Periodically driven systems, or Floquet systems, exhibit many novel dynamics and interesting out-of-equilibrium phases of matter. Those phases arising with the quantum systems' symmetries, such as global U(1) symmetry, can even show dynamical stability with symmetry protection. Here we experimentally demonstrate a U(1) symmetry-protected prethermal phase, via performing a digital-analog quantum simulation on a superconducting quantum processor. The dynamical stability of this phase is revealed by its robustness against external perturbations. We also find that the site-averaged square of the two-spin correlation function in this phase is stabilized by the interaction between the spins. Our work reveals a promising prospect in discovering emergent quantum dynamical phases with digital-analog quantum simulators.
Periodically driven systems, or Floquet systems, exhibit many novel dynamics and interesting out-of-equilibrium phases of matter. Those phases arising with the quantum systems' symmetries, such as global U(1) symmetry, can even show dynamical stability with symmetry protection. Here we experimentally demonstrate a U(1) symmetry-protected prethermal phase, via performing a digital-analog quantum simulation on a superconducting quantum processor. The dynamical stability of this phase is revealed by its robustness against external perturbations. We also find that the site-averaged square of the two-spin correlation function in this phase is stabilized by the interaction between the spins. Our work reveals a promising prospect in discovering emergent quantum dynamical phases with digital-analog quantum simulators.
Abstract Quantum many-body systems away from equilibrium host a rich variety of exotic phenomena that are forbidden by equilibrium thermodynamics. A prominent example is that of discrete time crystals 1–8 , in which time-translational symmetry is spontaneously broken in periodically driven systems. Pioneering experiments have observed signatures of time crystalline phases with trapped ions 9,10 , solid-state spin systems 11–15 , ultracold atoms 16,17 and superconducting qubits 18–20 . Here we report the observation of a distinct type of non-equilibrium state of matter, Floquet symmetry-protected topological phases, which are implemented through digital quantum simulation with an array of programmable superconducting qubits. We observe robust long-lived temporal correlations and subharmonic temporal response for the edge spins over up to 40 driving cycles using a circuit of depth exceeding 240 and acting on 26 qubits. We demonstrate that the subharmonic response is independent of the initial state, and experimentally map out a phase boundary between the Floquet symmetry-protected topological and thermal phases. Our results establish a versatile digital simulation approach to exploring exotic non-equilibrium phases of matter with current noisy intermediate-scale quantum processors 21 .
The simulation of non-equilibrium quantum many-body systems on noisy intermediate-scale quantum (NISQ) processors represents a central challenge and opportunity in modern condensed matter physics. Periodically driven (Floquet) systems can host exotic phases of matter with no equilibrium counterpart, most notably discrete time crystals (DTCs) characterized by spontaneous breaking of discrete time-translation symmetry and robust subharmonic responses. However, the realization of DTCs faces fundamental obstacles: driven many-body systems generically absorb energy and thermalize to an infinite-temperature state, destroying time-crystalline order. Two primary mechanisms have been identified to stabilize DTCs—many-body localization (MBL) through strong disorder, and Floquet prethermalization wherein high-frequency driving suppresses heating over exponentially long timescales. This work investigates the digital quantum simulation of prethermal DTCs on current superconducting quantum processors, with a focus on understanding and mitigating the impact of hardware noise. Recent experiments on 133-qubit heavy-hexagonal devices have demonstrated the realization of clean two-dimensional DTCs and incommensurately modulated DTCs (IM-DTCs) using kicked Ising models, observing period-doubling oscillations persisting for up to 100 Floquet cycles . Crucially, these simulations reveal that quantum noise, often perceived as detrimental, can in certain regimes stabilize novel prethermal DTC phases—a phenomenon identified as noise-induced DTCs supported by symmetry charge pumping or random gate fluctuations . The heavy-hexagonal lattice geometry, compared to square lattices, exhibits significantly slower quantum scrambling, thereby extending the prethermal plateau and enhancing DTC stability. We address two key challenges limiting the scalability of DTC simulations: limited qubit connectivity and environmental noise. By leveraging the universality of native gate sets, we demonstrate how to implement effective couplings among physically disconnected qubits at the cost of increased circuit depth, enabling the study of interaction-range effects on DTC stabilization—a phenomenon previously unobserved experimentally . Furthermore, we benchmark the performance of error mitigation protocols based on depolarising noise models, achieving excellent agreement between error-mitigated hardware data and tensor-network simulations in regimes where classical computations remain tractable . Our results highlight the complementary roles of quantum hardware and classical simulation: quantum processors provide access to regimes where entanglement growth outpaces tensor-network methods, while careful validation against classical benchmarks ensures the reliability of quantum outcomes. This study establishes a concrete pathway for using NISQ devices as experimental platforms for synthesizing and probing novel non-equilibrium quantum phases, advancing both our fundamental understanding of Floquet many-body dynamics and the practical capabilities of quantum simulation. The identification of noise as an active ingredient in phase stabilization suggests new directions for quantum engineering of spatiotemporal orders on near-term hardware.
Synchronization is a hallmark of collective behavior in classical nonlinear systems, yet its realization as a robust many-body phenomenon in coherent quantum systems remains largely unexplored. Here we demonstrate symmetry-protected quantum synchronization and a quantum chimera state in coherent Floquet dynamics on programmable superconducting quantum processors. By implementing stroboscopic evolution of a two-dimensional Heisenberg model on IBM heavy-hex devices, we observe that initially phase-randomized spins spontaneously self-organize into coherent lattice-wide oscillations. On 28 qubits, synchronization persists even for strongly randomized initial states and is stabilized by SU(2) symmetry, as confirmed by explicit symmetry breaking. Scaling up to 156 qubits reveals a qualitatively distinct regime. For weak initial randomness, global synchronization extends across the device. For strong randomness, the system fails to synchronize globally, yet subsets of qubits exhibit robust local phase coherence under homogeneous unitary dynamics. This coexistence of globally desynchronized and locally synchronized regions constitutes a quantum analogue of a classical chimera state. Statevector and matrix-product-state simulations reproduce both the symmetry-protected synchronization and the chimera coexistence, demonstrating that these phenomena arise from the intrinsic Floquet many-body dynamics. Our results establish symmetry-protected synchronization and quantum chimera states as experimentally accessible nonequilibrium dynamical phases in programable many-body quantum systems.
Abstract Symmetry-protected topological phases 1–4 cannot be described by any local order parameter and are beyond the conventional symmetry-breaking model 5 . 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.
Motivated by experimental observations of time-symmetry breaking behavior in a periodically driven (Floquet) system, we study a one-dimensional spin model to explore the stability of such Floquet discrete time crystals (DTCs) under the interplay between interaction and the microwave driving. For intermediate interactions and high drivings, from the time evolution of both stroboscopic spin polarization and mutual information between two ends, we show that Floquet DTCs can exist in a prethermal time regime without the tuning of strong disorder. For much weak interactions the system is a symmetry-unbroken phase, while for strong interactions it gives its way to a thermal phase. Through analyzing the entanglement dynamics, we show that large driving fields protect the prethermal DTCs from many-body localization and thermalization. Our results suggest that by increasing the spin interaction, one can drive the experimental system into optimal regime for observing a robust prethermal DTC phase.
Time-dependent drives hold the promise of realizing non-equilibrium many-body phenomena that are absent in undriven systems. Yet, drive-induced heating normally destabilizes the systems, which can be parametrically suppressed in the high-frequency regime by using periodic (Floquet) drives. It remains largely unknown to what extent highly controllable quantum simulators can suppress heating in non-periodically driven systems. Using the 78-qubit superconducting quantum processor, Chuang-tzu 2.0, we report the experimental observation of long-lived prethermal phases in many-body systems with tunable heating rates, driven by structured random protocols, characterized by n-multipolar temporal correlations. By measuring both the particle imbalance and subsystem entanglement entropy, we monitor the entire heating process over 1,000 driving cycles and observe the existence of the prethermal plateau. The prethermal lifetime is ‘doubly tunable’: one way by driving frequency, the other by multipolar order; it grows algebraically with the frequency with the universal scaling exponent 2n+1. Using quantum state tomography on different subsystems, we demonstrate a non-uniform spatial entanglement distribution and observe a crossover from area-law to volume-law entanglement scaling. With 78 qubits and 137 couplers in a 2D configuration, the entire far-from-equilibrium heating dynamics are beyond the reach of simulation using tensor-network numerical techniques. Our work highlights superconducting quantum processors as a powerful platform for exploring universal scaling laws and non-equilibrium phases of matter in driven systems in regimes where classical simulation faces formidable challenges.