Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems

Abstract

We present a new variational method, based on the matrix product operator (MPO) ansatz, for finding the steady state of dissipative quantum chains governed by master equations of the Lindblad form. Instead of requiring an accurate representation of the system evolution until the stationary state is attained, the algorithm directly targets the final state, thus allowing for a faster convergence when the steady state is a MPO with small bond dimension. Our numerical simulations for several dissipative spin models over a wide range of parameters illustrate the performance of the method and show that indeed the stationary state is often well described by a MPO of very moderate dimensions.

arXiv commentAccepted version

References in corpus (44)

• The density-matrix renormalization group in the age of matrix product states
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Efficient simulation of one-dimensional quantum many-body systems
• The Dicke Quantum Phase Transition with a Superfluid Gas in an Optical Cavity
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• An Area Law for One Dimensional Quantum Systems
• Matrix product states represent ground states faithfully
• Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
• DMRG and periodic boundary conditions: a quantum information perspective
• Topology by Dissipation in Atomic Quantum Wires
• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• Renormalization and tensor product states in spin chains and lattices
• Matrix product operator representations
• Dissipative Phase Transition in Central Spin Systems
• Dynamical Critical Phenomena in Driven-Dissipative Systems
• Atomic three-body loss as a dynamical three-body interaction
• Algebraic versus exponential decoherence in dissipative many-particle systems
• Solving Gapped Hamiltonians Locally
• Matrix product simulations of non-equilibrium steady states of quantum spin chains
• Antiferromagnetic phase transition in a nonequilibrium lattice of Rydberg atoms
• Algorithms for finite Projected Entangled Pair States
• Matrix Product States for dynamical simulation of infinite chains
• Variational principle for steady states of dissipative quantum many-body systems
• Quantum phase transition in a far from equilibrium steady state of XY spin chain
• A positive tensor network approach for simulating open quantum many-body systems
• Realization of the Dicke model using cavity-assisted Raman transitions
• Dicke-type phase transition in a spin-orbit coupled Bose-Einstein condensate
• Dynamical phases and intermittency of the dissipative quantum Ising model
• Approximating Gibbs states of local Hamiltonians efficiently with PEPS
• Dissipative Dynamics and Phase Transitions in Fermionic Systems
• Perturbative approach to Markovian open quantum systems
• Steady-state crystallization of Rydberg excitations in an optically driven lattice gas
• Density Matrix Renormalization Group in the Heisenberg Picture
• Purifications of multipartite states: limitations and constructive methods
• Matrix product operators and states: NP-hardness and undecidability
• Critical exponents of steady-state phase transitions in fermionic lattice models
• Precisely timing dissipative quantum information processing
• Self-Consistent Projection Operator Theory for Quantum Many-Body Systems
• Noise-driven quantum criticality
• Dynamical and Steady State Properties of a Bose-Hubbard Chain with Bond-Dissipation: A Study based on Matrix Product Operators
• Bose Hubbard model far from equilibrium

Cited by in corpus (152)

• Finite-temperature transport in one-dimensional quantum lattice models
• Spectral theory of Liouvillians for dissipative phase transitions
• Neural-Network Approach to Dissipative Quantum Many-Body Dynamics
• Reconciliation of quantum local master equations with thermodynamics
• Engineered Dissipation for Quantum Information Science
• Simulation methods for open quantum many-body systems
• Variational Quantum Monte Carlo Method with a Neural-Network Ansatz for Open Quantum Systems
• Variational neural network ansatz for steady states in open quantum systems
• Quantum Simulation with Interacting Photons
• Cluster mean-field approach to the steady-state phase diagram of dissipative spin systems
• Constructing neural stationary states for open quantum many-body systems
• A positive tensor network approach for simulating open quantum many-body systems
• Lecture Notes of Tensor Network Contractions
• Local vs global master equation with common and separate baths: superiority of the global approach in partial secular approximation
• Entanglement scaling of operators: a conformal field theory approach, with a glimpse of simulability of long-time dynamics in 1+1d
• Tensor Network Algorithms: a Route Map
• A simple tensor network algorithm for two-dimensional steady states
• Non-Markovian Dynamics in Chiral Quantum Networks with Spins and Photons
• A Matrix-Product-Operator Approach to the Nonequilibrium Steady State of Driven-Dissipative Quantum Arrays
• Quantum dynamics of thermalizing systems
• Dissipative spin chain as a non-Hermitian Kitaev ladder
• Quantum Neural Network States: A Brief Review of Methods and Applications
• Optimized auxiliary oscillators for the simulation of general open quantum systems
• Beyond mean-field bistability in driven-dissipative lattices: bunching-antibunching transition and quantum simulation
• Nonequilibrium Steady-State Transport in Quantum Impurity Models: a Thermofield and Quantum Quench Approach using Matrix Product States
• Auxiliary master equation approach within matrix product states: Spectral properties of the nonequilibrium Anderson impurity model
• Autoregressive Transformer Neural Network for Simulating Open Quantum Systems via a Probabilistic Formulation
• Critical behavior of dissipative two-dimensional spin lattices
• Lindblad-Driven Discretized Leads for Non-Equilibrium Steady-State Transport in Quantum Impurity Models: Recovering the Continuum Limit
• Modelling Non-Markovian Quantum Processes with Recurrent Neural Networks
• Phase diagram of incoherently driven strongly correlated photonic lattices
• Multicritical behavior in dissipative Ising models
• Integrability of $1D$ Lindbladians from operator-space fragmentation
• One-dimensional many-body entangled open quantum systems with tensor network methods
• Green's function methods for single molecule junctions
• Yang-Baxter integrable Lindblad equations
• Dissipative topological superconductors in number-conserving systems
• Simulating quantum light propagation through atomic ensembles using matrix product states
• Quantum contact process
• Linked cluster expansions for open quantum systems on a lattice
• Learning the dynamics of open quantum systems from their steady states
• Optimized auxiliary representation of a non-Markovian environment by a Lindblad equation
• Characterizing a non-equilibrium phase transition on a quantum computer
• Variational Quantum Algorithm for Non-equilibrium Steady States
• How an autonomous quantum Maxwell demon can harness correlated information
• Quantum Criticality in Open Quantum Spin Chains with Nonreciprocity
• Steady States of Infinite-Size Dissipative Quantum Chains via Imaginary Time Evolution
• Demonstration of dynamical control of three-level open systems with a superconducting qutrit
• A driven-dissipative quantum Monte Carlo method for open quantum systems
• Entanglement-Optimal Trajectories of Many-Body Quantum Markov Processes
• Renormalized Lindblad Driving: A Numerically-Exact Nonequilibrium Quantum Impurity Solver
• Fundamental limitations in the purifications of tensor networks
• Variational principle for quantum impurity systems in and out of equilibrium: application to Kondo problems
• Realistic simulations of spin squeezing and cooperative coupling effects in large ensembles of interacting two-level systems
• Solving the Liouvillian Gap with Artificial Neural Networks
• Open System Tensor Networks and Kramers' Crossover for Quantum Transport
• Self-consistent microscopic derivation of Markovian master equations for open quadratic quantum systems
• Gaussian Quantum Trajectories for the Variational Simulation of Open Quantum-Optical Systems
• Numerical Simulation of Critical Dissipative Non-Equilibrium Quantum Systems with an Absorbing State
• Resummation for Nonequilibrium Perturbation Theory and Application to Open Quantum Lattices
• Many-Body Open Quantum Systems
• Hybrid discrete-continuous truncated Wigner approximation for driven, dissipative spin systems
• Localization-enhanced and degraded topological-order in interacting p-wave wires
• Gutzwiller Monte Carlo approach for a critical dissipative spin model
• Optically bistable driven-dissipative Bose-Hubbard dimer: Gutzwiller approaches and entanglement
• Time evolution of open quantum many-body systems
• A scheme for automatic differentiation of complex loss functions
• Photon propagation through dissipative Rydberg media at large input rates
• Evolution of two-time correlations in dissipative quantum spin systems: aging and hierarchical dynamics
• Dynamical hysteresis properties of the driven-dissipative Bose-Hubbard model with a Gutzwiller Monte Carlo approach
• Optimal stochastic unraveling of disordered open quantum systems: application to driven-dissipative photonic lattices
• On the stability of the infinite Projected Entangled Pair Operator ansatz for driven-dissipative 2D lattices
• Boundary-driven Lindblad dynamics of random quantum spin chains : strong disorder approach for the relaxation, the steady state and the current
• Variational Renormalization Group for Dissipative Spin-Cavity Systems: Periodic Pulses of Nonclassical Photons from Mesoscopic Spin Ensembles
• Spontaneous Beliaev-Landau scattering out of equilibrium
• Analysis of a density matrix renormalization group approach for transport in open quantum systems
• Local master equations may fail to describe dissipative critical behavior
• Bath assisted transport in a three-site spin chain: global {\sl vs} local approach
• Truncated correlation hierarchy schemes for driven-dissipative multimode quantum systems
• Cluster Gutzwiller Monte Carlo approach for a critical dissipative spin model
• Renormalising entanglement distillation
• Arnoldi-Lindblad time evolution: Faster-than-the-clock algorithm for the spectrum of time-independent and Floquet open quantum systems
• Atomic Quantum Technologies for Quantum Matter and Fundamental Physics Applications
• Locally Purified Density Operators for Symmetry-Protected Topological Phases in Mixed States
• Dissipative random quantum spin chain with boundary-driving and bulk-dephasing: magnetization and current statistics in the Non-Equilibrium-Steady-State
• Far from equilibrium field theory for strongly coupled light and matter: dynamics of frustrated multi-mode cavity QED
• A quantum algorithm for the direct estimation of the steady state of open quantum systems
• Temperature Dependent Energy Diffusion in Chaotic Spin Chains
• Entanglement of formation of mixed many-body quantum states via Tree Tensor Operators
• Stable bipolarons in open quantum systems
• Spatial correlations in driven-dissipative photonic lattices
• Efficient variational approach to dynamics of a spatially extended bosonic Kondo model
• Multiple-scale analysis of open quantum systems
• Exact steady state of the open XX-spin chain: entanglement and transport properties
• User-friendly TWA for dissipative spin dynamics
• Time Evolution of Uniform Sequential Circuits
• Solvable BCS-Hubbard Liouvillians in arbitrary dimensions
• Quantum jumps in driven-dissipative disordered many-body systems
• Emergent Continuous Time Crystal in Dissipative Quantum Spin System without Driving
• Accuracy guarantees and quantum advantage in analogue open quantum simulation with and without noise
• Computational complexity of non-equilibrium steady states of quantum spin chains
• Adaptive variational low-rank dynamics for open quantum systems
• Variational approach to the dynamics of dissipative quantum impurity models
• Tailored jump operators for purely dissipative quantum magnetism
• Convex Optimization for Nonequilibrium Steady States on a Hybrid Quantum Processor
• Analytical approach to higher-order correlation functions in U(1) symmetric systems
• Deep Neural Networks as Variational Solutions for Correlated Open Quantum Systems
• Waiting-times statistics in boundary driven free fermion chains
• Unfolding quantum master equation into a system of real-valued equations: computationally effective expansion over the basis of $SU(N)$ generators
• Rényi free energy and variational approximations to thermal states
• Spectral theory of non-Markovian dissipative phase transitions
• Dissipative Symmetry-Protected Topological Order
• Dynamical heterogeneity and large deviations in the open quantum East glass model from tensor networks
• An Extension of ETH to Non-Equilibrium Steady States
• Crossover from the discontinuous to continuous phase transitions in dissipative spin system with collective decay
• Spin fluctuations after quantum quenches in the S=1 Haldane chain: numerical validation of the semi-semiclassical theory
• Exceptional stationary state in a dephasing many-body open quantum system
• Suppressing Decoherence in Quantum Plasmonic Systems by Spectral Hole Burning Effect
• Density Matrix Renormalization Group Algorithm For Mixed Quantum States
• Sampling asymmetric open quantum systems for artificial neural networks
• Time- and frequency-domain two-particle correlations of a driven dissipative Bose-Hubbard model
• Tensor-network approach to thermalization in open quantum many-body systems
• Exact steady state of perturbed open quantum systems
• Steady states of a driven dissipative dipolar XXZ chain
• Lindbladians with multiple steady states: theory and applications
• Non-equilibrium boundary driven quantum systems: models, methods and properties
• Tensor-network-based variational Monte Carlo approach to the non-equilibrium steady state of open quantum systems
• A matrix product operator approach to non-equilibrium Floquet steady states
• Thermalization at Low Temperatures via Weakly-Damped Multi-Site Baths
• Dissipation-Induced Mobility and Coherence in Frustrated Lattices
• General approach to find steady-state manifolds in Markovian and non-Markovian systems
• Large-scale stochastic simulation of open quantum systems
• Effects of Quantum Pair Creation and Annihilation on a Classical Exclusion Process: the transverse XY model with TASEP
• Exact solution of a quantum asymmetric exclusion process with particle creation and annihilation
• Meson thermalization with a hot medium in the open Schwinger model
• Model reduction of cavity nonlinear optics for photonic logic: A quasi-principal components approach
• Dynamics of two-dimensional open quantum lattice models with tensor networks
• Quantum phase transition in the one-dimensional Dicke-Hubbard model with coupled qubits
• Tomography-assisted noisy quantum circuit simulator using matrix product density operators
• Quantum stabilization of photonic spatial correlations
• Chemical master equation parameter exploration using DMRG
• Dynamical symmetry in quantum dissipative models
• Variational approach to open quantum systems with long-range competing interactions
• Linear response and exact hydrodynamic projections in Lindblad equations with decoupled Bogoliubov hierarchies
• Variational Transformer Ansatz for the Density Operator of Steady States in Dissipative Quantum Many-Body Systems
• Variational analysis of driven-dissipative bosonic fields
• Low-rank optimal control of quantum devices
• Fully differentiable optimization protocols for non-equilibrium steady states
• Phase Transitions in the Classical Simulability of Open Quantum Systems
• Fractal Path Strategies for Efficient 2D DMRG Simulations
• Efficient bit encoding of neural networks for Fock states
• Dissipative Yao-Lee Spin-Orbital Model: Exact Solvability and $\mathcal{P}\mathcal{T}$ Symmetry Breaking