Constructing Tensor Network Influence Functionals for General Quantum Dynamics

Abstract

We describe an iterative formalism to compute influence functionals that describe the general quantum dynamics of a subsystem beyond the assumption of linear coupling to a quadratic bath. We use a space-time tensor network representation of the influence functional and investigate its approximability in terms of the bond dimensions and time-like entanglement in the tensor network description. We study two numerical models, the spin-boson model and a model of interacting hard-core bosons in a 1D harmonic trap. We find that the influence functional and the intermediates involved in its construction can be efficiently approximated by low bond dimension tensor networks in certain dynamical regimes, which allows the quantum dynamics to be accurately computed for longer times than with direct time evolution methods. However, as one iteratively integrates out the bath, the correlations in the influence functional can first increase before decreasing, indicating that the final compressibility of the influence functional is achieved via non-trivial cancellation.

arXiv comment12 pages, 10 figures

References in corpus (32)

• The density-matrix renormalization group in the age of matrix product states
• Efficient simulation of one-dimensional quantum many-body systems
• Real time evolution using the density matrix renormalization group
• Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas
• Unifying time evolution and optimization with matrix product states
• Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
• Efficient non-Markovian quantum dynamics using time-evolving matrix product operators
• Non-Markovian quantum processes: complete framework and efficient characterisation
• Variational study of hard-core bosons in a 2-D optical lattice using Projected Entangled Pair States (PEPS)
• Taming the dynamical sign problem in real-time evolution of quantum many-body problems
• Non-Markovian Dynamical Maps: Numerical Processing of Open Quantum Trajectories
• Iterative real-time path integral approach to nonequilibrium quantum transport
• Finite temperature dynamical DMRG and the Drude weight of spin-1/2 chains
• Matrix Product States for dynamical simulation of infinite chains
• Spectral functions in one-dimensional quantum systems at T>0
• Memory Effects In Nonequilibrium Quantum Impurity Models
• Exploiting the causal tensor network structure of quantum processes to efficiently simulate non-Markovian path integrals
• Numerically exact path integral simulation of nonequilibrium quantum transport and dissipation
• Time evolution algorithms for Matrix Product States and DMRG
• Quantum dynamics of thermalizing systems
• Influence matrix approach to many-body Floquet dynamics
• Machine learning non-Markovian quantum dynamics
• Generalized Quantum Master Equations In and Out of Equilibrium: When Can One Win?
• Tensor network techniques for the computation of dynamical observables in 1D quantum spin systems
• Simulation complexity of open quantum dynamics: Connection with tensor networks
• Time-step targeting time-dependent and dynamical density matrix renormalization group algorithms with ab initio Hamiltonians
• Efficient simulation of non-Markovian system-environment interaction
• Inchworm Monte Carlo for exact non-adiabatic dynamics I. Theory and algorithms
• Note: On the memory kernel and the reduced system propagator
• Efficient Real-Time Path Integrals for Non-Markovian Spin-Boson Models

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• Numerically exact open quantum systems simulations for arbitrary environments using automated compression of environments
• A Tutorial on Quantum Master Equations: Tips and tricks for quantum optics, quantum computing and beyond
• An efficient method for quantum impurity problems out of equilibrium
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• Non-equilibrium quantum impurity problems via matrix-product states in the temporal domain
• A Multisite Decomposition of the Tensor Network Path Integrals
• Hierarchical equations of motion approach to hybrid fermionic and bosonic environments: Matrix product state formulation in twin space
• Tensor network simulation of chains of non-Markovian open quantum systems
• Overcoming the entanglement barrier in quantum many-body dynamics via space-time duality
• Non-Markovian Stochastic Schrödinger Equation: Matrix Product State Approach to the Hierarchy of Pure States
• Light cone tensor network and time evolution
• Quasi-Lindblad pseudomode theory for open quantum systems
• OQuPy: A Python package to efficiently simulate non-Markovian open quantum systems with process tensors
• Numerical evaluation and robustness of the quantum mean force Gibbs state
• ACE: A general-purpose non-Markovian open quantum systems simulation toolkit based on process tensors
• On temporal entropy and the complexity of computing the expectation value of local operators after a quench
• Equilibrium Quantum Impurity Problems via Matrix Product State Encoding of the Retarded Action
• Tensor network influence functionals in the continuous-time limit: connections to quantum embedding, bath discretization, and higher-order time propagation
• Optimizing performance of quantum operations with non-Markovian decoherence: the tortoise or the hare?
• Correlation Functions From Tensor Network Influence Functionals: The Case of the Spin-Boson Model
• Exact Hidden Markovian Dynamics in Quantum Circuits
• From Non-Markovian Dissipation to Spatiotemporal Control of Quantum Nanodevices
• Dynamical correlation functions from complex time evolution
• Simulating quantum dynamics in two-dimensional lattices with tensor network influence functional belief propagation
• Real-Time Simulation of Open Quantum Spin Chains with Inchworm Method
• Capturing long-range memory structures with tree-geometry process tensors
• Exact Correlation Functions for Dual-Unitary Quantum circuits with exceptional points
• Grassmann time-evolving matrix product operators: An efficient numerical approach for fermionic path integral simulations
• QCMaquis 4.0: Multi-Purpose Electronic, Vibrational, and Vibronic Structure and Dynamics Calculations with the Density Matrix Renormalization Group
• Controlling quantum many-body systems using reduced-order modelling
• Schwinger-Keldysh non-perturbative field theory of open quantum systems beyond the Markovian regime: Application to spin-boson and spin-chain-boson models
• Understanding and utilizing the inner bonds of process tensors
• Simulation of Spin Chains with off-diagonal Coupling Using Inchworm Method
• Input-Output Hierarchical Equations Of Motion
• Quantum correlations of a two-qubit system and the Aubry-André chain in bosonic environments
• Dynamics in the presence of local symmetry-breaking impurities
• Time evolving matrix product operator (TEMPO) method in a non-diagonal basis set based on derivative of the path integral expression
• Improved Memory Truncation Scheme for Quasi-Adiabatic Propagator Path Integral via Influence Functional Renormalization
• Learning the non-Markovian features of subsystem dynamics
• Statistics-encoded tensor network approach in disordered quantum many-body spin chains
• Process Tensor Approaches to Non-Markovian Quantum Dynamics
• Dynamical Tensor Train Approximation for Kinetic Equations