Ke Wang

Vortex interactions are commonly observed in atmospheric turbulence, plasma dynamics, and collective behaviors in biological systems. However, accurately simulating these complex interactions is highly challenging due to the need to capture fine-scale details over extended timescales, which places computational burdens on traditional methods. In this study, we introduce a quantum vortex method, reformulating the Navier–Stokes (NS) equations within a quantum mechanical framework to enable the simulation of multi-vortex interactions on a quantum computer. We construct the effective Hamiltonian for the vortex system and implement a spatiotemporal evolution circuit to simulate its dynamics over prolonged periods. By leveraging eight qubits on a superconducting quantum processor with gate fidelities of 99.97% for single-qubit gates and 99.76% for two-qubit gates, we successfully reproduce natural vortex interactions. Overall, we establish a framework that reformulates vortex dynamics into a normalized wavefunction representation compatible with quantum system unitary evolution, combined with the designed spatiotemporal encoding scheme, providing a concrete pathway toward leveraging quantum resources in fluid systems.

A long-standing challenge in quantum computing is developing technologies to overcome the inevitable noise in qubits. To enable meaningful applications in the early stages of fault-tolerant quantum computing, devising methods to suppress post-correction logical failures is becoming increasingly crucial. In this work, we propose and experimentally demonstrate the application of zero-noise extrapolation, a practical quantum error mitigation technique, to error correction circuits on superconducting processors. By amplifying the noise on physical qubits, the circuits yield outcomes that exhibit a predictable dependence on noise strength, following a polynomial function determined by the code distance. This property enables the effective application of polynomial extrapolation to mitigate logical errors. Our experiments demonstrate a universal reduction in logical errors across various quantum circuits, including fault-tolerant circuits of repetition and surface codes. We observe a favorable performance in multi-round error correction circuits, indicating that this method remains effective when the circuit depth increases. These results advance the frontier of quantum error suppression technologies, opening a practical way to achieve reliable quantum computing in the early fault-tolerant era.

Symmetry-protected topological phases^1–4 cannot be described by any local order parameter and are beyond the conventional symmetry-breaking model⁵. They are characterized by topological boundary modes that remain stable under symmetry respecting perturbations^1–4,6–8. In clean, gapped systems without disorder, the stability of these edge modes is restricted to the zero-temperature manifold; at finite temperatures, interactions with mobile thermal excitations lead to their decay^9–11. Here we report the observation of a distinct type of topological edge mode^12–14, which is protected by emergent symmetries and persists across the entire spectrum, in an array of 100 programmable superconducting qubits. Through digital quantum simulation of a one-dimensional disorder-free stabilizer Hamiltonian, we observe robust long-lived topological edge modes over up to 30 cycles for a wide range of initial states. We show that the interaction between these edge modes and bulk excitations can be suppressed by dimerizing the stabilizer strength, leading to an emergent U(1) × U(1) symmetry in the prethermal regime of the system. Furthermore, we exploit these topological edge modes as logical qubits and prepare a logical Bell state, which exhibits persistent coherence, despite the system being disorder-free and at finite temperature. Our results establish a viable digital simulation approach^15–18 to experimentally study topological matter at finite temperature and demonstrate a potential route to construct long-lived, robust boundary qubits in disorder-free systems.

The discovery of nontrivial topology in quantum critical states has revised the classification of quantum phase transitions and opened a new direction for exploiting topological phases. However, the experimental investigation of nontrivial topology in gapless many-body systems is challenging due to the inherent complex quantum entanglement. Here, we experimentally explore the topological properties in the critical cluster Ising model by preparing its low-lying critical states on a superconducting processor with up to 100 qubits. We develop an efficient method to probe the boundary g-function, which allows us to uniquely identify the nontrivial topology of the critical systems under study. Furthermore, we probe and recognize two-fold topological degeneracy in the entanglement spectrum under periodic boundary conditions and experimentally reveal the novel bulk-boundary correspondence in topological critical systems. Our results demonstrate the low-lying critical states as useful quantum resources for investigating the interplay between topology and quantum criticality.

Quantum nonlocality describes a stronger form of quantum correlation than that of entanglement. It refutes Einstein’s belief of local realism and is among the most distinctive and enigmatic features of quantum mechanics. It is a crucial resource for achieving quantum advantages in a variety of practical applications, ranging from cryptography and certified random number generation via self-testing to machine learning. Nevertheless, the detection of nonlocality, especially in quantum many-body systems, is notoriously challenging. Here, we report an experimental certification of genuine multipartite Bell-operator correlations, which signal nonlocality in quantum many-body systems, up to 24 qubits with a fully programmable superconducting quantum processor. In particular, we employ energy as a Bell-operator correlation witness and variationally decrease the energy of a many-body system across a hierarchy of thresholds, below which an increasing Bell-operator correlation depth can be certified from experimental data. We variationally prepare the low-energy state of a two-dimensional honeycomb model with 73 qubits and certify its Bell-operator correlations by measuring an energy that surpasses the corresponding classical bound with up to 48 standard deviations. In addition, we variationally prepare a sequence of low-energy states and certify their genuine multipartite Bell-operator correlations up to 24 qubits via energies measured efficiently by parity oscillation and multiple quantum coherence techniques. Our results establish a viable approach for preparing and certifying multipartite Bell-operator correlations, which provide not only a finer benchmark beyond entanglement for quantum devices, but also a valuable guide toward exploiting multipartite Bell correlations in a wide spectrum of practical applications.

Symmetry-protected topological phases cannot be described by any local order parameter and are beyond the conventional symmetry-breaking paradigm for understanding quantum matter. They are characterized by topological boundary modes that remain stable under symmetry respecting perturbations. In clean, gapped systems without disorder, the stability of these edge modes is restricted to the ground state manifold; at finite temperatures, interactions with mobile thermal excitations lead to their decay. Here, we report the observation of a distinct type of topological edge modes, which are protected by emergent symmetries and persist across the system's entire spectrum, in an array of 100 programmable superconducting qubits. In particular, through digital quantum simulation of the dynamics of a one-dimensional disorder-free stabilizer Hamiltonian, we observe robust long-lived topological edge modes over up to 30 cycles for a wide range of initial states. We show that the interaction between the topological edge modes and bulk thermal excitations can be suppressed by dimerizing the interactions across the two sublattices, dramatically prolonging the lifetime of these edge modes even at infinite temperature. These edge modes are protected not by disorder, but by an emergent U(1)×U(1) symmetry brought on by this dimerization. Furthermore, we exploit these topological edge modes as logical qubits and prepare a logical Bell state, which exhibits persistent coherence in the dimerized and off-resonant regime, despite the system being disorder-free and far from its ground state. Our results establish a viable digital simulation approach to experimentally study topological matter at finite-temperature and demonstrate a potential route to construct long-lived robust boundary qubits in disorder-free systems.

Tracking the time evolution of a quantum state allows one to verify the thermalization rate or the propagation speed of correlations in generic quantum systems. Inspired by the energy-time uncertainty principle, bounds have been demonstrated on the maximal speed at which a quantum state can change, resulting in immediate and practical tasks. Based on a programmable superconducting quantum processor, we test the dynamics of various emulated quantum mechanical systems encompassing single- and many-body states. We show that one can test the known quantum speed limits and that modifying a single Hamiltonian parameter allows the observation of the crossover of the different bounds on the dynamics. We also unveil the observation of minimal quantum speed limits in addition to more common maximal ones, i.e., the lowest rate of change of a unitarily evolved quantum state. Our results show a comprehensive experimental characterization of quantum speed limits and enhance the understanding for their subsequent study in engineered non-unitary conditions.