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A large qubit capacity and an individual readout capability are two crucial requirements for large-scale quantum computing and simulation1. As one of the leading physical platforms for quantum information processing, the ion trap has achieved a quantum simulation of tens of ions with site-resolved readout in a one-dimensional Paul trap2–4and of hundreds of ions with global observables in a two-dimensional (2D) Penning trap5,6. 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 the measured two-spin correlations 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 noisy intermediate-scale quantum algorithms7,8using 2D ion trap quantum simulators.

Trapped ions constitute one of the most promising systems for implementing quantum computing and networking1,2. For large-scale ion-trap-based quantum computers and networks, it is critical to have two types of qubit: one for computation and storage, and another for auxiliary operations such as qubit detection3, sympathetic cooling4–7and entanglement generation through photon links8,9. Although the two qubit types can be implemented using two different ion species3,10–13, this approach introduces substantial complexity into creating and controlling each qubit type14,15. Here we resolve these challenges by implementing two coherently convertible qubit types using one ion species. We encode the qubits into two pairs of clock states of the 171Yb+ions, and achieve microsecond-level conversion rates between the two types with one-way fidelities of 99.5%. We further demonstrate that operations on one qubit type, including sympathetic laser cooling, single-qubit gates and qubit detection, have crosstalk errors less than 0.06% on the other type, which is below the best-known error threshold of ~1% for fault-tolerant quantum computing using the surface code1,16. Our work establishes the feasibility and advantages of using coherently convertible dual-type qubits with the same ion species for large-scale quantum computing and networking.

Logical qubit encoding and quantum error correction (QEC) protocols have been experimentally demonstrated in various physical systems with multiple physical qubits, generally without reaching the break-even point, at which the lifetime of the quantum information exceeds that of the single best physical qubit within the logical qubit. Logical operations are challenging, owing to the necessary non-local operations at the physical level, making bosonic logical qubits that rely on higher Fock states of a single oscillator attractive, given their hardware efficiency. QEC that reaches the break-even point and single logical-qubit operations have been demonstrated using the bosonic cat code. Here, we experimentally demonstrate repetitive QEC approaching the break-even point of a single logical qubit encoded in a hybrid system consisting of a superconducting circuit and a bosonic cavity using a binomial bosonic code. This is achieved while simultaneously maintaining full control of the single logical qubit, including encoding, decoding and a high-fidelity universal quantum gate set with 97% average process fidelity. The corrected logical qubit has a lifetime 2.8 times longer than that of its uncorrected counterpart. We also perform a Ramsey experiment on the corrected logical qubit, reporting coherence twice as long as for the uncorrected case.

A long-time quantum memory capable of storing and measuring quantum information at the single-qubit level is an essential ingredient for practical quantum computation and communication1,2 . Currently, the coherence time of a single qubit is limited to less than 1 min, as demonstrated in trapped ion systems3–5 , although much longer coherence times have been reported in ensembles of trapped ions6,7 and nuclear spins of ionized donors8,9 . Here, we report the observation of a coherence time of over 10 min for a single qubit in a 171Yb+ion sympathetically cooled by a 138Ba+ion in the same Paul trap, which eliminates the problem of qubit-detection inefficiency from heating of the qubit ion10,11 . We also apply a few thousand dynamical decoupling pulses to suppress ambient noise from magnetic-field fluctuation s and phase noise from the local os cillator8,9,12–16 . The long-time quantum memory of the single trapped ion qubit would be the essential component of scalable quantum computers1,17,18 , quantum networks2,19,20 and quantum money21,22 . The longest coherence time of a single qubit of more than ten minutes is observed in a 171Yb+ion. After sympathetically cooling the 171Yb+ion qubit with a 138Ba+ion, noise from magnetic-field fluctuations and the local oscillator is suppressed by a dynamic decoupling scheme.

Distributed quantum information processing requires a reliable quantum memory and a faithful carrier of quantum information. Atomic qubits have very long coherence times and are thus excellent candidates for quantum information storage, whereas photons are ideal for the transport of quantum information as they can travel long distances with a minimum of decoherence. We discuss the theoretical and experimental combination of these two systems and their use for not only quantum information transfer but also scalable quantum computation architectures.

We review theoretical proposals for implementation of quantum computing and quantum communication with quantum optical methods.

In the version of this Letter originally published, in Fig. 2c legend, the entry ‘LO phase noise’ should not have been included. This has now been corrected in the online versions.