Mengxiang Zhang

Temporal non-analyticities in the rate function of the Loschmidt echo manifests a class of dynamical quantum phase transitions (DQPTs) that has emerged as a powerful framework for understanding far-from-equilibrium many-body dynamics. While such DQPT has been extensively studied theoretically in spin-boson systems such as the Dicke model, their experimental observation remains elusive. In particular, the dynamics of DQPT in asymmetric spin subspaces and under the influence of spin dissipation are largely unexplored. Here, we report an experimental study of temporal DQPT in a generalized Dicke model using a trapped-ion quantum simulator. By coupling a linear chain of $\rm{^{40}Ca^{+}}$ ions to a collective center-of-mass motional mode, we probe the quench dynamics starting from both symmetric and asymmetric initial states. We extract the rate function and identify temporal turn-around points that are in quantitative agreement with theoretical predictions. Additionally, we investigate the impact of spin dissipation on these dynamics. Our results establish an experimental platform for probing complex many-body out-of-equilibrium phenomena and advance the development of hybrid oscillator-spin quantum simulators.

Trapped-ion systems are one of the leading platforms for quantum information processing, where a key challenge is to scale up system size while maintaining high-fidelity two-qubit operations. A promising approach is to build high-performance modules interconnected via strong coupling. In particular, axial motional modes provide a feasible means of coupling short ion chains. However, previous implementations of fully connected 5-ion modules based on axial modes have been limited to fidelities of $96.6-98.0\%$. Here, we demonstrate two-qubit quantum logic gates in a 5-ion $^{40}$Ca$^{+}$ chain using axial modes, achieving fidelities exceeding $99\%$ for adjacent pairs and over $98\%$ for arbitrary pairs by carefully tackling dominant error sources. Our results are beneficial to the development of scalable ion-trap quantum processors, quantum simulation and quantum-enhanced metrology.

Quantum error correction (QEC) is essential for practical quantum computing, as it protects fragile quantum information from errors by encoding it in high-dimensional Hilbert spaces. Conventional QEC protocols typically require repeated syndrome measurements, real-time feedback, and the use of multiple physical qubits for encoding. Such implementations pose significant technical complexities, particularly for trapped-ion systems, with high demands on precision and scalability. Here, we realize autonomous QEC with a logical qubit encoded in multiple internal spin states of a single trapped ion, surpassing the break-even point for qubit lifetime. Our approach leverages engineered spin-motion couplings to transfer error-induced entropy into motional modes, which are subsequently dissipated through sympathetic cooling with an ancilla ion, fully eliminating the need for measurement and feedback. By repetitively applying this autonomous QEC protocol under injected low-frequency noise, we extend the logical qubit lifetime to approximately 11.6 ms, substantially outperforming lifetime for both the physical qubit ($\simeq$0.9 ms) and the uncorrected logical qubit ($\simeq$0.8 ms), thereby beating the break-even point with autonomous protection of quantum information without measurement or post-selection. This work presents an efficient approach to fault-tolerant quantum computing that harnesses the intrinsic multi-level structure of trapped ions, providing a distinctive path toward scalable architectures and robust quantum memories with reduced overhead.

The nontrivial degeneracies in non-Hermitian systems, exceptional points (EPs), have attracted extensive attention due to intriguing phenomena. Compared with commonly observed second-order EPs, high-order EPs show rich physics due to their extended dimension and parameter space, ranging from the coalescence of EPs into higher order to potential applications in topological properties. However, these features also pose challenges in controlling multiple coherent and dissipative elements in a scaled system. Here we experimentally demonstrate a native programmable control to simulate a high-order non-Hermitian Hamiltonian in a multi-dimensional trapped ion system. We simulate a series of non-Hermitian systems with varied parameters and observe the coalescence of second-order EPs into a fourth-order EP. Our results pave the way for scalable quantum simulation of high-dimensional dissipative systems and can be beneficial for the application of high-order EPs in quantum sensing and quantum control.

Quantum information processing with multi-level systems (qudits) provides additional features and applications than the two-level systems. However, qudits are more prone to dephasing and dynamical decoupling for qudits has never been experimentally demonstrated. Here, as a proof-of-principle demonstration, we experimentally apply dynamical decoupling to protect superpositions with three levels of a trapped $^9\rm{Be}^+$ ion from ambient noisy magnetic field, prolonging coherence by up to approximately an order of magnitude. Our demonstration, straightforwardly scalable to more levels, may open up a path toward long coherence quantum memory, metrology and information processing with qudits.

Triply degenerate points (TDPs), which correspond to new types of topological semimetals, can support novel quasiparticles possessing effective integer spins while preserving Fermi statistics. Here by mapping the momentum space to the parameter space of a three-level system in a trapped ion, we experimentally explore the transitions between different types of TDPs driven by spin-tensor--momentum couplings. We observe the phase transitions between TDPs with different topological charges by measuring the Berry flux on a loop surrounding the gap-closing lines, and the jump of the Berry flux gives the jump of the topological charge (up to a $2π$ factor) across the transitions. For the Berry flux measurement, we employ a new method by examining the geometric rotations of both spin vectors and tensors, which lead to a generalized solid angle equal to the Berry flux. The controllability of multi-level ion offers a versatile platform to study high-spin physics and our work paves the way to explore novel topological phenomena therein.

Along with the scaling of dimensions in quantum systems, transitions between the system's energy levels would become close in frequency, which are conventionally resolved by weak and lengthy pulses. Here, we extend and experimentally demonstrate analytically based swift quantum control techniques on a four-level trapped ion system, where we perform individual or simultaneous control over two pairs of spectrally nearby transitions with tailored time-varied drive, achieving operational fidelities ranging from 99.2(3)\% to 99.6(3)\%. Remarkably, we achieve approximately an order of magnitude speed up comparing with the case of weak square pulse for a general control. Therefore, our demonstration may be beneficial to a broad range of quantum systems with crowded spectrum, for spectroscopy, quantum information processing and quantum simulation.