Speed limits and locality in many-body quantum dynamics

Abstract

We review the mathematical speed limits on quantum information processing in many-body systems. After the proof of the Lieb-Robinson Theorem in 1972, the past two decades have seen substantial developments in its application to other questions, such as the simulatability of quantum systems on classical or quantum computers, the generation of entanglement, and even the properties of ground states of gapped systems. Moreover, Lieb-Robinson bounds have been extended in non-trivial ways, to demonstrate speed limits in systems with power-law interactions or interacting bosons, and even to prove notions of locality that arise in cartoon models for quantum gravity with all-to-all interactions. We overview the progress which has occurred, highlight the most promising results and techniques, and discuss some central outstanding questions which remain open. To help bring newcomers to the field up to speed, we provide self-contained proofs of the field's most essential results.

arXiv commentreview article. 93 pages, 10 figures, 1 table. v2: minor changes

References in corpus (196)

• Fault-tolerant quantum computation by anyons
• Quantum sensing
• Three qubits can be entangled in two inequivalent ways
• The density-matrix renormalization group
• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• Area laws for the entanglement entropy - a review
• Quantum information with Rydberg atoms
• M Theory As A Matrix Model: A Conjecture
• Probing many-body dynamics on a 51-atom quantum simulator
• Many body localization and thermalization in quantum statistical mechanics
• A bound on chaos
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Localization of interacting fermions at high temperature
• Comments on the Sachdev-Ye-Kitaev model
• Many-body localization, thermalization, and entanglement
• Entanglement entropy and conformal field theory
• Quantum computational chemistry
• Black holes and the butterfly effect
• Quantum Error Correction for Quantum Memories
• Fast Scramblers
• An Area Law for One Dimensional Quantum Systems
• Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins
• Quantum walks: a comprehensive review
• Realizing a lattice spin model with polar molecules
• Light-cone-like spreading of correlations in a quantum many-body system
• Complexity Equals Action
• Quantum spin squeezing
• Stabilizer Codes and Quantum Error Correction
• Operator Spreading in Random Unitary Circuits
• Lieb-Schultz-Mattis in Higher Dimensions
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Quantum Entanglement Growth Under Random Unitary Dynamics
• Localized shocks
• On Many-Body Localization for Quantum Spin Chains
• Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet
• Spectral Gap and Exponential Decay of Correlations
• Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
• Schrieffer-Wolff transformation for quantum many-body systems
• Implementation of Cavity Squeezing of a Collective Atomic Spin
• Thermalization and prethermalization in isolated quantum systems: a theoretical overview
• The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual
• Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
• Measuring the scrambling of quantum information
• Random Quantum Circuits
• Quantum Many-Body Scars and Hilbert Space Fragmentation: A Review of Exact Results
• Interaction Quench in the Hubbard model
• Theory of universal incoherent metallic transport
• Towards the fast scrambling conjecture
• Lieb-Robinson Bounds and the Exponential Clustering Theorem
• Quasi-adiabatic Continuation of Quantum States: The Stability of Topological Ground State Degeneracy and Emergent Gauge Invariance
• Quantum chaos challenges many-body localization
• Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models
• Hydrodynamics of electrons in graphene
• Verified Quantum Information Scrambling
• A Universal Operator Growth Hypothesis
• Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System
• Lieb-Robinson and the butterfly effect
• Diffusive hydrodynamics of out-of-time-ordered correlators with charge conservation
• A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems
• Pre-thermal phases of matter protected by time-translation symmetry
• Undecidability of the Spectral Gap (short version)
• Low Depth Quantum Simulation of Electronic Structure
• Observation of Elastic Doublon Decay in the Fermi-Hubbard Model
• Entangling operations and their implementation using a small amount of entanglement
• Universal Charge Diffusion and the Butterfly Effect
• Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves
• Does scrambling equal chaos?
• Nearly-linear light cones in long-range interacting quantum systems
• Unifying fast scrambling, thermalization and entanglement through the measurement of FOTOCs in the Dicke model
• Operator growth in the SYK model
• Many-body chaos at weak coupling
• Stability of Frustration-Free Hamiltonians
• Planckian Dissipation in Metals
• Locality in Quantum and Markov Dynamics on Lattices and Networks
• Quantum State Preparation with Optimal Circuit Depth: Implementations and Applications
• Symmetry-protected phases for measurement-based quantum computation
• The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
• Exponential Decay of Correlations Implies Area Law
• Weak Quantum Chaos
• Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems
• Light-cone effect and supersonic correlations in one- and two-dimensional bosonic superfluids
• Quantum Epidemiology: Operator Growth, Thermal Effects, and SYK
• Onset of many-body chaos in the $O(N)$ model
• Lieb-Robinson Bound and Locality for General Markovian Quantum Dynamics
• Measurement as a shortcut to long-range entangled quantum matter
• Lifetime of double occupancies in the Fermi-Hubbard model
• An area law for entanglement from exponential decay of correlations
• Quantum algorithm for simulating real time evolution of lattice Hamiltonians
• Locality of temperature
• Hierarchy of topological order from finite-depth unitaries, measurement and feedforward
• Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems
• An introduction to measurement based quantum computation
• Efficient quantum algorithms for $GHZ$ and $W$ states, and implementation on the IBM quantum computer
• Quantum butterfly effect in weakly interacting diffusive metals
• Quantum Circuits assisted by LOCC: Transformations and Phases of Matter
• Finite speed of quantum scrambling with long range interactions
• Strictly linear light cones in long-range interacting systems of arbitrary dimensions
• Propagation front of correlations in an interacting Bose gas
• An upper bound on transport
• Entanglement rates and area laws
• Euclidean operator growth and quantum chaos
• Quasi-Locality Bounds for Quantum Lattice Systems. Part I. Lieb-Robinson Bounds, Quasi-Local Maps, and Spectral Flow Automorphisms
• Long-Range Prethermal Phases of Nonequilibrium Matter
• Quantization of Hall Conductance For Interacting Electrons on a Torus
• Hierarchy of linear light cones with long-range interactions
• Stochastic Error Cancellation in Analog Quantum Simulation
• Simulating adiabatic evolution of gapped spin systems
• A computationally universal phase of quantum matter
• Long-lived interacting phases of matter protected by multiple time-translation symmetries in quasiperiodically-driven systems
• Entanglement area laws for long-range interacting systems
• Treelike interactions and fast scrambling with cold atoms
• Topological Order from Measurements and Feed-Forward on a Trapped Ion Quantum Computer
• Clustering of conditional mutual information for quantum Gibbs states above a threshold temperature
• Locality and digital quantum simulation of power-law interactions
• An improved 1D area law for frustration-free systems
• A Multi-Dimensional Lieb-Schultz-Mattis Theorem
• Fast State Transfer and Entanglement Renormalization Using Long-Range Interactions
• An improved Lieb-Robinson bound for many-body Hamiltonians with power-law interactions
• Fast scrambling on sparse graphs
• Minimal Model for Fast Scrambling
• Falling Toward Charged Black Holes
• Improved thermal area law and quasi-linear time algorithm for quantum Gibbs states
• Information propagation for interacting particle systems
• Exponentially Slow Heating in Short and Long-range Interacting Floquet Systems
• Operator size at finite temperature and Planckian bounds on quantum dynamics
• Locality in Quantum Systems
• Quantum Skew Divergence
• Absence of fast scrambling in thermodynamically stable long-range interacting systems
• Supersonic quantum communication
• Area law of non-critical ground states in 1D long-range interacting systems
• Lieb-Robinson bounds and the simulation of time evolution of local observables in lattice systems
• Tightening the Lieb-Robinson Bound in Locally-Interacting Systems
• Thermal Hall conductance and a relative topological invariant of gapped two-dimensional systems
• Bounds in Nonequilibrium Quantum Dynamics
• Signaling and Scrambling with Strongly Long-Range Interactions
• Strong quantum metrological limit from many-body physics
• Kinetic theory for classical and quantum many-body chaos
• An area law for 2D frustration-free spin systems
• Short-Depth Circuits for Dicke State Preparation
• Scrambling in the Dicke model
• Classical simulation of short-time quantum dynamics
• Lieb-Robinson bound and almost-linear light-cone in interacting boson systems
• Optimal State Transfer and Entanglement Generation in Power-law Interacting Systems
• Lieb-Robinson bounds for spin-boson lattice models and trapped ions
• Quantum operator growth bounds for kicked tops and semiclassical spin chains
• Weak integrability breaking perturbations of integrable models
• Fast scrambling without appealing to holographic duality
• Bound on quantum scrambling with all-to-all interactions
• Many-body quantum dynamics slows down at low density
• A Separation of Out-of-time-ordered Correlation and Entanglement
• Maximal speed for macroscopic particle transport in the Bose-Hubbard model
• Ultrafast Variational Simulation of Non-trivial Quantum States with Long Range Interactions
• Undecidability of the Spectral Gap in One Dimension
• Finite speed of quantum information in models of interacting bosons at finite density
• On Lieb-Robinson bounds for the Bose-Hubbard model
• Quantum butterfly effect in polarized Floquet systems
• Local tests of global entanglement and a counterexample to the generalized area law
• Scrambling and Lyapunov Exponent in Unitary Networks with Tunable Interactions
• Quasi-adiabatic Continuation for Disordered Systems: Applications to Correlations, Lieb-Schultz-Mattis, and Hall Conductance
• Operator growth bounds from graph theory
• Ground states of unfrustrated spin Hamiltonians satisfy an area law
• Locality and Heating in Periodically Driven, Power-law Interacting Systems
• Doublon relaxation in the Bose-Hubbard model
• Sufficient Condition for Entanglement Area Laws in Thermodynamically Gapped Spin Systems
• Saturating the quantum Cramér-Rao bound using LOCC
• Exact Universal Chaos, Speed Limit, Acceleration, Planckian Transport Coefficient, "Collapse" to equilibrium, and Other Bounds in Thermal Quantum Systems
• Capacity of Entanglement for Non-local Hamiltonian
• Quantum Scrambling and State Dependence of the Butterfly Velocity
• A noncommutative martingale convexity inequality
• Area law in one dimension: Degenerate ground states and Renyi entanglement entropy
• Optimal Frobenius light cone in spin chains with power-law interactions
• Non-perturbative dynamics of the operator size distribution in the Sachdev-Ye-Kitaev model
• Exponential clustering of bipartite quantum entanglement at arbitrary temperatures
• Prethermalization and the local robustness of gapped systems
• Light-cone like spreading of single-particle correlations in the Bose-Hubbard model after a quantum quench in the strong coupling regime
• Optimizing sparse fermionic Hamiltonians
• Universal Error Bound for Constrained Quantum Dynamics
• Realistic Area-Law Bound on Entanglement from Exponentially Decaying Correlations
• Quantum many-body dynamics on the star graph
• Experimental demonstration of the advantage of adaptive quantum circuits
• Lieb-Robinson bounds for classical anharmonic lattice systems
• Size and momentum of an infalling particle in the black hole interior
• Lieb-Robinson bounds and strongly continuous dynamics for a class of many-body fermion systems in ${\mathbb{R}}^d$
• Operator growth bounds in a cartoon matrix model
• Entanglement rates for Renyi, Tsallis and other entropies
• Maximal Speed of Quantum Propagation
• Locality and error correction in quantum dynamics with measurement
• Fast high-fidelity multi-qubit state transfer with long-range interactions
• Disordered Lieb-Robinson bounds in one dimension
• Entanglement bounds on the performance of quantum computing architectures
• Maximal Speed of Propagation in Open Quantum Systems
• Concentration of OTOC and Lieb-Robinson velocity in random Hamiltonians
• Quantum-capacity bounds in spin-network communication channels
• Locality of gapped ground states in systems with power-law decaying interactions
• Gapped Quantum Systems: From Higher Dimensional Lieb-Schultz-Mattis to the Quantum Hall Effect

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• Witnessing Entanglement and Quantum Correlations in Condensed Matter: A Review
• Operational Metric for Quantum Chaos and the Corresponding Spatiotemporal Entanglement Structure
• Dynamics of inhomogeneous spin ensembles with all-to-all interactions: breaking permutational invariance
• Optimal quantum algorithm for Gibbs state preparation
• Taming quantum systems: A tutorial for using shortcuts-to-adiabaticity, quantum optimal control, and reinforcement learning
• Low-density parity-check codes as stable phases of quantum matter
• Krylov Subspace Methods for Quantum Dynamics with Time-Dependent Generators
• Theory of metastable states in many-body quantum systems
• A Solvable Model of Quantum Darwinism-Encoding Transitions
• Fast and Accurate Greenberger-Horne-Zeilinger Encoding Using All-to-all Interactions
• Causality, localization, and universality of monitored quantum walks with long-range hopping
• Heisenberg-limited metrology with perturbing interactions
• Universal Spreading of Conditional Mutual Information in Noisy Random Circuits
• The dynamical $\alpha$-Rényi entropies of local Hamiltonians grow at most linearly in time
• Optimal light cone for macroscopic particle transport in long-range systems: A quantum speed limit approach
• On Lieb-Robinson bounds for a class of continuum fermions
• A universal speed limit for spreading of coherence
• Solving Free Fermion Problems on a Quantum Computer
• Quantum teleportation implies symmetry-protected topological order
• Preparing matrix product states via fusion: constraints and extensions
• Nonstabilizerness generation in a multiparticle quantum walk
• From Light-Cone to Supersonic Propagation of Correlations by Competing Short- and Long-Range Couplings
• Many-body quantum catalysts for transforming between phases of matter
• State-dependent mobility edge in kinetically constrained models
• Robust Estimation of Nonlinear Properties of Quantum Processes
• Fractonic Quantum Quench in Dipole-constrained Bosons
• Frobenius light cone and the shift unitary
• Lieb-Robinson correlation function for the quantum transverse field Ising model
• Nearly query-optimal classical shadow estimation of unitary channels
• Generating Symmetry-Protected Long-Range Entanglement in Many-Body Systems
• Sub-ballistic operator growth in spin chains with heavy-tailed random fields
• Locality bounds for quantum dynamics at low energy
• Optimal Local Measurements in Single-Parameter Quantum Metrology
• Lieb-Robinson bounds with exponential-in-volume tails
• Predictive complexity of quantum subsystems
• Configurable photonic simulator for quantum field dynamics
• Entanglement area law and Lieb-Schultz-Mattis theorem in long-range interacting systems, and symmetry-enforced long-range entanglement
• Majorana string simulation of nonequilibrium dynamics in two-dimensional lattice fermion systems
• Quantum Speed Limits and the Ultimate Scaling of the Quantum Sensors
• Bounded-Error Quantum Simulation via Hamiltonian and Lindbladian Learning
• Quantum Routing and Entanglement Dynamics Through Bottlenecks