Temporal Entanglement in Chaotic Quantum Circuits

Abstract

The concept of space-evolution (or space-time duality) has emerged as a promising approach for studying quantum dynamics. The basic idea involves exchanging the roles of space and time, evolving the system using a space transfer matrix rather than the time evolution operator. The infinite-volume limit is then described by the fixed points of the latter transfer matrix, also known as influence matrices. To establish the potential of this method as a bona fide computational scheme, it is important to understand whether the influence matrices can be efficiently encoded in a classical computer. Here we begin this quest by presenting a systematic characterisation of their entanglement -- dubbed temporal entanglement -- in chaotic quantum systems. We consider the most general form of space-evolution, i.e., evolution in a generic space-like direction, and present two fundamental results. First, we show that temporal entanglement always follows a volume law in time. Second, we identify two marginal cases -- (i) pure space evolution in generic chaotic systems (ii) any space-like evolution in dual-unitary circuits -- where Rényi entropies with index larger than one are sub-linear in time while the von Neumann entanglement entropy grows linearly. We attribute this behaviour to the existence of a product state with large overlap with the influence matrices. This unexpected structure in the temporal entanglement spectrum might be the key to an efficient computational implementation of the space evolution.

arXiv commentmajor improvements in the presentation; new exact results on dual unitary circuits added; 36 pages, 23 figures

References in corpus (111)

• Many-Body Physics with Ultracold Gases
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• The density-matrix renormalization group in the age of matrix product states
• Efficient classical simulation of slightly entangled quantum computations
• Efficient simulation of one-dimensional quantum many-body systems
• Real time evolution using the density matrix renormalization group
• Characterizing Quantum Supremacy in Near-Term Devices
• Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Time-dependent variational principle for quantum lattices
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Unifying time evolution and optimization with matrix product states
• Robust randomized benchmarking of quantum processes
• Matrix product states represent ground states faithfully
• Operator Spreading in Random Unitary Circuits
• Measurement-Induced Phase Transitions in the Dynamics of Entanglement
• Quantum Entanglement Growth Under Random Unitary Dynamics
• Experimental Observation of a Generalized Gibbs Ensemble
• Probing entanglement entropy via randomized measurements
• Measurement-driven entanglement transition in hybrid quantum circuits
• Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
• Ballistic spreading of entanglement in a diffusive nonintegrable system
• Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
• Random Quantum Circuits
• Unitary-projective entanglement dynamics
• Characterizing Quantum Gates via Randomized Benchmarking
• Entropy scaling and simulability by Matrix Product States
• Finite-temperature transport in one-dimensional quantum lattice models
• On the Entangling Power of Quantum Evolutions
• Exact Spectral Form Factor in a Minimal Model of Many-Body Quantum Chaos
• Generalized HydroDynamics on an Atom Chip
• Random Quantum Circuits are Approximate 2-designs
• Diffusive hydrodynamics of out-of-time-ordered correlators with charge conservation
• Solution of a minimal model for many-body quantum chaos
• Spin transport in a tunable Heisenberg model realized with ultracold atoms
• Exact Correlation Functions for Dual-Unitary Lattice Models in 1+1 Dimensions
• Emergent statistical mechanics of entanglement in random unitary circuits
• Rényi Entropies from Random Quenches in Atomic Hubbard and Spin Models
• Quantum gas microscopy of Kardar-Parisi-Zhang superdiffusion
• Random Quantum Circuits and Pseudo-Random Operators: Theory and Applications
• Spectral statistics in spatially extended chaotic quantum many-body systems
• Exact dynamics in dual-unitary quantum circuits
• Operator space entanglement entropy in transverse Ising chain
• Postselection-free entanglement dynamics via spacetime duality
• Matrix Product States for dynamical simulation of infinite chains
• Entanglement spreading in a minimal model of maximal many-body quantum chaos
• Generalized hydrodynamics in strongly interacting 1D Bose gases
• Unitary circuits of finite depth and infinite width from quantum channels
• Operator Entanglement in Interacting Integrable Quantum Systems: the Case of the Rule 54 Chain
• Spectral statistics and many-body quantum chaos with conserved charge
• Sub-ballistic growth of Rényi entropies due to diffusion
• Entanglement scaling of operators: a conformal field theory approach, with a glimpse of simulability of long-time dynamics in 1+1d
• Is efficiency of classical simulations of quantum dynamics related to integrability?
• The entanglement membrane in chaotic many-body systems
• Ergodic and non-ergodic dual-unitary quantum circuits with arbitrary local Hilbert space dimension
• Fractal, logarithmic and volume-law entangled non-thermal steady states via spacetime duality
• Operator Entanglement in Local Quantum Circuits I: Chaotic Dual-Unitary Circuits
• Superdiffusion in spin chains
• Quantum dynamics of thermalizing systems
• What randomized benchmarking actually measures
• Observing emergent hydrodynamics in a long-range quantum magnet
• Scrambling in Random Unitary Circuits: Exact Results
• Exact thermalization dynamics in the "Rule 54" Quantum Cellular Automaton
• Pseudo Entropy in dS/CFT and Time-like Entanglement Entropy
• Measurement Protocol for the Entanglement Spectrum of Cold Atoms
• Timelike entanglement entropy
• Operator Space Entanglement Entropy in XY Spin Chains
• Unitary $n$-designs via random quenches in atomic Hubbard and Spin models: Application to the measurement of Rényi entropies
• Probing scrambling using statistical correlations between randomized measurements
• Maximum velocity quantum circuits
• Influence matrix approach to many-body Floquet dynamics
• Time-dependent variational principle in matrix-product state manifolds: pitfalls and potential
• Many-body topological invariants from randomized measurements
• Dynamical free energy and the Loschmidt-echo for a class of quantum quenches in the Heisenberg spin chain
• Local pairing of Feynman histories in many-body Floquet models
• Formation of robust bound states of interacting microwave photons
• Tensor network techniques for the computation of dynamical observables in 1D quantum spin systems
• Efficient and feasible state tomography of quantum many-body systems
• From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
• Exact convergence times for generation of random bipartite entanglement
• Creating ensembles of dual unitary and maximally entangling quantum evolutions
• Temporal entanglement, quasiparticles and the role of interactions
• Non-analytic behavior of the Loschmidt echo in XXZ spin chains: exact results
• Operator Entanglement in Local Quantum Circuits II: Solitons in Chains of Qubits
• Random Matrix Spectral Form Factor of Dual-Unitary Quantum Circuits
• Many-body delocalisation as symmetry breaking
• Entanglement dynamics in Rule 54: Exact results and quasiparticle picture
• Connecting Entanglement in Time and Space: Improving the Folding Algorithm
• Computational power of one- and two-dimensional dual-unitary quantum circuits
• An efficient method for quantum impurity problems out of equilibrium
• Eigenstate thermalization in dual-unitary quantum circuits: Asymptotics of spectral functions
• Exact relaxation to Gibbs and non-equilibrium steady states in the quantum cellular automaton Rule 54
• Entanglement-ergodic quantum systems equilibrate exponentially well
• Entanglement Barriers in Dual-Unitary Circuits
• Evidence of Kardar-Parisi-Zhang scaling on a digital quantum simulator
• Entanglement Negativity and Mutual Information after a Quantum Quench: Exact Link from Space-Time Duality
• Maximal entanglement velocity implies dual unitarity
• Dynamical phase transitions in sampling complexity
• Scaling of temporal entanglement in proximity to integrability
• Diffusion and operator entanglement spreading
• Statistics of the Spectral Form Factor in the Self-Dual Kicked Ising Model
• Operator backflow and the classical simulation of quantum transport
• Overcoming the entanglement barrier in quantum many-body dynamics via space-time duality
• Light cone tensor network and time evolution
• Growth of entanglement of generic states under dual-unitary dynamics
• Nonequilibrium steady-state Kubo formula: equality of transport coefficients
• Barrier from chaos: operator entanglement dynamics of the reduced density matrix
• Quantum computational supremacy in the sampling of bosonic random walkers on a one-dimensional lattice
• Exact Spectral Statistics in Strongly Localised Circuits
• Space-like dynamics in a reversible cellular automaton
• Thermalisation Dynamics and Spectral Statistics of Extended Systems with Thermalising Boundaries

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• Quantum information spreading in generalised dual-unitary circuits
• On temporal entropy and the complexity of computing the expectation value of local operators after a quench
• The entanglement membrane in exactly solvable lattice models
• Exact pre-transition effects in kinetically constrained circuits: dynamical fluctuations in the Floquet-East model
• Exactly solvable many-body dynamics from space-time duality
• Solvable entanglement dynamics in quantum circuits with generalized space-time duality
• Exact Hidden Markovian Dynamics in Quantum Circuits
• Eigenstate Correlations in Dual-Unitary Quantum Circuits: Partial Spectral Form Factor
• Temporal Entanglement Barriers in Dual-Unitary Clifford Circuits with Measurements
• Simulating quantum dynamics in two-dimensional lattices with tensor network influence functional belief propagation
• Capturing long-range memory structures with tree-geometry process tensors
• Exact Correlation Functions for Dual-Unitary Quantum circuits with exceptional points
• Exact results on the dynamics of the stochastic Floquet-East model
• Energy-filtered quantum states and the emergence of non-local correlations
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• Process Tensor Approaches to Non-Markovian Quantum Dynamics
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