Uncovering Local Integrability in Quantum Many-Body Dynamics

Abstract

Interacting many-body quantum systems and their dynamics, while fundamental to modern science and technology, are formidable to simulate and understand. However, by discovering their symmetries, conservation laws, and integrability one can unravel their intricacies. Here, using up to 124 qubits of a fully programmable quantum computer, we uncover local conservation laws and integrability in one- and two-dimensional periodically-driven spin lattices in a regime previously inaccessible to such detailed analysis. We focus on the paradigmatic example of disorder-induced ergodicity breaking, where we first benchmark the system crossover into a localized regime through anomalies in the one-particle-density-matrix spectrum and other hallmark signatures. We then demonstrate that this regime stems from hidden local integrals of motion by faithfully reconstructing their quantum operators, thus providing a detailed portrait of the system's integrable dynamics. Our results demonstrate a versatile strategy for extracting the hidden dynamical structure from noisy experiments on large-scale quantum computers.

9 pages, 4 figures (main text) + 21 pages, 20 figures (supplementary)

References in corpus (47)

• Many body localization and thermalization in quantum statistical mechanics
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Many-body localization, thermalization, and entanglement
• Observation of many-body localization of interacting fermions in a quasi-random optical lattice
• The many-body localization phase transition
• Error mitigation for short-depth quantum circuits
• Exploring the many-body localization transition in two dimensions
• Phenomenology of fully many-body-localized systems
• A phenomenology of certain many-body-localized systems
• Local conservation laws and the structure of the many-body localized states
• Many-body localization in a quantum simulator with programmable random disorder
• Quantum Error Mitigation
• Many-body localization in periodically driven systems
• Noise tailoring for scalable quantum computation via randomized compiling
• Probing entanglement in a many-body-localized system
• Integrals of motion in the Many-Body localized phase
• Spectral signatures of many-body localization with interacting photons
• Quantum chaos challenges many-body localization
• Stability and instability towards delocalization in MBL systems
• The randomized measurement toolbox
• Mitigating measurement errors in multi-qubit experiments
• Observation of Time-Crystalline Eigenstate Order on a Quantum Processor
• Periodically Driving a Many-Body Localized Quantum System
• Constructing local integrals of motion in the many-body localized phase
• Avalanches and many-body resonances in many-body localized systems
• Remarks on the notion of quantum integrability
• Many-body localization characterized from a one-particle perspective
• Review: Local Integrals of Motion in Many-Body Localized systems
• Quantum critical behavior at the many-body-localization transition
• Scalable error mitigation for noisy quantum circuits produces competitive expectation values
• On general relation between quantum ergodicity and fidelity of quantum dynamics
• Bounds on Information Propagation in Disordered Quantum Spin Chains
• Markovian baths and quantum avalanches
• Observation of energy resolved many-body localization
• A Floquet Model for the Many-Body Localization Transition
• Signatures of bath-induced quantum avalanches in a many-body--localized system
• Signatures of the Many-body Localized Regime in Two Dimensions
• Local and Quasilocal Conserved Quantities in Integrable Systems
• One-particle density matrix characterization of many-body localization
• Phenomenology of the Prethermal Many-Body Localized Regime
• Spectral tensor networks for many-body localization
• Suppressing quantum circuit errors due to system variability
• Apparent slow dynamics in the ergodic phase of a driven many-body localized system without extensive conserved quantities
• Undecidability of the fate of relaxation in one-dimensional quantum systems
• Undecidability in quantum thermalization
• Local Integrals of Motion for Topologically Ordered Many-Body Localized Systems
• Local constants of motion imply information propagation

Cited by in corpus (15)

• Benchmarking the performance of quantum computing software
• Scalable Quantum Simulations of Scattering in Scalar Field Theory on 120 Qubits
• Dynamical simulations of many-body quantum chaos on a quantum computer
• Inhomogeneous SU(2) symmetries in homogeneous integrable U(1) circuits and transport
• Sequency Hierarchy Truncation (SeqHT) for Adiabatic State Preparation and Time Evolution in Quantum Simulations
• Suppressing chaos with mixed superconducting qubit devices
• Thermal avalanches in isolated many-body localized systems
• Anomalous energy correlations and spectral form factor in the nonergodic phase of the $\beta$-ensemble
• Exploiting many-body localization for scalable variational quantum simulation
• Prethermalization, shadowing breakdown, and the absence of Trotterization transition in quantum circuits
• Anomalous transport in U(1)-symmetric quantum circuits
• Critical Dynamics of the Anderson Transition on Small-World Graphs
• Shift of quantum critical point of discrete time crystal on a noisy quantum simulator
• Unified theory of local integrals of motion
• Temperature and conditions for thermalization after canonical quenches