L. He

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.

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.

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.

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.

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.

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.

Symmetries play a crucial role in the classification of topological phases of matter. Although recent studies have established a powerful framework to search for and classify topological phases based on symmetry indicators, there exists a large class of fragile topology beyond the description. The Euler class characterizing the topology of two-dimensional real wave functions is an archetypal fragile topology underlying some important properties, such as non-Abelian braiding of crossing nodes and higher-order topology. However, as a minimum model of fragile topology, the two-dimensional topological Euler insulator consisting of three bands remains a significant challenge to be implemented in experiments. Here, we experimentally realize a three-band Hamiltonian to simulate a topological Euler insulator with a trapped-ion quantum simulator. Through quantum state tomography, we successfully evaluate the Euler class, Wilson loop flow and entanglement spectra to show the topological properties of the Hamiltonian. We also measure the Berry phases of the lowest energy band, illustrating the existence of four crossing points protected by the Euler class. The flexibility of the trapped-ion quantum simulator further allows us to probe dynamical topological features including skyrmion-antiskyrmion pairs and Hopf links in momentum-time space from quench dynamics. Our results show the advantage of quantum simulation technologies for studying exotic topological phases and open a new avenue for investigating fragile topological phases in experiments.

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.

Experimental realization of a universal set of quantum logic gates is the central requirement for implementation of a quantum computer. An all-geometric approach to quantum computation offered a paradigm for implementation where all the quantum gates are achieved based on the Berry phases and their non-abelian extensions, the holonomies, from geometric transformation of quantum states in the Hilbert space. Apart from its fundamental interest and rich mathematical structure, the geometric approach has some built-in noise-resilient features. On the experimental side, geometric phases and holonomies have been observed using nuclear magnetic resonance with thermal ensembles of liquid molecules, however, such systems are known to be non-scalable for quantum computing. There are proposals to implement geometric quantum computation in scalable experimental platforms such as trapped ions, superconducting qubits, or quantum dots, and a recent experiment has realized geometric single-bit gates with the superconducting system. Here, we report the experimental realization of a universal set of geometric quantum gates with solid-state spins of the diamond defects. The diamond defects provide a scalable experimental platform with the potential for room-temperature quantum computing, which has attracted strong interest in recent years. Based on advance of coherent control in this system, our experiment shows that all-geometric and potentially robust quantum computation can be realized with solid-state spin qubits.