Probing many-body quantum chaos with quantum simulators
arXiv:2106.15530 · doi:10.1103/PhysRevX.12.011018
Abstract
The spectral form factor (SFF), characterizing statistics of energy eigenvalues, is a key diagnostic of many-body quantum chaos. In addition, partial spectral form factors (PSFFs) can be defined which refer to subsystems of the many-body system. They provide unique insights into energy eigenstate statistics of many-body systems, as we show in an analysis on the basis of random matrix theory and of the eigenstate thermalization hypothesis. We propose a protocol that allows the measurement of the SFF and PSFFs in quantum many-body spin models, within the framework of randomized measurements. Aimed to probe dynamical properties of quantum many-body systems, our scheme employs statistical correlations of local random operations which are applied at different times in a single experiment. Our protocol provides a unified testbed to probe many-body quantum chaotic behavior, thermalization and many-body localization in closed quantum systems which we illustrate with numerical simulations for Hamiltonian and Floquet many-body spin-systems.
16+14 pages, 14 figures. The presentation throughout the paper is improved, without any change in the core content and results. New figure and appendix added. Matches with the published version
References in corpus (20)
- Thermalization and its mechanism for generic isolated quantum systems
- Many body localization and thermalization in quantum statistical mechanics
- Many-Body Physics with Individually-Controlled Rydberg Atoms
- Randomized Benchmarking of Quantum Gates
- Equilibrium states of generic quantum systems subject to periodic driving
- Testing whether all eigenstates obey the Eigenstate Thermalization Hypothesis
- Evenly distributed unitaries: on the structure of unitary designs
- Periodically driven ergodic and many-body localized quantum systems
- Information Scrambling in Computationally Complex Quantum Circuits
- Symmetrised Characterisation of Noisy Quantum Processes
- Chaos, Complexity, and Random Matrices
- Symmetry-resolved entanglement detection using partial transpose moments
- Efficient estimation of Pauli observables by derandomization
- Non-ergodic phases in strongly disordered random regular graphs
- From non-ergodic eigenvectors to local resolvent statistics and back: a random matrix perspective
- Theoretical and Experimental Perspectives of Quantum Verification
- Optimal Entanglement Certification from Moments of the Partial Transpose
- Quantum Chaos, Delocalization, and Entanglement in Disordered Heisenberg Models
- Quantum scrambling with classical shadows
- Importance sampling of randomized measurements for probing entanglement
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- The randomized measurement toolbox
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- Many-Body Quantum Chaos and Space-time Translational Invariance
- Dynamical quantum ergodicity from energy level statistics
- A randomized measurement toolbox for an interacting Rydberg-atom quantum simulator
- Quantifying information scrambling via Classical Shadow Tomography on Programmable Quantum Simulators
- Robustness of quantum chaos and anomalous relaxation in open quantum circuits
- Exact universal bounds on quantum dynamics and fast scrambling
- Probing quantum chaos in multipartite systems
- Quantum Computing Universal Thermalization Dynamics in a (2+1)D Lattice Gauge Theory
- Kernel-Function Based Quantum Algorithms for Finite Temperature Quantum Simulation
- Random matrix universality in dynamical correlation functions at late times
- Unravelling quantum chaos using persistent homology
- Pseudochaotic Many-Body Dynamics as a Pseudorandom State Generator
- Quantum Chaos and Universal Trotterisation Behaviours in Digital Quantum Simulations