Y. -K. Wu

Quantum low-density parity-check (qLDPC) codes admit high encoding rates but require nonlocal entangling gates for syndrome measurement. Instead of physically moving the qubits which slows down with the increasing qubit number, here we propose to achieve parallel nonlocal entangling gates on a two-dimensional (2D) ion crystal using frequency-multiplexing. Adiabatic conditions ensure the suppression of gate infidelity and crosstalk error, as well as their robustness against slow drift in the trap frequency which is a leading error source in ion trap. We consider a numerical example of a $[[248,10,18]]$ bivariate bicycle code on a 2D crystal of 512 ions. By optimizing the mapping of the qubits and the assignment of the frequency bands for multiplexing, we show that a moderate laser power is sufficient for parallelism, and that a logical error rate of $10^{-12}$ can be achieved under realistic noise parameters.

Non-Gaussian evolution of high-order spin correlations characterizes important properties of quantum many-body systems. In practice, decoherence, statistical fluctuation and miscalibration of experimental parameters all hinder the witness of non-Gaussian dynamics. Here we demonstrate the crossover between Gaussian and non-Gaussian dynamics on a two-dimensional XY model with long-range and spatially structured interaction using a trapped ion quantum simulator. We prepare different initial densities of magnon excitations and verify the dynamics of single-spin observables for the engineered Hamiltonian. Then we compare the high-order spin correlations with the mean-field solution and the Holstein-Primakoff approximation, and demonstrate the non-Gaussian behavior in a way independent of the calibration errors. Our work provides a verifiable path from classically simulatable dynamics to regimes where quantum advantage may emerge.

The maintenance of quantum entanglement lays the elementary building block of quantum information processing, requiring an integration of long coherence time, sufficient storage capacity, and high-fidelity entangling gates. Here we encode two-qubit entangled states into the decoherence-free subspaces (DFS) of four ions in a cryogenic trap. By crosstalk-free sympathetic cooling under dual-type encoding and multi-state detection which discards the collision-induced leakage error, we achieve a storage lifetime of about one hour for the entangled logical states. We further study the second-order DFS and show its advantage in suppressing the spatially nonuniform noise over the first-order DFS. Our work paves the way for applications of DFS quantum memories in quantum computing, quantum network and precision measurement.

The dual-type qubit scheme is an emerging method to suppress crosstalk errors in scalable trapped-ion quantum computation and quantum network. Here we report a hardware-economic way to control dual-type $^{171}\mathrm{Yb}^+$ qubits using a single $355\,$nm mode-locked pulsed laser. Utilizing its broad frequency comb structure, we drive the Raman transitions of both qubit types encoded in the $S_{1/2}$ and the $F_{7/2}$ hyperfine levels, and probe their carrier transitions and the motional sidebands. We further demonstrate a direct entangling gate between the two qubit types. Our work can simplify the manipulation of the $^{171}\mathrm{Yb}^+$ qubits both at the hardware and the software level.

Quantum networks and quantum repeaters represent the promising avenues for building large-scale quantum information systems, serving as foundational infrastructure for distributed quantum computing, long-distance quantum communication, and networked quantum sensing. A critical step in realizing a functional quantum network is the efficient and high-fidelity establishment of heralded entanglement between remote quantum nodes. Multiplexing offers a powerful strategy to accelerate remote entanglement distribution, particularly over long optical fibers. Here, we demonstrate the first multiplexing-enhanced heralded entanglement between two trapped-ion quantum network nodes. By multiplexing $10$ temporal photonic modes, we achieve a 4.59-fold speedup in ion-ion entanglement generation and attain an entanglement fidelity of $95.9\pm1.5\%$ over $1.2$ km of fiber. Employing a dual-type architecture, our system is readily scalable to multiple nodes, thereby establishing a key building block for future large-scale quantum networks.

A quantum memory is an essential element for quantum computation, quantum network and quantum metrology. Previously, a single-qubit quantum memory with a coherence time of about an hour has been realized in a dual-species setup where a coolant ion provides sympathetic cooling for a memory ion of different species. However, the frequent random position hopping between the ions in the room-temperature trap limits the technique there only applicable to single-qubit storage. Here we report a multi-ion quantum memory in a cryogenic trap based on the dual-type scheme, and demonstrate a coherence time above two hours for a logical qubit encoded in the decoherence-free subspace, i.e. two-ion entangled states, after correcting the dominant leakage error. Our scheme alleviates the necessity of an ultra-stable frequency reference for the stored qubit, and has a preferable scalability owing to the same mass of the metastable-state memory ions and the ground-state coolant ion.

Trapped ions constitute a promising platform for implementation of a quantum network. Recently, a dual-type qubit scheme has been realized in a quantum network node where the communication qubits and the memory qubits are encoded in different energy levels of the same ion species, such that the generation of ion-photon entanglement on the communication qubits has negligible crosstalk error on the preloaded quantum information in the memory qubits. However, to achieve the versatile applications of a quantum network, a crucial component of the dual-type node, namely the entangling gate between the communication and the memory qubits, is still missing. Here we report a dual-type quantum network node equipped with ion-photon entanglement generation, crosstalk-free quantum memory and entangling gates between the dual-type qubits simultaneously. We demonstrate its practical applications including the quantum state teleportation and the preparation of multipartite entangled state. Our work achieves the necessary components of a dual-type quantum network node and paves the way toward its applications in a large-scale quantum internet.

Quantum network and quantum repeater are promising ways to scale up a quantum information system to enable various applications with unprecedented performance. As a current bottleneck of building a long-distance quantum network, the distribution rate of heralded entanglement between remote network nodes is typically much lower than the decoherence rate of each local node, which obstructs the implementation of a metropolitan-scale quantum network with more than two remote nodes. A promising scheme to accelerate the remote entanglement distribution is through multiplexing enhancement based on a multimode quantum network node. In this work, we experimentally realize a functional $5$-ion quantum network node with two different types of qubits inside. We employ a hybrid multiplexing scheme combining the methods of multiple excitation and ion shuttling, in which maximally $44$ time-bin modes are generated and sent through a long fiber to boost the entangling rate. Via this scheme, we can generate heralded ion-photon entanglement with a high fidelity of $96.8\%$/$94.6\%$/$89.8\%$ with a success rate of $263\,\text{s}^{-1}$/$40\,\text{s}^{-1}$/$4.28\,\text{s}^{-1}$, over a fiber of $3\,$m/$1\,$km/$12\,$km, respectively. In addition, the memory qubit can protect the stored quantum information from the destructive ion-photon entangling attempts via dual-type encoding and a memory coherence time of $366\,$ms is achieved. This coherence time has exceeded the expected entanglement generation time $234\,$ms over a $12\,$km fiber, which is realized for the first time in a metropolitan-scale quantum network node.

The requirement for Hermiticity in quantum mechanics ensures the reality of energies, while the parity-time symmetry offers an alternative route to achieve this goal. Interestingly, in a three-level system, the parity-time symmetry-breaking can lead to a third-order exceptional point with distinctive topological properties and enhanced sensitivity. To experimentally implement this in open quantum systems, it is essential to introduce two well-controlled loss channels. However, the requirement for these two loss channels presents a challenge in experimental implementation due to the lack of methods to realize the dynamics governed by an effective non-Hermitian Hamiltonian. Here we address the challenge by employing two approaches to eliminate the effects of quantum jump terms so that the dynamics is governed by an effective non-Hermitian Hamiltonian in a dissipative trapped ion with two loss channels. Based on this, we experimentally observe the parity-time symmetry-breaking-induced third-order exceptional point through non-Hermitian absorption spectroscopy. In particular, we perform quantum state tomography to directly demonstrate the coalescence of three eigenstates into a single eigenstate at the exceptional point. Finally, we identify an intrinsic third order Liouvillian exceptional point associated with a parity-time symmetry breaking via quench dynamics. Our experiments can be extended to observe other non-Hermitian phenomena involving more than two levels and potentially find applications in quantum information technology.

Quantum simulators with hundreds of qubits and engineerable Hamiltonians have the potential to explore quantum many-body models that are intractable for classical computers. However, learning the simulated Hamiltonian, a prerequisite for any applications of a quantum simulator, remains an outstanding challenge due to the fast increasing time cost with the qubit number and the lack of high-fidelity universal gate operations in the noisy intermediate-scale quantum era. Here we demonstrate the Hamiltonian learning of a two-dimensional ion trap quantum simulator with 300 qubits. We employ global manipulations and single-qubit-resolved state detection to efficiently learn the all-to-all-coupled Ising model Hamiltonian, with the required quantum resources scaling at most linearly with the qubit number. Our work paves the way for wide applications of large-scale ion trap quantum simulators.

We study a hardware-efficient variational quantum algorithm ansatz tailored for the trapped-ion quantum simulator, HEA-TI. We leverage programmable single-qubit rotations and global spin-spin interactions among all ions, reducing the dependence on resource-intensive two-qubit gates in conventional gate-based methods. We apply HEA-TI to state engineering of cluster states and analyze the scaling of required quantum resources. We also apply HEA-TI to solve the ground state problem of chemical molecules $\mathrm{H_{2}}$, $\mathrm{LiH}$ and $\mathrm{F_{2}}$. We numerically analyze the quantum computing resources required to achieve chemical accuracy and examine the performance under realistic experimental noise and statistical fluctuation. The efficiency of this ansatz is shown to be comparable to other commonly used variational ansatzes like UCCSD, with the advantage of substantially easier implementation in the trapped-ion quantum simulator. This approach showcases the hardware-efficient ansatz as a powerful tool for the application of the near-term quantum computer.

Two-dimensional (2D) ion crystals have become a promising way to scale up qubit numbers for ion trap quantum information processing. However, to realize universal quantum computing in this system, individually addressed high-fidelity two-qubit entangling gates still remain challenging due to the inevitable micromotion of ions in a 2D crystal as well as the technical difficulty in 2D addressing. Here we demonstrate two-qubit entangling gates between any ion pairs in a 2D crystal of four ions. We use symmetrically placed crossed acousto-optic deflectors (AODs) to drive Raman transitions and achieve an addressing crosstalk error below 0.1%. We design and demonstrate a gate sequence by alternatingly addressing two target ions, making it compatible with any single-ion addressing techniques without crosstalk from multiple addressing beams. We further examine the gate performance versus the micromotion amplitude of the ions and show that its effect can be compensated by a recalibration of the laser intensity without degrading the gate fidelity. Our work paves the way for ion trap quantum computing with hundreds to thousands of qubits on a 2D ion crystal.

Trapped atomic ions constitute one of the leading physical platforms for building the quantum repeater nodes to realize large-scale quantum networks. In a long-distance trapped-ion quantum network, it is essential to have crosstalk-free dual-type qubits: one type, called the communication qubit, to establish an entangling interface with telecom photons; and the other type, called the memory qubit, to store quantum information immune from photon scattering under entangling attempts. Here, we report the first experimental implementation of a telecom-compatible and crosstalk-free quantum network node based on two trapped $^{40}$Ca$^{+}$ ions. The memory qubit is encoded on a long-lived metastable level to avoid crosstalk with the communication qubit encoded in another subspace of the same ion species, and a quantum wavelength conversion module is employed to generate ion-photon entanglement over a $12\,$km fiber in a heralded style. Our work therefore constitutes an important step towards the realization of quantum repeaters and long-distance quantum networks.

The spin-boson model is a prototypical model for open quantum dynamics. Here we simulate the spin-boson model using a chain of trapped ions where a spin is coupled to a structured reservoir of bosonic modes. We engineer the spectral density of the reservoir by adjusting the ion number, the target ion location, the laser detuning to the phonon sidebands, and the number of frequency components in the laser, and we observe their effects on the collapse and revival of the initially encoded information. Our work demonstrates the ion trap as a powerful platform for simulating open quantum dynamics with complicated reservoir structures.

A large qubit capacity and an individual readout capability are two crucial requirements for large-scale quantum computing and simulation. As one of the leading physical platforms for quantum information processing, the ion trap has achieved quantum simulation of tens of ions with site-resolved readout in 1D Paul trap, and that of hundreds of ions with global observables in 2D Penning trap. However, integrating these two features into a single system is still very challenging. Here we report the stable trapping of 512 ions in a 2D Wigner crystal and the sideband cooling of their transverse motion. We demonstrate the quantum simulation of long-range quantum Ising models with tunable coupling strengths and patterns, with or without frustration, using 300 ions. Enabled by the site resolution in the single-shot measurement, we observe rich spatial correlation patterns in the quasi-adiabatically prepared ground states, which allows us to verify quantum simulation results by comparing with the calculated collective phonon modes and with classical simulated annealing. We further probe the quench dynamics of the Ising model in a transverse field to demonstrate quantum sampling tasks. Our work paves the way for simulating classically intractable quantum dynamics and for running NISQ algorithms using 2D ion trap quantum simulators.

Generating ion-photon entanglement is a crucial step for scalable trapped-ion quantum networks. To avoid the crosstalk on memory qubits carrying quantum information, it is common to use a different ion species for ion-photon entanglement generation such that the scattered photons are far off-resonant for the memory qubits. However, such a dual-species scheme requires elaborate control of the portion and the location of different ion species, and can be subject to inefficient sympathetic cooling. Here we demonstrate a trapped-ion quantum network node in the dual-type qubit scheme where two types of qubits are encoded in the $S$ and $F$ hyperfine structure levels of ${}^{171}\mathrm{Yb}^+$ ions. We generate ion photon entanglement for the $S$-qubit in a typical timescale of hundreds of milliseconds, and verify its small crosstalk on a nearby $F$-qubit with coherence time above seconds. Our work demonstrates an enabling function of the dual-type qubit scheme for scalable quantum networks.

Storage lifetime and capacity are two important factors to characterize the performance of a quantum memory. Here we report the stable trapping of above 200 ions in a cryogenic setup, and demonstrate the combination of the multi-qubit capacity and long storage lifetime by measuring the coherence time of randomly chosen ions to be on the order of hundreds of milliseconds. We apply composite microwave pulses to manipulate qubit states globally for efficient characterization of different storage units simultaneously, and we compare the performance of the quantum memory with and without the sympathetic cooling laser, thus unambiguously show the necessity of sympathetic cooling for the long-time storage of multiple ionic qubits.

The trapped ion quantum simulator has demonstrated qualitative properties of different physical models for up to tens of ions. In particular, a linear ion chain naturally hosts long-range Ising interactions under the laser driving, which has been used for various phenomena such as quantum phase transition, localization, thermalization and information propagation. For near-term practical usage, a central task is to find more quantitative applications of the noisy quantum simulators that are robust to small errors in the parameters. Here we report the quantum simulation of a long-range transverse-field Ising model using up to 61 ions and probe the critical behavior of its quantum phase transition through the Kibble-Zurek mechanism. By calibrating and verifying the coupling coefficients, we realize the same model for increasing ion numbers, so as to extract a critical exponent free of the finite size effect. For ferromagnetic interaction, our experimental result agrees well with the previous numerical predictions. As for the anti-ferromagnetic case, signals are too weak to fit a critical exponent due to the frustration in the interaction, but still consistent with the theory.

Jaynes-Cummings-Hubbard (JCH) model is a fundamental many-body model for light-matter interaction. As a leading platform for quantum simulation, the trapped ion system has realized the JCH model for two to three ions. Here we report the quantum simulation of the JCH model using up to 32 ions. We verify the simulation results even for large ion numbers by engineering low excitations and thus low effective dimensions; then we extend to 32 excitations for an effective dimension of $2^{77}$, which is difficult for classical computers. By regarding the phonon modes as baths, we explore Markovian or non-Markovian spin dynamics in different parameter regimes of the JCH model, similar to quantum emitters in a structured photonic environment. We further examine the dependence of the non-Markovian dynamics on the effective Hilbert space dimension. Our work demonstrates the trapped ion system as a powerful quantum simulator for many-body physics and open quantum systems.

Supersymmetry (SUSY) helps solve the hierarchy problem in high-energy physics and provides a natural groundwork for unifying gravity with other fundamental interactions. While being one of the most promising frameworks for theories beyond the Standard Model, its direct experimental evidence in nature still remains to be discovered. Here we report experimental realization of a supersymmetric quantum mechanics (SUSY QM) model, a reduction of the SUSY quantum field theory for studying its fundamental properties, using a trapped ion quantum simulator. We demonstrate the energy degeneracy caused by SUSY in this model and the spontaneous SUSY breaking. By a partial quantum state tomography of the spin-phonon coupled system, we explicitly measure the supercharge of the degenerate ground states, which are superpositions of the bosonic and the fermionic states. Our work demonstrates the trapped-ion quantum simulator as an economic yet powerful platform to study versatile physics in a single well-controlled system.

Quantum simulation of 1D relativistic quantum mechanics has been achieved in well-controlled systems like trapped ions, but properties like spin dynamics and response to external magnetic fields that appear only in higher dimensions remain unexplored. Here we simulate the dynamics of a 2D Weyl particle. We show the linear dispersion relation of the free particle and the discrete Landau levels in a magnetic field, and we explicitly measure the spatial and spin dynamics from which the conservation of helicity and properties of antiparticles can be verified. Our work extends the application of an ion trap quantum simulator in particle physics with the additional spatial and spin degrees of freedom.

Dissipation is often considered as a detrimental effect in quantum systems for unitary quantum operations. However, it has been shown that suitable dissipation can be useful resources both in quantum information and quantum simulation. Here, we propose and experimentally simulate a dissipative phase transition (DPT) model using a single trapped ion with an engineered reservoir. We show that the ion's spatial oscillation mode reaches a steady state after the alternating application of unitary evolution under a quantum Rabi model Hamiltonian and sideband cooling of the oscillator. The average phonon number of the oscillation mode is used as the order parameter to provide evidence for the DPT. Our work highlights the suitability of trapped ions for simulating open quantum systems and shall facilitate further investigations of DPT with various dissipation terms.

Trapped ions constitute one of the most promising systems for implementing quantum computing and networking. For large-scale ion-trap-based quantum computers and networks, it is critical to have two types of qubits, one for computation and storage, while the other for auxiliary operations like runtime qubit detection, sympathetic cooling, and repetitive entanglement generation through photon links. Dual-type qubits have previously been realized in hybrid systems using two ion species, which, however, introduces significant experimental challenges for laser setup, gate operations as well as the control of the fraction and positioning of each qubit type within an ion crystal. Here we solve these problems by implementing two coherently-convertible qubit types using the same ion species. We encode the qubits into two pairs of clock states of the 171Yb+ ions, and achieve fast and high-fidelity conversion between the two types using narrow-band lasers. We further demonstrate that operations on one qubit type, including sympathetic laser cooling, gates and qubit detection, have crosstalk errors less than 0.03% on the other type, well below the error threshold for fault-tolerant quantum computing. Our work showcases the feasibility and advantages of using coherently convertible dual-type qubits with the same ion species for future large-scale quantum computing and networking.

Quantum phase transitions (QPTs) are usually associated with many-body systems with large degrees of freedom approaching the thermodynamic limit. In such systems, the many-body ground state shows abrupt changes at zero temperature when the control parameter of the Hamiltonian is scanned across a quantum critical point. Recently it has been realized that a QPT can also occur in a simple system composed of only a two-level atom and a single-mode bosonic field, described by the quantum Rabi model (QRM). Here we report the first experimental demonstration of a QPT in the QRM using a single trapped ion. We measure the average spin-up state population of the ion and the average phonon number in its spatial oscillation mode as two order parameters and observe the clear evidences of the phase transition via slow quench of the coupling between the ion and its spatial motion. An experimental probe of the phase transitions in a fundamental quantum optics model without imposing the thermodynamic limit opens up a new window for the controlled study of QPTs and quantum critical phenomena.

Ion trap is one of the most promising candidates for quantum computing. Current schemes mainly focus on a linear chain of up to about one hundred ions in a Paul trap. To further scale up the qubit number, one possible direction is to use 2D or 3D ion crystals (Wigner crystals). In these systems, ions are generally subjected to large micromotion due to the strong fast-oscillating electric field, which can significantly influence the performance of entangling gates. In this work, we develop an efficient numerical method to design high-fidelity entangling gates in a general 3D ion crystal. We present numerical algorithms to solve the equilibrium configuration of the ions and their collective normal modes. We then give a mathematical description of the micromotion and use it to generalize the gate scheme for linear ion chains into a general 3D crystal. The involved time integral of highly oscillatory functions is expanded into a fast-converging series for accurate and efficient evaluation and optimization. As a numerical example, we show a high-fidelity entangling gate design between two ions in a 100-ion crystal, with a theoretical fidelity of 99.9\%.

Building blocks of quantum computers have been demonstrated in small to intermediate-scale systems. As one of the leading platforms, the trapped ion system has attracted wide attention. A significant challenge in this system is to combine fast high-fidelity gates with scalability and convenience in ion trap fabrication. Here we propose an architecture for large-scale quantum computing with a two-dimensional array of atomic ions trapped at such large distance which is convenient for ion-trap fabrication but usually believed to be unsuitable for quantum computing as the conventional gates would be too slow. Using gate operations far outside of the Lamb-Dicke region, we show that fast and robust entangling gates can be realized in any large ion arrays. The gate operations are intrinsically parallel and robust to thermal noise, which, together with their high speed and scalability of the proposed architecture, makes this approach an attractive one for large-scale quantum computing.