Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial
arXiv:2202.07060 · doi:10.1103/PRXQuantum.5.010201
Abstract
This tutorial article introduces the physics of quantum information scrambling in quantum many-body systems. The goals are to understand how to precisely quantify the spreading of quantum information and how causality emerges in complex quantum systems. We introduce a general framework to study the dynamics of quantum information, including detection and decoding. We show that the dynamics of quantum information is closely related to operator dynamics in the Heisenberg picture, and, under certain circumstances, can be precisely quantified by the so-called out-of-time ordered correlator~(OTOC). The general behavior of OTOC is discussed based on several toy models, including the Sachdev-Ye-Kitaev model, random circuit models, and Brownian models, in which OTOC is analytically tractable. We introduce numerical methods, including exact diagonalization and tensor network methods, to calculate OTOC for generic quantum many-body systems. We also survey current experimental schemes for measuring OTOC in various quantum simulators.
42 pages, 11 figures; a tutorial article, comments are welcome; improved presentation, reference updated
References in corpus (17)
- The density-matrix renormalization group in the age of matrix product states
- Thermalization and its mechanism for generic isolated quantum systems
- Black holes as mirrors: quantum information in random subsystems
- Random Quantum Circuits
- Strong and weak thermalization of infinite non-integrable quantum systems
- Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System
- Slow scrambling in disordered quantum systems
- Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves
- Quantum dynamics of thermalizing systems
- Scrambling in Random Unitary Circuits: Exact Results
- Quantum parallelism as a tool for ensemble spin dynamics calculations
- Operator backflow and the classical simulation of quantum transport
- Quantum Information Scrambling in Quantum Many-body Scarred Systems
- Note on entropy dynamics in the Brownian SYK model
- Quantum bounds and fluctuation-dissipation relations
- Loschmidt echo in many-spin systems: a quest for intrinsic decoherence and emergent irreversibility
- Experimental Measurement of Out-of-Time-Ordered Correlators at Finite Temperature
Cited by in corpus (70)
- Quantum Dynamics in Krylov Space: Methods and Applications
- Efficient quantum algorithms for stabilizer entropies
- A Maximum Entropy Principle in Deep Thermalization and in Hilbert-Space Ergodicity
- Roadmap on Quantum Thermodynamics
- Stabilizer entropy in non-integrable quantum evolutions
- OQuPy: A Python package to efficiently simulate non-Markovian open quantum systems with process tensors
- Full Eigenstate Thermalization via Free Cumulants in Quantum Lattice Systems
- Quantifying non-stabilizerness via information scrambling
- Observation of anomalous information scrambling in a Rydberg atom array
- State estimation with quantum extreme learning machines beyond the scrambling time
- Assessing and Advancing the Potential of Quantum Computing: A NASA Case Study
- Volume-entangled exact scar states in the PXP and related models in any dimension
- Speed limits to the growth of Krylov complexity in open quantum systems
- Subsystem Information Capacity in Random Circuits and Hamiltonian Dynamics
- Beyond Energy: Teleporting Current, Charge, and More
- Microcanonical Free Cumulants in lattice systems
- Chaotic and quantum dynamics in driven-dissipative bosonic chains
- Operator Space Entangling Power of Quantum Dynamics and Local Operator Entanglement Growth in Dual-Unitary Circuits
- Diagnosing Quantum Many-body Chaos in Non-Hermitian Quantum Spin Chain via Krylov Complexity
- Statistical and dynamical aspects of quantum chaos in a kicked Bose-Hubbard dimer
- Operator size growth in Lindbladian SYK
- 3D supergravity from Virasoro TQFT: Gravitational partition function and Out-of-time-order correlator
- Streamlined Krylov construction and classification of ergodic Floquet systems
- Hayden-Preskill recovery in chaotic and integrable unitary circuit dynamics
- Information Scrambling in Free Fermion Systems with a Sole Interaction
- Hayden-Preskill Recovery in Hamiltonian Systems
- Exploring quantum ergodicity of unitary evolution through the Krylov approach
- Probing quantum chaos with the entropy of decoherent histories
- Simulating Floquet scrambling circuits on trapped-ion quantum computers
- Entanglement Properties of SU(2) Gauge Theory
- Dynamics of operator size distribution in q-local quantum Brownian SYK and spin models
- Sensing Out-of-Equilibrium and Quantum Non-Gaussian environments via induced Time-Reversal Symmetry Breaking on the quantum-probe dynamics
- Area laws and thermalization from classical entropies in a Bose-Einstein condensate
- Landau-Zener without a Qubit: Unveiling Multiphoton Interference, Synthetic Floquet Dimensions, and Dissipative Quantum Chaos
- Long-time Quantum Scrambling and Generalized Tensor Product Structures
- Logarithmic light cone, slow entanglement growth, and quantum memory
- Extensive Long-Range Entanglement at Finite Temperatures from a Nonequilibrium Bias
- Bipartite OTOC in open quantum systems: information scrambling and irreversibility
- Transient and steady-state chaos in dissipative quantum systems
- Quantum speed limit for the OTOC from an open systems perspective
- Operator Spreading in Random Unitary Circuits with Unitary-invariant Gate Distributions
- Hierarchical analytical approach to universal spectral correlations in Brownian Quantum Chaos
- Quantum Chaos in Non-Markovian Open Quantum Systems: Interferometric OTOC, Loschmidt Echo and Commutator Operator Norm
- Macroscopic Particle Transport in Dissipative Long-Range Bosonic Systems
- Global Out of Time Order Correlators as a Signature of Scrambling Dynamics of Local Observables
- Information scrambling in quantum walks: Discrete-time formulation of Krylov complexity
- Lieb-Robinson correlation function for the quantum transverse field Ising model
- Out-of-time-ordered correlators of mean-field bosons via Bogoliubov theory
- Nearly query-optimal classical shadow estimation of unitary channels
- Ruelle-Pollicott Decay of Out-of-Time-Order Correlators in Many-Body Systems
- Spectral chaos bounds from scaling theory of maximally efficient quantum-dynamical scrambling
- SU(d)-Symmetric Random Unitaries: Quantum Scrambling, Error Correction, and Machine Learning
- Information scrambling and entanglement dynamics in Floquet Time Crystals
- Tensor Product Structure Geometry under Unitary Channels
- Simulating sparse SYK model with a randomized algorithm on a trapped-ion quantum computer
- Symmetry Properties of Quantum Dynamical Entropy
- Learning out-of-time-ordered correlators with classical kernel methods
- Bridging Classical and Quantum Information Scrambling with the Operator Entanglement Spectrum
- Quantum information scrambling in adiabatically-driven critical systems
- Out-of-time-order correlators for Swanson Hamiltonian with interaction terms
- Out-of-time ordered correlation functions for the localized electrons in the Falicov-Kimball model
- Interferometric and Bipartite OTOC for Non-Markovian Open Quantum Spin-Chains and Lipkin-Meshkov-Glick Model
- On a Matrix Ensemble for Arbitrary Complex Quantum Systems
- Exploring the properties of quantum scars in a toy model
- Chaos and quantum regimes in -photon driven, dissipative bosonic chains
- Krylov Winding and Emergent Coherence in Operator Growth Dynamics
- Emergence of non-Markovian Decoherent Histories in Integrable Environment: A "Tape Recorder" Model for Local Quantum Observables
- Diagnosing chaos with projected ensembles of process tensors
- Non-destructive optical read-out and manipulation of circular Rydberg atoms
- Out-of-time-order correlators bridge classical transport and quantum dynamics