Many-body phenomena far from equilibrium present challenges beyond reach by classical computational resources. Digital quantum computers provide a possible way forward but noise limits their use in the near term. We propose a scheme to simulate and characterize many-body Floquet systems hosting a rich variety of phases that operates with a shallow circuit, defined as a quantum circuit that does not scale with system sizes. Starting from a periodic circuit that simulates the dynamical evolution of a Floquet system, we introduce quasiperiodicity to the circuit parameters to prevent thermalization by introducing many-body localization. By inspecting the time-averaged properties of the many-body integrals of motion, the phase structure can then be probed using random measurements. This approach avoids the need to compute the ground state and operates at finite energy density. We numerically demonstrate this scheme with a simulation of the Floquet Ising model of time crystals and present results clearly distinguishing different Floquet phases that are protected by many-body localization. Our results pave the way for mapping out phase diagrams of exotic systems on near-term quantum devices.
Many-body phenomena far from equilibrium present challenges beyond reach by classical computational resources. Digital quantum computers provide a possible way forward but noise limits their use in the near term. We propose a scheme to simulate and characterize many-body Floquet systems hosting a rich variety of phases that operates with a shallow circuit, defined as a quantum circuit that does not scale with system sizes. Starting from a periodic circuit that simulates the dynamical evolution of a Floquet system, we introduce quasiperiodicity to the circuit parameters to prevent thermalization by introducing many-body localization. By inspecting the time-averaged properties of the many-body integrals of motion, the phase structure can then be probed using random measurements. This approach avoids the need to compute the ground state and operates at finite energy density. We numerically demonstrate this scheme with a simulation of the Floquet Ising model of time crystals and present results clearly distinguishing different Floquet phases that are protected by many-body localization. Our results pave the way for mapping out phase diagrams of exotic systems on near-term quantum devices.
Many-body phenomena far from equilibrium present challenges beyond reach by classical computational resources. Digital quantum computers provide a possible way forward but noise limits their use in the near-term. We propose a scheme to simulate and characterize many-body Floquetsystems hosting a rich variety of phases that operates with a shallow depth circuit. Starting from a "clean" periodic circuit that simulates the dynamical evolution of a Floquet system, we introduce quasi-periodicity to the circuit parameters to prevent thermalization by introducing many-body localization. By inspecting the time averaged properties of the many-body integrals of motion, the phase structure can then be probed using random measurements. This approach avoids the need to compute the ground state and operates at finite energy density. We numerically demonstrate this scheme with a simulation of the Floquet Ising model of time-crystals and present results clearly distinguishing different Floquet phases in the absence of quasi-periodicity in the circuit parameters. Our results pave the way for mapping phase diagrams of exotic systems on near-term quantum devices.
Many-body localization (MBL) provides a mechanism by which interacting quantum systems evade thermalization, leading to persistent memory of initial conditions and slow entanglement growth. Probing these dynamical signatures in large systems and at long evolution times remains challenging for both classical simulations and current quantum devices. Here we experimentally investigate the ergodic-MBL crossover in quasiperiodic Floquet Ising systems using up to 144 qubits on an IBM Quantum processor. By implementing deep Floquet circuits reaching up to 5000 cycles, we access long-time many-body dynamics beyond the regime explored in previous quantum computing experiments. Measurements of autocorrelation functions reveal a smooth crossover from rapid thermalization at weak quasiperiodic potential strength to persistent correlations in the strong-disorder regime. Notably, in addition to the one-dimensional system, we also observe clear signatures consistent with localization behavior in the two-dimensional system. Furthermore, the quantum Fisher information exhibits logarithmic growth over thousands of Floquet cycles, providing evidence for slow entanglement spreading characteristic of the MBL regime. These results demonstrate that programmable quantum processors can serve as experimental platforms for probing nonergodic quantum many-body dynamics and exploring localization phenomena in regimes beyond the reach of classical simulations.
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 .
Floquet engineering—the periodic driving of quantum systems—offers a powerful pathway to realize exotic nonequilibrium phases, including topological Floquet insulators and discrete time crystals. However, computing the quasienergy band structure of interacting, many-body Floquet systems remains a formidable challenge for classical computers due to the exponential growth of the Hilbert space and the difficulty of diagonalizing the non-Hermitian effective Floquet Hamiltonian. In this work, we introduce and experimentally demonstrate a variational quantum algorithm (VQA) tailored specifically for the near-term computation of Floquet quasienergy bands. Unlike standard variational eigensolvers that minimize static energy expectations, our approach employs a parameterized quantum circuit to prepare variational trial states and directly extracts the quasienergy spectrum via a Hadamard-test-based cost function that measures the complex overlap with the single-period Floquet unitary propagator. By scanning the conserved crystal momentum, we reconstruct the full quasienergy dispersion for both one- and two-dimensional lattice models. We benchmark the algorithm against exact diagonalization for system sizes up to N=8N=8 qubits and subsequently deploy it on superconducting transmon processors, systematically characterizing the impact of decoherence, gate infidelity, and readout errors on the resolved band structure. To mitigate hardware noise, we integrate zero-noise extrapolation and measurement-error mitigation, recovering quasienergy features with fidelities exceeding 90% for shallow circuit depths. Our results establish that variational phase-estimation protocols offer a scalable, hardware-efficient route to exploring driven quantum matter, providing a practical toolkit for simulating Floquet topological phenomena on current-generation quantum devices well before the advent of fault-tolerant quantum computation.
Isolated, many-body quantum systems, evolving under their intrinsic dynamics, exhibit a multitude of exotic phenomena and raise foundational questions about statistical mechanics. A flurry of theoretical work has been devoted to understanding how these systems reach thermal equilibrium in the absence of coupling to an external bath and, when thermalization does not occur, investigating the emergent non-equilibrium phases of matter. With the advent of synthetic quantum systems, such as ultra-cold atoms in optical lattices or trapped ions, these questions are no longer academic and can be directly studied in the laboratory. This dissertation explores the non-equilibrium phenomena that stem from the interplay between interactions, disorder, symmetry, topology, and external driving. First, we study how strong disorder, leading to many-body localization, can arrest the heating of a Floquet system and stabilize symmetry-protected topological order that does not have a static analogue. We analyze its dynamical and entanglement properties, highlight its duality to a discrete time crystal, and propose an experimental implementation in a cold-atom setting.Quenched disorder and the many-body localized state are crucial ingredients in protecting macroscopic quantum coherence. We explore the stability of many-body localization in two and higher dimensions and analyze its robustness to rare regions of weak disorder.We then study a second example of non-thermal behavior, namely integrability. We show that a class of random spin models, realizable in systems of atoms coupled to an optical cavity, gives rise to a rich dynamical phase diagram, which includes regions of integrability, classical chaos, and of a novel integrable structure whose conservation laws are reminiscent of the integrals of motion found in a many-body localized phase.The third group of disordered, non-ergodic systems we consider, spin glasses, have fascinating connections to complexity theory and the hardness of constraint satisfaction. We define a statistical ensemble that interpolates between the classical and quantum limits of such a problem and show that there exists a sharp boundary separating satisfiable and unsatisfiable phases.
Current quantum hardware is limited by noise and decoherence, which restrict the depth of unitary circuits that can be implemented with high fidelity. We investigate how the compressibility of time-evolution operators depends on the dynamical regime of the underlying many-body system. As a testbed, we study a one-dimensional Floquet random circuit with a tunable competition between interactions and on-site disorder. Using tensor-network simulations, we characterize operator growth through the operator-entanglement entropy of the Floquet unitary as well as of out-of-time-ordered correlators (OTOCs). We find rapid operator scrambling at weak disorder, while strong disorder leads to slow OTOC-front propagation and logarithmic or near-logarithmic operator-entanglement growth over the accessible time window. We then optimize shallow brickwall circuits to approximate the Floquet evolution and show that strong-disorder circuits can be compressed to substantially smaller depths than weak-disorder circuits at fixed logarithmic fidelity density. These results suggest that localized or slowly scrambling dynamics provide a favorable regime for compressed quantum simulation on noisy devices.