A positive tensor network approach for simulating open quantum many-body systems

Abstract

Open many-body quantum systems play an important role in quantum optics and condensed-matter physics, and capture phenomena like transport, interplay between Hamiltonian and incoherent dynamics, and topological order generated by dissipation. We introduce a versatile and practical method to numerically simulate one-dimensional open quantum many-body dynamics using tensor networks. It is based on representing mixed quantum states in a locally purified form, which guarantees that positivity is preserved at all times. Moreover, the approximation error is controlled with respect to the trace norm. Hence, this scheme overcomes various obstacles of the known numerical open-system evolution schemes. To exemplify the functioning of the approach, we study both stationary states and transient dissipative behaviour, for various open quantum systems ranging from few to many bodies.

13 pages, 7 figures, significant material on error bounds added

References in corpus (17)

• The density-matrix renormalization group in the age of matrix product states
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Quantum trajectories and open many-body quantum systems
• Simple pulses for elimination of leakage in weakly nonlinear qubits
• Algorithms for finite Projected Entangled Pair States
• Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems
• Non-equilibrium delocalization-localization transition of photons in circuit QED
• Matrix product operators and states: NP-hardness and undecidability
• Unconstrained Tree Tensor Network: An adaptive gauge picture for enhanced performance
• Unifying variational methods for simulating quantum many-body systems
• Simulation of time evolution with the MERA
• Heating dynamics of bosonic atoms in a noisy optical lattice
• Light scattering and dissipative dynamics of many fermionic atoms in an optical lattice
• Time evolution of projected entangled pair states in the single layer picture
• Dynamical and Steady State Properties of a Bose-Hubbard Chain with Bond-Dissipation: A Study based on Matrix Product Operators
• Real-space renormalization yields finite correlations

Cited by in corpus (137)

• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• Neural-Network Approach to Dissipative Quantum Many-Body Dynamics
• 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
• Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems
• Cluster mean-field approach to the steady-state phase diagram of dissipative spin systems
• Constructing neural stationary states for open quantum many-body systems
• Review on novel methods for lattice gauge theories
• Lecture Notes of Tensor Network Contractions
• The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
• A simple tensor network algorithm for two-dimensional steady states
• Quantum dynamics of thermalizing systems
• Time Evolution of an Infinite Projected Entangled Pair State: an Efficient Algorithm
• Geometry of variational methods: dynamics of closed quantum systems
• Tensor-Network Simulations of the Surface Code under Realistic Noise
• A tensor network annealing algorithm for two-dimensional thermal states
• A Tutorial on Quantum Master Equations: Tips and tricks for quantum optics, quantum computing and beyond
• Nonequilibrium Steady-State Transport in Quantum Impurity Models: a Thermofield and Quantum Quench Approach using Matrix Product States
• Autoregressive Transformer Neural Network for Simulating Open Quantum Systems via a Probabilistic Formulation
• Lindblad-Driven Discretized Leads for Non-Equilibrium Steady-State Transport in Quantum Impurity Models: Recovering the Continuum Limit
• Phase diagram of incoherently driven strongly correlated photonic lattices
• One-dimensional many-body entangled open quantum systems with tensor network methods
• Integrability of $1D$ Lindbladians from operator-space fragmentation
• Green's function methods for single molecule junctions
• Open source Matrix Product States: Opening ways to simulate entangled many-body quantum systems in one dimension
• Quantum contact process
• Quantum simulation of dissipative collective effects on noisy quantum computers
• Learning the dynamics of open quantum systems from their steady states
• Linked cluster expansions for open quantum systems on a lattice
• Quantum error mitigation via matrix product operators
• 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
• Simulating Noisy Quantum Circuits with Matrix Product Density Operators
• Steady States of Infinite-Size Dissipative Quantum Chains via Imaginary Time Evolution
• Renormalized Lindblad Driving: A Numerically-Exact Nonequilibrium Quantum Impurity Solver
• Entanglement-Optimal Trajectories of Many-Body Quantum Markov Processes
• Fundamental limitations in the purifications of tensor networks
• Linear-time general decoding algorithm for the surface code
• 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
• Rise and fall, and slow rise again, of operator entanglement under dephasing
• Dissipative phase transitions in the fully-connected Ising model with $p$-spin interaction
• Numerical Simulation of Critical Dissipative Non-Equilibrium Quantum Systems with an Absorbing State
• Many-Body Open Quantum Systems
• Efficient simulation of sparse Markovian quantum dynamics
• Superdiffusive quantum stochastic walk definable of arbitrary directed graph
• Enhanced TEMPO algorithm for quantum path integrals with off-diagonal system-bath coupling: applications to photonic quantum networks
• Time Evolution of an Infinite Projected Entangled Pair State: an Algorithm from First Principles
• Optimal stochastic unraveling of disordered open quantum systems: application to driven-dissipative photonic lattices
• Dilaton-induced open quantum dynamics
• A tree tensor network approach to simulating Shor's algorithm
• On the stability of the infinite Projected Entangled Pair Operator ansatz for driven-dissipative 2D lattices
• Experimental demonstration of a directionally-unbiased linear-optical multiport
• A new method for directly computing reduced density matrices
• Tensor Networks for Lattice Gauge Theories beyond one dimension: a Roadmap
• Comparing bipartite entropy growth in open-system matrix-product simulation methods
• Renormalising entanglement distillation
• Probabilistic low-rank factorization accelerates tensor network simulations of critical quantum many-body ground states
• Dynamics of the order-parameter statistics in the long-range Ising model
• Tensor network representations from the geometry of entangled states
• Improving compressed sensing with the diamond norm
• Accelerating Quantum Relaxation via Temporary Reset: A Mpemba-Inspired Approach
• Neural Projected Quantum Dynamics: a systematic study
• Combined tensor network/cluster expansion method using logic gates: Illustrated for (bi-)excitons by a single layer MoS${}_2$ model system
• Locally Purified Density Operators for Symmetry-Protected Topological Phases in Mixed States
• Quantum State Tomography for Matrix Product Density Operators
• Quantum State Tomography with Locally Purified Density Operators and Local Measurements
• Kibble-Zurek scaling of the one-dimensional Bose-Hubbard model at finite temperatures
• A quantum algorithm for the direct estimation of the steady state of open quantum systems
• Benchmarking treewidth as a practical component of tensor-network--based quantum simulation
• Density-of-states of many-body quantum systems from tensor networks
• Entanglement of formation of mixed many-body quantum states via Tree Tensor Operators
• Effective dimension reduction with mode transformations: Simulating two-dimensional fermionic condensed matter systems
• Tensor network noise characterization for near-term quantum computers
• Simulating open quantum systems with giant atoms
• Adaptive variational low-rank dynamics for open quantum systems
• Tailored jump operators for purely dissipative quantum magnetism
• Convex Optimization for Nonequilibrium Steady States on a Hybrid Quantum Processor
• Tree tensor network hierarchical equations of motion based on time-dependent variational principle for efficient open quantum dynamics in structured thermal environments
• Locally purified density operators for noisy quantum circuits
• Unfolding quantum master equation into a system of real-valued equations: computationally effective expansion over the basis of $SU(N)$ generators
• Waiting-times statistics in boundary driven free fermion chains
• Rényi free energy and variational approximations to thermal states
• Simulating Lindbladian evolution with non-abelian symmetries: Ballistic front propagation in the $SU(2)$ Hubbard model with a localized loss
• Thermalization of long range Ising model in different dynamical regimes: a full counting statistics approach
• A tensor network approach to sensing quantum light-matter interactions
• Crossover from the discontinuous to continuous phase transitions in dissipative spin system with collective decay
• Open quantum dynamics of strongly coupled oscillators with multi-configuration time-dependent Hartree propagation and Markovian quantum jumps
• Exponentially reduced circuit depths in Lindbladian simulation
• A hierarchical equations of motion (HEOM) analog for systems with delay: illustrated on inter-cavity photon propagation
• 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
• Prolonging a discrete time crystal by quantum-classical feedback
• Non-equilibrium boundary driven quantum systems: models, methods and properties
• Finite-temperature Rydberg arrays: quantum phases and entanglement characterization
• Thermalization at Low Temperatures via Weakly-Damped Multi-Site Baths
• A matrix product operator approach to non-equilibrium Floquet steady states
• Exact solution of a quantum asymmetric exclusion process with particle creation and annihilation
• Diffusive-Gutzwiller approach to the quadratically driven photonic lattice
• Tensor-network-based variational Monte Carlo approach to the non-equilibrium steady state of open quantum systems
• Coarse-grained spectral projection (CGSP): a deep learning-assisted approach to quantum unitary dynamics
• Large-scale stochastic simulation of open quantum systems
• Learning topological states from randomized measurements using variational tensor network tomography
• Non-unitarity maximizing unraveling of open quantum dynamics
• Accuracy of time-dependent GGE under weak dissipation
• Meson thermalization with a hot medium in the open Schwinger model
• Dynamics of two-dimensional open quantum lattice models with tensor networks
• Optimal bounds on the positivity of a matrix from a few moments
• Time-dependent variational principle for open quantum systems with artificial neural networks
• Finite temperature tensor network algorithm for frustrated two-dimensional quantum materials
• Real-time Sign-Problem-Suppressed Quantum Monte Carlo Algorithm For Noisy Quantum Circuit Simulations
• Dynamical symmetry in quantum dissipative models
• Dynamical deconfinement transition driven by density of excitations
• A Riemannian Approach to the Lindbladian Dynamics of a Locally Purified Tensor Network
• On the Noisy Road to Open Quantum Dynamics: The Place of Stochastic Hamiltonians
• Full- and low-rank exponential Euler integrators for the Lindblad equation
• Gauge-Fixing Quantum Density Operators At Scale
• Optimal sampling of tensor networks targeting wave function's fast decaying tails
• 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
• Resolving mean-field solutions of dissipative phase transitions using permutational symmetry
• Entanglement transitions in a boundary-driven open quantum many-body system
• Dissipative Yao-Lee Spin-Orbital Model: Exact Solvability and $\mathcal{P}\mathcal{T}$ Symmetry Breaking
• A Randomized Method for Simulating Lindblad Equations and Thermal State Preparation
• Determination of the critical exponents in dissipative phase transitions: Coherent anomaly approach
• Fully differentiable optimization protocols for non-equilibrium steady states
• GCAMPS: A Scalable Classical Simulator for Qudit Systems
• Operator entanglement in $\mathrm{SU}(2)$-symmetric dissipative quantum many-body dynamics
• Low-rank optimal control of quantum devices
• Classical simulation of noisy quantum circuits via locally entanglement-optimal unravelings
• Locally Purified Maximally Mixed States At Scale: Entanglement Pruning and Symmetries
• Circuit connectivity boosts by quantum-classical-quantum interfaces
• New perspectives on quantum kernels through the lens of entangled tensor kernels