Non-perturbative treatment of non-Markovian dynamics of open quantum systems

Abstract

We identify the conditions that guarantee equivalence of the reduced dynamics of an open quantum system (OQS) for two different types of environments - one a continuous bosonic environment leading to a unitary system-environment evolution and the other a discrete-mode bosonic environment resulting in a system-mode (non-unitary) Lindbladian evolution. Assuming initial Gaussian states for the environments, we prove that the two OQS dynamics are equivalent if both the expectation values and two-time correlation functions of the environmental interaction operators are the same at all times for the two configurations. Since the numerical and analytical description of a discrete-mode environment undergoing a Lindbladian evolution is significantly more efficient than that of a continuous bosonic environment in a unitary evolution, our result represents a powerful, non-perturbative tool to describe complex and possibly highly non-Markovian dynamics. As a special application, we recover and generalize the well-known pseudomodes approach to open system dynamics.

arXiv comment5+4 pages, 2 figures, Close to the version accepted for publication in Physical Review Letters

References in corpus (46)

• Non-Markovian dynamics in open quantum systems
• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Open Quantum Systems. An Introduction
• Quantum Metrology in Non-Markovian Environments
• Building logical qubits in a superconducting quantum computing system
• Vibrations, Quanta and Biology
• Protecting entanglement via the quantum Zeno effect
• Efficient simulation of strong system-environment interactions
• Non-Markovian Dynamics of Quantum Discord
• General non-Markovian dynamics of open quantum systems
• Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials
• Integrated optical addressing of an ion qubit
• Magnet field sensing beyond the standard quantum limit under the effect of decoherence
• Nonequilibrium thermodynamics in the strong coupling and non-Markovian regime based on a reaction coordinate mapping
• Theory of Pseudomodes in Quantum Optical Processes
• The ultimate precision limits for noisy frequency estimation
• Quantum Thermodynamics: A Nonequilibrium Green's Functions Approach
• Performance of a quantum heat engine at strong reservoir coupling
• Cavity-based architecture to preserve quantum coherence and entanglement
• Universal Markovian reduction of Brownian particle dynamics
• Pseudomodes as an effective description of memory: Non-Markovian dynamics of two-state systems in structured reservoirs
• Mesoscopic Spin-Boson Models of Trapped Ions
• Mappings of open quantum systems onto chain representations and Markovian embeddings
• Dynamics of the spin-boson model with a structured environment
• Quantum simulator of an open quantum system using superconducting qubits: exciton transport in photosynthetic complexes
• The effect of dipole-dipole interaction for two atoms with different couplings in non-Markovian environment
• Iterative algorithm versus analytic solutions of the parametrically driven dissipative quantum harmonic oscillator
• Lindblad-Driven Discretized Leads for Non-Equilibrium Steady-State Transport in Quantum Impurity Models: Recovering the Continuum Limit
• Quantum heat machines equivalence and work extraction beyond Markovianity, and strong coupling via heat exchangers
• Nonequlibrium particle and energy currents in quantum chains connected to mesoscopic Fermi reservoirs
• Non-Markovian quantum input-output networks
• Non-Markovian quantum state diffusion for absorption spectra of molecular aggregates
• Open systems with error bounds: spin boson model with spectral density variations
• Optimized auxiliary representation of a non-Markovian environment by a Lindblad equation
• Non-Markovian effects in electronic and spin transport
• Non-Markovian Open Quantum Systems: Input-Output Fields, Memory, Monitoring
• Quantum Langevin equations for optomechanical systems
• Input and output in damped quantum systems III: Formulation of damped systems driven by Fermion fields
• Entanglement trapping in a non-stationary structured reservoir
• Improved scaling of Time-Evolving Block-Decimation algorithm through Reduced-Rank Randomized Singular Value Decomposition
• Stability analysis of multiple nonequilibrium fixed points in self-consistent electron transport calculations
• The coherent interaction between matter and radiation - A tutorial on the Jaynes-Cummings model
• Quantum continuous measurements: The stochastic Schroedinger equations and the spectrum of the output
• Quantum interference induced by initial system-environment correlations
• Pseudomodes and the corresponding transformation of the temperature-dependent bath correlation function
• Simulating spin-boson models with trapped ions

Cited by in corpus (160)

• Non-Markovian quantum processes: complete framework and efficient characterisation
• Efficient simulation of finite-temperature open quantum systems
• Quantum thermal absorption machines: refrigerators, engines and clocks
• Virtual excitations in the ultra-strongly-coupled spin-boson model: physical results from unphysical modes
• Few-mode Field Quantization of Arbitrary Electromagnetic Spectral Densities
• Taming Quantum Noise for Efficient Low Temperature Simulations of Open Quantum Systems
• Machine learning non-Markovian quantum dynamics
• System-environment correlations and Markovian embedding of quantum non-Markovian 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
• Quantum thermometry by single-qubit dephasing
• Simulation complexity of open quantum dynamics: Connection with tensor networks
• Dissipation-assisted matrix product factorization
• Generalized theory of pseudomodes for exact descriptions of non-Markovian quantum processes
• Exact dynamics of non-additive environments in non-Markovian open quantum systems
• Universal Prony fitting decomposition for optimized hierarchical quantum master equations
• Tensor-network method to simulate strongly interacting quantum thermal machines
• Green's function methods for single molecule junctions
• Tomographically reconstructed master equations for any open quantum dynamics
• Universal anti-Kibble-Zurek scaling in fully-connected systems
• Few-mode Field Quantization for Multiple Emitters
• Quantum systems correlated with a finite bath: nonequilibrium dynamics and thermodynamics
• Quantum probing beyond pure dephasing
• Exact Simulation of Pigment-Protein Complexes Unveils Vibronic Renormalization of Electronic Parameters in Ultrafast Spectroscopy
• Strong coupling effects in quantum thermal transport with the reaction coordinate method
• Spin-Dependent Momentum Conservation of Electron-Phonon Scattering in Chirality-Induced Spin Selectivity
• Stochastic Representation of Non-Markovian Fermionic Quantum Dissipation
• Almost Markovian processes from closed dynamics
• Markovian Treatment of non-Markovian Dynamics of Open Fermionic Systems
• Precursors of non-Markovianity
• A Lindblad master equation capable of describing hybrid quantum systems in the ultra-strong coupling regime
• Non-Markovian Quantum Exceptional Points
• Non-Hermitian Pseudomodes for Strongly Coupled Open Quantum Systems: Unravelings, Correlations and Thermodynamics
• Stochastic Equation of Motion Approach to Fermionic Dissipative Dynamics. I. Formalism
• Quantum light-matter interaction and controlled phonon scattering in a photonic Fano cavity
• Randomized benchmarking for non-Markovian noise
• Quantum Simulation of Spin-Boson Models with Structured Bath
• Quantum Probes for Ohmic Environments at Thermal Equilibrium
• Seeking a quantum advantage with trapped-ion quantum simulations of condensed-phase chemical dynamics
• Rate operator unravelling for open quantum system dynamics
• Heat transport through a superconducting artificial atom
• A quantum-classical decomposition of Gaussian quantum environments: a stochastic pseudomode model
• Ab initio quantum models for thin-film x-ray cavity QED
• Ab initio few-mode theory for quantum potential scattering problems
• Quasi-Lindblad pseudomode theory for open quantum systems
• Towards Quantum Simulation of Non-Markovian Open Quantum Dynamics: A Universal and Compact Theory
• Non-perturbative effects in corrections to quantum master equation arising in Bogolubov-van Hove limit
• The Fermionic influence superoperator: a canonical derivation for the development of methods to simulate the influence of a Fermionic environment on a quantum system with arbitrary parity symmetry
• Trapped-Ion Quantum Simulation of Electron Transfer Models with Tunable Dissipation
• Quantum thermodynamics with fast driving and strong coupling via the mesoscopic leads approach
• A pseudo-fermion method for the exact description of fermionic environments: from single-molecule electronics to Kondo resonance
• Pushing the limits of the reaction-coordinate mapping
• Fingerprint and universal Markovian closure of structured bosonic environments
• Certifying multi-mode light-matter interaction in lossy resonators
• Systematic coarse-graining of environments for the non-perturbative simulation of open quantum systems
• Quantum simulation of multiphoton and nonlinear dissipative spin-boson models
• A quantum algorithm for solving open system dynamics on quantum computers using noise
• Convergence guarantees for discrete mode approximations to non-Markovian quantum baths
• Full Microscopic Simulations Uncover Persistent Quantum Effects in Primary Photosynthesis
• Collective bath coordinate mapping of "hierarchy" in hierarchical equations of motion
• Quantum Phase Transition of Many Interacting Spins Coupled to a Bosonic Bath: static and dynamical properties
• A healthier semi-classical dynamics
• A statistical quasi-particles thermofield theory with Gaussian environments: System-bath entanglement theorem for nonequilibrium correlation functions
• Spin-boson model as a simulator of non-Markovian multiphoton Jaynes-Cummings models
• Kerr nonlinearity induced strong spin-magnon coupling
• On the connection between microscopic description and memory effects in open quantum system dynamics
• A mixed perturbative-nonperturbative treatment for strong light-matter interactions
• Correlations, information backflow, and objectivity in a class of pure dephasing models
• Analytic expressions for the steady-state current with finite extended reservoirs
• Modeling the unphysical pseudomode model with physical ensembles: simulation, mitigation, and restructuring of non-Markovian quantum noise
• Structured quantum collision models: generating coherence with thermal resources
• Dissipatons as generalized Brownian particles for open quantum systems: Dissipaton-embedded quantum master equation
• Fixing detailed balance in ancilla-based dissipative state engineering
• Enhanced coherent light-matter interaction and room-temperature quantum yield of plasmonic resonances engineered by a chiral exceptional point
• Optimized noise-assisted simulation of the Lindblad equation with time-dependent coefficients on a noisy quantum processor
• Dressed bound states at chiral exceptional points
• Dynamics of a quantum system interacting with white non-Gaussian baths: Poisson noise master equation
• Anomalous spontaneous emission dynamics at chiral exceptional points
• Entropy production in the mesoscopic-leads formulation of quantum thermodynamics
• Exact Hidden Markovian Dynamics in Quantum Circuits
• Thermal cycle and polaron formation in structured bosonic environments
• Pseudomode treatment of strong-coupling quantum thermodynamics
• Pseudomode expansion of many-body correlation functions
• Minimal pole representation for spectral functions
• Non-perturbative treatment of open-system multi-time expectation values in Gaussian bosonic environments
• A solvable class of non-Markovian quantum multipartite dynamics
• Simulating quantum dynamics in two-dimensional lattices with tensor network influence functional belief propagation
• A tensor network approach to sensing quantum light-matter interactions
• Adiabatic quantum trajectories in engineered reservoirs
• Quantum Parametric Oscillator Heat Engines in Squeezed Thermal Baths: Foundational Theoretical Issues
• Coupled Lindblad pseudomode theory for simulating open quantum systems
• Nuclear Magnetic Resonance model of an entangled sensor under noise
• Unifying methods for optimal control in non-Markovian quantum systems via process tensors
• Designing open quantum systems for enabling quantum enhanced sensing through classical measurements
• Grassmann time-evolving matrix product operators: An efficient numerical approach for fermionic path integral simulations
• Parametric approximation as open quantum systems problem
• A standard form of master equations for general non-Markovian jump processes: the Laplace-space embedding framework and asymptotic solution
• Collisional open quantum dynamics with a generally correlated environment: Exact solvability in tensor networks
• Spectral Density Modulation and Universal Markovian Closure of Fermionic Environments
• About the performance of perturbative treatments of the spin-boson dynamics within the hierarchical equations of motion approach
• Efficient construction of tensor-network representations of many-body Gaussian states
• Non-equilibrium boundary driven quantum systems: models, methods and properties
• Nearly Markovian maps and entanglement-based bound on corresponding non-Markovianity
• Non-monotonic population and coherence evolution in Markovian open-system dynamics
• Efficient Pseudomode Representation and Complexity of Quantum Impurity Models
• Simulating Non-Markovian Dynamics in Multidimensional Electronic Spectroscopy via Quantum Algorithm
• Spatially resolved photon statistics of general nanophotonic systems
• Unveiling coherent dynamics in non-Markovian open quantum systems: exact expression and recursive perturbation expansion
• Vacuum-field-induced state mixing
• Quantum Mpemba Effect Induced by Non-Markovian Exceptional Points
• Finite-Dimensional Stinespring Curves Can Approximate Any Dynamics
• Real-time propagation of adaptive sampling selected configuration interaction wave function
• Quantum feedback control with a transformer neural network architecture
• Exact Model Reduction for Continuous-Time Open Quantum Dynamics
• Nonequilibrium dual-boson approach
• Integral representation of finite temperature non-Markovian evolution of some RWA systems
• Towards robust variational quantum simulation of Lindblad dynamics via stochastic Magnus expansion
• Quantum Hierarchical Fokker-Planck Equations with U(1) Gauge Fields (U(1)-QHFPE): A Computational Framework for Aharonov-Bohm Effects
• Quantum stochastic thermodynamics in the mesoscopic-leads formulation
• Dephasing-assisted transport in a tight-binding chain with a linear potential
• Quantifying spectral signatures of non-Markovianity beyond the Born-Redfield master equation
• Input-Output Hierarchical Equations Of Motion
• Controllable non-Markovianity in phase relaxation
• Quantum Cramer-Rao Precision Limit of Noisy Continuous Sensing
• Correlated and Critical Phenomena in Multipartite Quantum Non-Markovianity
• Time-Convolutionless Master Equation Applied to Adiabatic Elimination
• Interplay between external driving, dissipation and collective effects in the Markovian and non-Markovian regimes
• Fermionic duality: General symmetry of open systems with strong dissipation and memory
• Witnessing environment dimension through temporal correlations
• Error Bounds for Open Quantum Systems with Harmonic Bosonic Bath
• Moment expansion method for composite open quantum systems including a damped oscillator mode
• Multimode-cavity picture of non-Markovian waveguide QED
• Equilibration and Typicality in Quantum Processes
• Delocalized Excitation Transfer in Open Quantum Systems with Long-Range Interactions
• Dissipation and non-thermal states in cryogenic cavities
• Heat operator approach to quantum stochastic thermodynamics in the strong-coupling regime
• Universal dissipators for driven open quantum systems and the correction to linear response
• Non-Gaussian Phase Transition and Cascade of Instabilities in the Dissipative Quantum Rabi Model
• Extended Non-Markovian Stochastic Schrödinger Equation with Complex Frequency Modes for General Basis Functions
• Simulating Electron Transfer on Noisy Quantum Computers
• Modified coherence of quantum spins in a damped pure-dephasing model
• Testing bath correlation functions for open quantum dynamics simulations
• Finite-frequency noise in non-Markovian systems: A Markovian embedding approach
• Subtleties in the pseudomodes formalism
• Process Tensor Approaches to Non-Markovian Quantum Dynamics
• Protecting spin squeezing from decoherence
• Purified pseudomode model for nonlinear system-bath interactions
• Quantum vs Classical Thermal Transport at Low Temperatures
• Non-Markovian dynamics in nonstationary Gaussian baths: a hierarchy of pure states approach
• Effective Hamiltonian approach to the exact dynamics of open system by complex discretization approximation for environment
• Position-Resolved Resonance Quantization for Lossy Cavities
• From Superradiance to Superabsorption: An Exact Treatment of Non-Markovian Cooperative Radiation
• Markovian Embeddings of Non-Markovian Open System Dynamics
• paces: Parallelized Application of Co-Evolving Subspaces, a method for computing quantum dynamics on GPUs
• Approaching the scaling limit of transport through lattices with dephasing
• Beyond mean-field dynamics of the Dicke model with non-Markovian dephasing
• Making Non-Markovian master equations accessible with approximate environments
• Quantum dynamics of a bosonic mode and a two-level system interacting with several reservoirs
• Switching of the information backflow between a helical spin system and non-Markovian bath