Efficient non-Markovian quantum dynamics using time-evolving matrix product operators

Abstract

In order to model realistic quantum devices it is necessary to simulate quantum systems strongly coupled to their environment. To date, most understanding of open quantum systems is restricted either to weak system-bath couplings, or to special cases where specific numerical techniques become effective. Here we present a novel general numerical approach to efficiently describe the time evolution of a quantum system coupled to a non-Markovian environment. We demonstrate the power and flexibility of our method by numerically identifying the localisation transition of the Ohmic spin-boson model, and considering a model with widely separated environmental timescales arising for a pair of spins embedded in a common environment.

10 pages, 5 figures

References in corpus (18)

• The density-matrix renormalization group in the age of matrix product states
• Dissipative Phase Transition in Central Spin Systems
• Minimally Entangled Typical Thermal State Algorithms
• Strong Coupling of a Single Electron in Silicon to a Microwave Photon
• Numerical Renormalization Group for Bosonic Systems and Application to the Subohmic Spin-Boson Model
• Observation of non-Markovian dynamics of a single quantum dot in a micropillar cavity
• Dynamics, Synchronization and Quantum Phase Transitions of Two Dissipative Spins
• Studying Light-Harvesting Models with Superconducting Circuits
• Coherent and incoherent dynamics in excitonic energy transfer: correlated fluctuations and off-resonance effects
• Population inversion of driven two-level systems in a structureless bath
• Inchworm Monte Carlo for exact non-adiabatic dynamics II. Benchmarks and comparison with established methods
• Non-Markovian dynamics of double quantum dot charge qubits due to acoustic phonons
• Path integral description of combined Hamiltonian and non-Hamiltonian dynamics in quantum dissipative system
• Nonlinear cavity feeding and unconventional photon statistics in solid-state cavity QED revealed by many-level real-time path-integral calculations
• Efficient Real-Time Path Integrals for Non-Markovian Spin-Boson Models
• The quantum phase transition and correlations in the multi-spin-boson model
• Capturing exponential variance using polynomial resources: applying tensor networks to non-equilibrium stochastic processes
• Multi-dimensional Tensor Network Simulation of Open Quantum Dynamics in Singlet Fission

Cited by in corpus (258)

• Quantum stochastic processes and quantum non-Markovian phenomena
• Quantum thermal absorption machines: refrigerators, engines and clocks
• Quantum dots for photonic quantum information technology
• Exploiting the causal tensor network structure of quantum processes to efficiently simulate non-Markovian path integrals
• Numerically exact open quantum systems simulations for arbitrary environments using automated compression of environments
• Open quantum system dynamics and the mean force Gibbs state
• Taming Quantum Noise for Efficient Low Temperature Simulations of Open Quantum Systems
• Polaritonic Coupled-Cluster Theory
• Influence matrix approach to many-body Floquet dynamics
• Machine learning non-Markovian quantum dynamics
• Optimized auxiliary oscillators for the simulation of general open quantum systems
• Quantum Engines and Refrigerators
• Efficient exploration of Hamiltonian parameter space for optimal control of non-Markovian open quantum systems
• A Tutorial on Quantum Master Equations: Tips and tricks for quantum optics, quantum computing and beyond
• Simulation complexity of open quantum dynamics: Connection with tensor networks
• QuTiP-BoFiN: A bosonic and fermionic numerical hierarchical-equations-of-motion library with applications in light-harvesting, quantum control, and single-molecule electronics
• Dissipation-assisted matrix product factorization
• Exact dynamics of non-additive environments in non-Markovian open quantum systems
• Weak and ultrastrong coupling limits of the quantum mean force Gibbs state
• Retrieving ideal precision in noisy quantum optical metrology
• The Structure of Quantum Stochastic Processes with Finite Markov Order
• An efficient method for quantum impurity problems out of equilibrium
• Quantum heat statistics with time-evolving matrix product operators
• Completely Positive, Simple, and Possibly Highly Accurate Approximation of the Redfield Equation
• A theoretical perspective on molecular polaritonics
• Real time evolution of Anderson impurity models via tensor network influence functionals
• Driven dissipative dynamics and topology of quantum impurity systems
• Non-equilibrium quantum impurity problems via matrix-product states in the temporal domain
• Tomographically reconstructed master equations for any open quantum dynamics
• A Multisite Decomposition of the Tensor Network Path Integrals
• Non-Markovian features in semiconductor quantum optics: Quantifying the role of phonons in experiment and theory
• Tensor network based machine learning of non-Markovian quantum processes
• Constructing Tensor Network Influence Functionals for General Quantum Dynamics
• Hierarchical equations of motion approach to hybrid fermionic and bosonic environments: Matrix product state formulation in twin space
• Noise-assisted digital quantum simulation of open systems
• Quantum Brownian Motion for Magnets
• Efficient simulation of open quantum systems coupled to a fermionic bath
• Periodically refreshed baths to simulate open quantum many-body dynamics
• Speed-ups to isothermality: Enhanced quantum thermal machines through control of the system-bath coupling
• Environmental non-additivity and Franck-Condon physics in non-equilibrium quantum systems
• Path-integral methodology and simulations of quantum thermal transport: Full counting statistics approach
• Tight bound on finite-resolution quantum thermometry at low temperatures
• Using the Environment to Understand non-Markovian Open Quantum Systems
• Open Quantum System Dynamics from Infinite Tensor Network Contraction
• Accuracy of the quantum regression theorem for photon emission from a quantum dot
• Efficient many-body non-Markovian dynamics of organic polaritons
• Scaling of temporal entanglement in proximity to integrability
• Many-body quantum state diffusion for non-Markovian dynamics in strongly interacting systems
• The Hidden Phase of the Spin-Boson Model
• Capturing non-Markovian dynamics with the reaction coordinate method
• Sublinear scaling in non-Markovian open quantum systems simulations
• Non-Markovian Stochastic Schrödinger Equation: Matrix Product State Approach to the Hierarchy of Pure States
• Non-Hermitian Pseudomodes for Strongly Coupled Open Quantum Systems: Unravelings, Correlations and Thermodynamics
• Analog Quantum Simulation of the Dynamics of Open Quantum Systems with Quantum Dots and Microelectronic Circuits
• Quantum Simulation of Spin-Boson Models with Structured Bath
• Mapping Electronic Decoherence Pathways in Molecules
• Rate operator unravelling for open quantum system dynamics
• Nonequilibrium open quantum systems with multiple bosonic and fermionic environments: A hierarchical equations of motion approach
• Path-integral approach for nonequilibrium multi-time correlation functions of open quantum systems coupled to Markovian and non-Markovian environments
• Seeking a quantum advantage with trapped-ion quantum simulations of condensed-phase chemical dynamics
• Grassmann Time-Evolving Matrix Product Operators for Quantum Impurity Models
• Non-Markovian perturbation theories for phonon effects in strong-coupling cavity quantum electrodynamics
• OQuPy: A Python package to efficiently simulate non-Markovian open quantum systems with process tensors
• Quasi-Lindblad pseudomode theory for open quantum systems
• A pseudo-fermion method for the exact description of fermionic environments: from single-molecule electronics to Kondo resonance
• Trapped-Ion Quantum Simulation of Electron Transfer Models with Tunable Dissipation
• Fingerprint and universal Markovian closure of structured bosonic environments
• State Dependent Ring Polymer Molecular Dynamics for Investigating Excited Nonadiabatic Dynamics
• From strong to weak temperature dependence of the two-photon entanglement resulting from the biexciton cascade inside a cavity
• A discrete memory-kernel for multi-time correlations in non-Markovian quantum processes
• Exact Quantum Dynamics in Structured Environments
• Probing non-Markovian quantum dynamics with data-driven analysis: Beyond "black-box" machine learning models
• Numerical evaluation and robustness of the quantum mean force Gibbs state
• Certifying multi-mode light-matter interaction in lossy resonators
• Systematic coarse-graining of environments for the non-perturbative simulation of open quantum systems
• Tensor Network Path Integral Study of Dynamics in B850 LH2 Ring with Atomistically Derived Vibrations
• A Pairwise Connected Tensor Network Representation of Path Integrals
• Electron-phonon decoupling due to strong light-matter interactions
• Quantum Pyragas control: Selective-control of individual photon probabilities
• Enhanced TEMPO algorithm for quantum path integrals with off-diagonal system-bath coupling: applications to photonic quantum networks
• Unveiling non-Markovian spacetime signalling in open quantum systems with long-range tensor network dynamics
• ACE: A general-purpose non-Markovian open quantum systems simulation toolkit based on process tensors
• Highly efficient and indistinguishable single-photon sources via phonon-decoupled two-color excitation
• Simulating Non-Markovian Quantum Dynamics on NISQ Computers Using the Hierarchical Equations of Motion
• Geometric-Arithmetic Master Equation in Large and Fast Open Quantum Systems
• MPSDynamics.jl: Tensor network simulations for finite-temperature (non-Markovian) open quantum system dynamics
• Simulating optical linear absorption for mesoscale molecular aggregates: an adaptive hierarchy of pure states approach
• Convergence guarantees for discrete mode approximations to non-Markovian quantum baths
• On temporal entropy and the complexity of computing the expectation value of local operators after a quench
• Atomic Quantum Technologies for Quantum Matter and Fundamental Physics Applications
• Spectral Density Classification For Environment Spectroscopy
• Equilibrium Quantum Impurity Problems via Matrix Product State Encoding of the Retarded Action
• Kibble-Zurek mechanism in a Dissipative Transverse Ising Chain
• QuantumDynamics.jl: A modular approach to simulations of dynamics of open quantum systems
• Compact and complete description of non-Markovian dynamics
• Spin-boson model as a simulator of non-Markovian multiphoton Jaynes-Cummings models
• Effective-Hamiltonian theory: An approximation to the equilibrium state of open quantum systems
• Full Microscopic Simulations Uncover Persistent Quantum Effects in Primary Photosynthesis
• Tensor network influence functionals in the continuous-time limit: connections to quantum embedding, bath discretization, and higher-order time propagation
• Stable bipolarons in open quantum systems
• Heat Current in Non-Markovian Open Systems
• Anomalous transport of small polarons arises from transient lattice relaxation or immovable boundaries
• Dynamics of a strongly coupled quantum heat engine -- computing bath observables from the hierarchy of pure states
• Quantum annealing of pure and random Ising chains coupled to a bosonic environment
• Diagrammatic Monte Carlo for Dissipative Quantum Impurity Models
• Controlling Matter Phases beyond Markov
• On the sampling complexity of open quantum systems
• Invalidation of the Bloch-Redfield Equation in Sub-Ohmic Regime via a Practical Time-Convolutionless Fourth-Order Master Equation
• Single Qubit Error Mitigation by Simulating Non-Markovian Dynamics
• Grassmann Time-Evolving Matrix Product Operators for Equilibrium Quantum Impurity Problems
• Bath-induced interactions and transient dynamics in open quantum systems at strong coupling: Effective Hamiltonian approach
• Memory Effects in Quantum Processes
• Temperature-independent almost perfect photon entanglement from quantum dots via the SUPER scheme
• Single-photon emitters in WSe${}_2$: Critical role of phonons on excitation schemes and indistinguishability
• A Smolyak algorithm adapted to a system-bath separation: application to an encapsulated molecule with large amplitude motions
• Non-Markovian Quantum State Diffusion for Spin Environments
• 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
• Effective Modeling of Open Quantum Systems by Low-rank Discretization of Structured Environments
• Assessment of weak-coupling approximations on a driven two-level system under dissipation
• Real-time Impurity Solver Using Grassmann Time-Evolving Matrix Product Operators
• Dephasing and pseudo-coherent quantum dynamics in super-Ohmic environments
• Process tensor approaches to modeling two-dimensional spectroscopy
• Effects of non-Markovian squeezed bath on the dynamics of open systems
• Solving quantum impurity problems on the L-shaped Kadanoff-Baym contour
• Bexcitonics: Quasi-particle approach to open quantum dynamics
• Infinite Grassmann Time-Evolving Matrix Product Operator Method in the Steady State
• Unveiling quantum entanglement and correlation of sub-Ohmic and Ohmic baths for quantum phase transitions in dissipative systems
• TorchQC -- A framework for efficiently integrating machine and deep learning methods in quantum dynamics and control
• Dissipative dynamics of a driven qubit: interplay between non-adiabatic dynamics and noise effects from weak to strong coupling regime
• Page-curve-like entanglement dynamics in open quantum systems
• Tree tensor network hierarchical equations of motion based on time-dependent variational principle for efficient open quantum dynamics in structured thermal environments
• Dynamical correlation functions from complex time evolution
• From Non-Markovian Dissipation to Spatiotemporal Control of Quantum Nanodevices
• A tensor network approach to sensing quantum light-matter interactions
• Environmentally Induced Entanglement -- Anomalous Behavior in the Adiabatic Regime
• Driven quantum dot coupled to a fractional quantum Hall edge
• Temporal Entanglement Barriers in Dual-Unitary Clifford Circuits with Measurements
• Spectral theory of non-Markovian dissipative phase transitions
• Simulating quantum dynamics in two-dimensional lattices with tensor network influence functional belief propagation
• Absorbing Boundary Conditions for Time-dependent Schrödinger equations: A Density-matrix Formulation
• Loschmidt echo, emerging dual unitarity and scaling of generalized temporal entropies after quenches to the critical point
• Succinct Description and Efficient Simulation of Non-Markovian Open Quantum Systems
• High-purity and stable single-photon emission in bilayer WSe${}_2$ via phonon-assisted excitation
• Continuous and time-discrete non-Markovian system-reservoir interactions: Dissipative coherent quantum feedback in Liouville space
• Efficient construction of the Feynman-Vernon influence functional as matrix product states
• Real-Time Simulation of Open Quantum Spin Chains with Inchworm Method
• Analytical evaluation of the coefficients of the Hu-Paz-Zhang master equation: Ohmic spectral density, zero temperature, and consistency check
• Quantum correlation functions through tensor network path integral
• Quantify the Non-Markovian Process with Intervening Projections in a Superconducting Processor
• Enhanced entanglement in multi-bath spin-boson models
• Capturing long-range memory structures with tree-geometry process tensors
• Transient dynamical phase diagram of the spin-boson model
• Efficient population transfer in a quantum dot exciton under phonon-induced decoherence via shortcuts to adiabaticity
• Impact of Spatial Inhomogeneity on Excitation Energy Transport in the Fenna-Matthews-Olson Complex
• Impact of solvent on state-to-state population transport in multistate systems using coherences
• Principles underlying efficient exciton transport unveiled by information-geometric analysis
• On the Role of Non-Diagonal System-Environment Interactions in Bridge-Mediated Electron Transfer
• Non-Linear Correlation Functions and Zero-Point Energy Flow in Mixed Quantum-Classical Semiclassical Dynamics
• Extending Non-Perturbative Simulation Techniques for Open-Quantum Systems to Excited-State Proton Transfer and Ultrafast Non-Adiabatic Dynamics
• Stochastic simulation of dissipative quantum oscillators
• Quantifying the accuracy of steady states obtained from the Universal Lindblad Equation
• Coherent backaction between spins and an electronic bath: Non-Markovian dynamics and low-temperature quantum thermodynamic electron cooling
• General Framework for Quantifying Dissipation Pathways in Open Quantum Systems. II. Numerical Validation and the Role of Non-Markovianity
• Collisional open quantum dynamics with a generally correlated environment: Exact solvability in tensor networks
• Spin-boson model under dephasing: Markovian vs Non-Markovian dynamics
• Unifying methods for optimal control in non-Markovian quantum systems via process tensors
• Separation of scales: Dynamical approximations for composite quantum systems
• Signatures of Non-Markovianity in Cavity-QED with Color Centers in 2D Materials
• Sixth-order time-convolutionless master equation and beyond: Late-time resummations, two types of divergences, and the limits of validity
• State Diagrams to determine Tree Tensor Network Operators
• Extracting Dynamical Maps of Non-Markovian Open Quantum Systems
• A hierarchical equations of motion (HEOM) analog for systems with delay: illustrated on inter-cavity photon propagation
• Quantum work statistics at strong reservoir coupling
• Exact non-Markovian evolution with multiple reservoirs
• Grassmann time-evolving matrix product operators: An efficient numerical approach for fermionic path integral simulations
• Non-Markovian dynamics of a two-level system in a bosonic bath and a Gaussian fluctuating environment with finite correlation time
• Impact of the phonon environment on the nonlinear quantum-dot-cavity QED. I. Path-integral approach
• Tree-like process tensor contraction for automated compression of environments
• Spectral Density Modulation and Universal Markovian Closure of Fermionic Environments
• Non-Markovian Quantum Heat Statistics with the Reaction Coordinate Mapping
• Accelerating two-dimensional electronic spectroscopy simulations with a probe qubit protocol
• Pulse shaping for on-demand emission of single Raman photons from a quantum-dot biexciton
• Efficient construction of tensor-network representations of many-body Gaussian states
• Distributing Memory Effects in an Open Two-Qubit System
• Dressed Quantum Trajectories: Novel Approach to the non-Markovian Dynamics of Open Quantum Systems on a Wide Time Scale
• On the unraveling of open quantum dynamics
• Information Loss Pathways in a Numerically Exact Simulation of a non-Markovian Open Quantum System
• One-dimensional photonic wire as a single-photon source: Implications of cavity QED to a phonon bath of reduced dimensionality
• Long-Range Order and Quantum Criticality in a Dissipative Spin Chain
• Path integral Lindblad master equation through transfer tensor method & the generalized quantum master equation
• Non-Markovian effects in stochastic resonance in a two level system
• Controlling quantum many-body systems using reduced-order modelling
• Environment-Induced Rabi Oscillations in the Optomechanical Boson-Boson Model
• Dynamical approximations for composite quantum systems: Assessment of error estimates for a separable ansatz
• Dephasing-assisted transport in a tight-binding chain with a linear potential
• Simulation of Spin Chains with off-diagonal Coupling Using Inchworm Method
• Understanding and utilizing the inner bonds of process tensors
• Input-Output Hierarchical Equations Of Motion
• nuHOPS: A quantum trajectory method for highly excited environments in non-Markovian open quantum dynamics
• Path Integral Formalism for Quantum Open Systems
• Spectral signatures of the Markovian to Non-Markovian transition in open quantum systems
• Effective Hamiltonian approach to the quantum phase transitions in the extended Jaynes-Cummings model
• Schwinger-Keldysh non-perturbative field theory of open quantum systems beyond the Markovian regime: Application to spin-boson and spin-chain-boson models
• Infinite Grassmann time-evolving matrix product operator method for zero-temperature equilibrium quantum impurity problems
• Machine learning non-Markovian two-level quantum noise spectroscopy
• Efficient tensor-network simulation for the few-atom multimode Dicke model via coupling-matrix transformation
• Quantum correlations of a two-qubit system and the Aubry-André chain in bosonic environments
• Dissipation Pathways in a Photosynthetic Complex
• Entropic witness for quantum memory in open system dynamics
• Optimal encoding of two dissipative interacting qubits
• General framework for quantifying dissipation pathways in open quantum systems. III. Off-diagonal system-bath couplings
• Hybrid acousto-optical swing-up state control in a quantum dot
• Half Landau-Zener ramp to a quantum phase transition in a dissipative single spin sodel
• Efficient tensor network simulation of multi-emitter non-Markovian systems
• Influence functional of many-body systems: temporal entanglement and matrix-product state representation
• Impact of Loss Mechanisms on Linear Spectra of Excitonic and Polaritonic Aggregates
• Verifying Quantum Memory in the Dynamics of Spin Boson Models
• Correlated and Critical Phenomena in Multipartite Quantum Non-Markovianity
• High-frequency tails in spectral densities
• Path Integral Approach to Input-Output Theory
• Infinite Grassmann time-evolving matrix product operators for quantum impurity problems after a quench
• Non-perturbative exciton transfer rate analysis of the Fenna-Matthews-Olson photosynthetic complex under reduced and oxidised conditions
• Summing Real Time Feynman Paths of Lattice Polaron with Matrix Product States
• Learning the non-Markovian features of subsystem dynamics
• Non-Gaussian Phase Transition and Cascade of Instabilities in the Dissipative Quantum Rabi Model
• Improved Memory Truncation Scheme for Quasi-Adiabatic Propagator Path Integral via Influence Functional Renormalization
• Heat operator approach to quantum stochastic thermodynamics in the strong-coupling regime
• Transient Dynamical Phase Diagram of the Spin-Boson Model at Finite Temperature
• A tensor network representation of path integrals: Implementation and analysis
• Moment expansion method for composite open quantum systems including a damped oscillator mode
• Extracting Coupling-Mode Spectral Densities with Two-Dimensional Electronic Spectroscopy
• A Non-Hermitian State-to-State Analysis of Transport in Aggregates with Multiple Endpoints
• Modified coherence of quantum spins in a damped pure-dephasing model
• A Davydov Ansatz approach to accurate system-bath dynamics in the presence of multiple baths with distinct temperatures
• Time evolving matrix product operator (TEMPO) method in a non-diagonal basis set based on derivative of the path integral expression
• Time-delayed collective dynamics in waveguide QED and bosonic quantum networks
• Scalable tensor network algorithm for quantum impurity problems
• Simple yet Accurate Stochastic Approach to the Quantum Phase Noise of Nanolasers
• Phase Transitions in the Classical Simulability of Open Quantum Systems
• Non-Markovianity Benefits Quantum Dynamics Simulation
• Purified pseudomode model for nonlinear system-bath interactions
• Diagnosing chaos with projected ensembles of process tensors
• Testing bath correlation functions for open quantum dynamics simulations
• Zero-Cost Corrections to Influence Functional Coefficients from Bath Response Functions
• Beyond mean-field dynamics of the Dicke model with non-Markovian dephasing
• Making Non-Markovian master equations accessible with approximate environments
• Quantendynamik offener Systeme, Trendbericht Theoretische Chemie 2020, Teil 3
• Modeling Quantum Noise in Nanolasers using Markov Chains
• Position-Resolved Resonance Quantization for Lossy Cavities
• Markovian Embeddings of Non-Markovian Open System Dynamics
• Uniform process tensor approach for the calculation of multi-time correlation functions of non-Markovian open systems
• Effective Hamiltonian approach to the exact dynamics of open system by complex discretization approximation for environment
• Reduced Dynamical Maps in Finite Temperature Vibronic Coupling Models via Choi Matrices: Numerical Methods and Applications
• Non-Markovian decoherence of a two-level system in a Lorentzian bosonic reservoir and a stochastic environment with finite correlation time
• Effect of Temperature Gradient on Quantum Transport
• Self-consistent approach to the dynamics of excitation energy transfer in multichromophoric systems
• Adaptive Kink Filtration: Achieving Asymptotic Size-Independence of Path Integral Simulations Utilizing the Locality of Interactions