns of localized defects.