Open Quantum System Dynamics from Infinite Tensor Network Contraction

Abstract

Approaching the long-time dynamics of non-Markovian open quantum systems presents a challenging task if the bath is strongly coupled. Recent proposals address this problem through a representation of the so-called process tensor in terms of a tensor network. We show that for Gaussian environments highly efficient contraction to matrix product operator (MPO) form can be achieved with infinite MPO evolution methods, leading to significant computational speed-up over existing proposals. The result structurally resembles open system evolution with carefully designed auxiliary degrees of freedom, as in hierarchical or pseudomode methods. Here, however, these degrees of freedom are generated automatically by the MPO evolution algorithm. Moreover, the semi-group form of the resulting propagator enables us to explore steady-state physics, such as phase transitions.

References in corpus (41)

• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
• Perspective: Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)
• Efficient simulation of strong system-environment interactions
• The iTEBD algorithm beyond unitary evolution
• Spectral theory of Liouvillians for dissipative phase transitions
• Efficient non-Markovian quantum dynamics using time-evolving matrix product operators
• Non-Markovian quantum processes: complete framework and efficient characterisation
• Numerical Renormalization Group for Bosonic Systems and Application to the Subohmic Spin-Boson Model
• Variational optimization algorithms for uniform matrix product states
• Hierarchy of stochastic pure states for open quantum system dynamics
• Observation of non-Markovian micro-mechanical Brownian motion
• Enhanced quantum entanglement in the non-Markovian dynamics of biomolecular excitons
• Tangent-space methods for uniform matrix product states
• Exploiting the causal tensor network structure of quantum processes to efficiently simulate non-Markovian path integrals
• Quantum phase transitions in the sub-ohmic spin-boson model: Failure of the quantum-classical mapping
• Observation of non-Markovian dynamics of a single quantum dot in a micropillar cavity
• Virtual excitations in the ultra-strongly-coupled spin-boson model: physical results from unphysical modes
• Equilibrium and non-equilibrium dynamics of the sub-ohmic spin-boson model
• Vibrational Heat Transport in Molecular Junctions
• Accuracy Assessment of Perturbative Master Equations -- Embracing Non-Positivity
• Numerically exact open quantum systems simulations for arbitrary environments using automated compression of environments
• Non-Markovian model of photon-assisted dephasing by electron-phonon interactions in a coupled quantum-dot-cavity system
• Taming Quantum Noise for Efficient Low Temperature Simulations of Open Quantum Systems
• Optimized auxiliary oscillators for the simulation of general open quantum systems
• Efficient exploration of Hamiltonian parameter space for optimal control of non-Markovian open quantum systems
• Exact dynamics of non-additive environments in non-Markovian open quantum systems
• The Accuracy of Perturbative Master Equations
• Exact open quantum system dynamics using the Hierarchy of Pure States (HOPS)
• Ultraslow quantum dynamics in a sub-Ohmic heat bath
• Real time evolution of Anderson impurity models via tensor network influence functionals
• Apoptosis of moving, non-orthogonal basis functions in many-particle quantum dynamics
• Many-body quantum state diffusion for non-Markovian dynamics in strongly interacting systems
• The Hidden Phase of the Spin-Boson Model
• Tensor network simulation of chains of non-Markovian open quantum systems
• Sublinear scaling in non-Markovian open quantum systems simulations
• Non-Markovian Stochastic Schrödinger Equation: Matrix Product State Approach to the Hierarchy of Pure States
• Atom-only theories for U(1) symmetric cavity-QED models
• Invalidation of the Bloch-Redfield Equation in Sub-Ohmic Regime via a Practical Time-Convolutionless Fourth-Order Master Equation
• Environmentally Induced Entanglement -- Anomalous Behavior in the Adiabatic Regime

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• Non-Hermitian Pseudomodes for Strongly Coupled Open Quantum Systems: Unravelings, Correlations and Thermodynamics
• Seeking a quantum advantage with trapped-ion quantum simulations of condensed-phase chemical dynamics
• OQuPy: A Python package to efficiently simulate non-Markovian open quantum systems with process tensors
• ACE: A general-purpose non-Markovian open quantum systems simulation toolkit based on process tensors
• Dynamics of a strongly coupled quantum heat engine -- computing bath observables from the hierarchy of pure states
• Correlation Functions From Tensor Network Influence Functionals: The Case of the Spin-Boson Model
• Process tensor approaches to modeling two-dimensional spectroscopy
• Infinite Grassmann Time-Evolving Matrix Product Operator Method in the Steady State
• Pseudomode treatment of strong-coupling quantum thermodynamics
• Semi-group influence matrices for non-equilibrium quantum impurity models
• Efficient construction of the Feynman-Vernon influence functional as matrix product states
• Spectral theory of non-Markovian dissipative phase transitions
• Unifying methods for optimal control in non-Markovian quantum systems via process tensors
• Grassmann time-evolving matrix product operators: An efficient numerical approach for fermionic path integral simulations
• Sixth-order time-convolutionless master equation and beyond: Late-time resummations, two types of divergences, and the limits of validity
• Tree-like process tensor contraction for automated compression of environments
• nuHOPS: A quantum trajectory method for highly excited environments in non-Markovian open quantum dynamics
• Universal Quench Dynamics of an Open Quantum System
• Input-Output Hierarchical Equations Of Motion
• Path Integral Formalism for Quantum Open Systems
• Understanding and utilizing the inner bonds of process tensors
• Entropic witness for quantum memory in open system dynamics
• Efficient tensor network simulation of multi-emitter non-Markovian systems
• Verifying Quantum Memory in the Dynamics of Spin Boson Models
• Improved Memory Truncation Scheme for Quasi-Adiabatic Propagator Path Integral via Influence Functional Renormalization
• Extracting Coupling-Mode Spectral Densities with Two-Dimensional Electronic Spectroscopy
• Beyond mean-field dynamics of the Dicke model with non-Markovian dephasing
• Process Tensor Approaches to Non-Markovian Quantum Dynamics
• Testing bath correlation functions for open quantum dynamics simulations
• Dissipative Yao-Lee Spin-Orbital Model: Exact Solvability and $\mathcal{P}\mathcal{T}$ Symmetry Breaking
• Modeling Quantum Noise in Nanolasers using Markov Chains
• Uniform process tensor approach for the calculation of multi-time correlation functions of non-Markovian open systems
• Purified pseudomode model for nonlinear system-bath interactions