Neural-Network Approach to Dissipative Quantum Many-Body Dynamics

Abstract

In experimentally realistic situations, quantum systems are never perfectly isolated and the coupling to their environment needs to be taken into account. Often, the effect of the environment can be well approximated by a Markovian master equation. However, solving this master equation for quantum many-body systems, becomes exceedingly hard due to the high dimension of the Hilbert space. Here we present an approach to the effective simulation of the dynamics of open quantum many-body systems based on machine learning techniques. We represent the mixed many-body quantum states with neural networks in the form of restricted Boltzmann machines and derive a variational Monte-Carlo algorithm for their time evolution and stationary states. We document the accuracy of the approach with numerical examples for a dissipative spin lattice system.

References in corpus (47)

• Quantum Computing in the NISQ era and beyond
• The density-matrix renormalization group in the age of matrix product states
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• An Open-System Quantum Simulator with Trapped Ions
• Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
• The iTEBD algorithm beyond unitary evolution
• Dissipative Phase Transition in Central Spin Systems
• A Dissipatively Stabilized Mott Insulator of Photons
• Observation of a dissipative phase transition in a one-dimensional circuit QED lattice
• Reconstructing quantum states with generative models
• Machine Learning Topological States
• Exact nonequilibrium steady state of a strongly driven open XXZ chain
• Symmetries and many-body excited states with neural-network quantum states
• Equivalence of restricted Boltzmann machines and tensor network states
• Weak binding between two aromatic rings: feeling the van der Waals attraction by quantum Monte Carlo methods
• 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
• Neural-Network Quantum States, String-Bond States, and Chiral Topological States
• Localization and Glassy Dynamics Of Many-Body 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
• A positive tensor network approach for simulating open quantum many-body systems
• Constructing neural stationary states for open quantum many-body systems
• Latent Space Purification via Neural Density Operators
• Polariton crystallization in driven arrays of lossy nonlinear resonators
• A simple tensor network algorithm for two-dimensional steady states
• Quantum critical regime in a quadratically-driven nonlinear photonic lattice
• A Matrix-Product-Operator Approach to the Nonequilibrium Steady State of Driven-Dissipative Quantum Arrays
• Corner space renormalization method for driven-dissipative 2D correlated systems
• Exact Nonequilibrium Steady State of an Open Hubbard Chain
• Chiral Topological Phases from Artificial Neural Networks
• Quenches near Ising quantum criticality as a challenge for artificial neural networks
• Modelling Non-Markovian Quantum Processes with Recurrent Neural Networks
• One-dimensional many-body entangled open quantum systems with tensor network methods
• Quantum dynamical field theory for non-equilibrium phase transitions in driven open systems
• Linked cluster expansions for open quantum systems on a lattice
• Quantum dynamics in transverse-field Ising models from classical networks
• Observation of the Crossover from Photon Ordering to Delocalization in Tunably Coupled Resonators
• Steady States of Infinite-Size Dissipative Quantum Chains via Imaginary Time Evolution
• A driven-dissipative quantum Monte Carlo method for open quantum systems
• Neural-network states for the classical simulation of quantum computing
• Gutzwiller Monte Carlo approach for a critical dissipative spin model
• Interacting lattice systems with quantum dissipation: a quantum Monte Carlo study

Cited by in corpus (155)

• Machine learning and the physical sciences
• Engineered Dissipation for Quantum Information Science
• Fermionic neural-network states for ab-initio electronic structure
• 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
• Constructing neural stationary states for open quantum many-body systems
• Artificial Intelligence and Machine Learning for Quantum Technologies
• NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems
• Machine Learning for Quantum Matter
• Neural Quantum States of frustrated magnets: generalization and sign structure
• Quantum Simulation of Open Quantum Systems Using a Unitary Decomposition of Operators
• NetKet: A Machine Learning Toolkit for Many-Body Quantum Systems
• Machine learning quantum states in the NISQ era
• Restricted Boltzmann Machines for Quantum States with Nonabelian or Anyonic Symmetries
• Variational Monte Carlo calculations of $\mathbf{A}\le 4$ nuclei with an artificial neural-network correlator ansatz
• A Tutorial on Quantum Master Equations: Tips and tricks for quantum optics, quantum computing and beyond
• Autoregressive Transformer Neural Network for Simulating Open Quantum Systems via a Probabilistic Formulation
• Capturing Non-Markovian Dynamics on Near-Term Quantum Computers
• Entanglement Classification via Neural Network Quantum States
• Helping restricted Boltzmann machines with quantum-state representation by restoring symmetry
• Physics-informed neural networks for quantum control
• Experimental quantum homodyne tomography via machine learning
• Learning entropy production via neural networks
• Boosting Monte Carlo simulations of spin glasses using autoregressive neural networks
• Gauge Invariant and Anyonic Symmetric Transformer and RNN Quantum States for Quantum Lattice Models
• Unbiasing time-dependent Variational Monte Carlo by projected quantum evolution
• Solving Quasiparticle Band Spectra of Real Solids using Neural-Network Quantum States
• Realising and compressing quantum circuits with quantum reservoir computing
• Breaking Adiabatic Quantum Control with Deep Learning
• Drawing Phase Diagrams of Random Quantum Systems by Deep Learning the Wave Functions
• Variational Quantum Algorithm for Non-equilibrium Steady States
• Deep learning of quantum entanglement from incomplete measurements
• Eigenstate extraction with neural-network tomography
• Entanglement-Optimal Trajectories of Many-Body Quantum Markov Processes
• Hybrid convolutional neural network and PEPS wave functions for quantum many-particle states
• Purifying Deep Boltzmann Machines for Thermal Quantum States
• Solving the Liouvillian Gap with Artificial Neural Networks
• Role of stochastic noise and generalization error in the time propagation of neural-network quantum states
• Scaling of neural-network quantum states for time evolution
• Variational Monte Carlo with Large Patched Transformers
• Self-consistent microscopic derivation of Markovian master equations for open quadratic quantum systems
• Nuclei with up to $\mathbf{A}=6$ nucleons with artificial neural network wave functions
• A Neural-Network Variational Quantum Algorithm for Many-Body Dynamics
• Dynamics with autoregressive neural quantum states: application to critical quench dynamics
• Absorbing phase transition with a continuously varying exponent in a quantum contact process: a neural network approach
• Numerical Simulation of Critical Dissipative Non-Equilibrium Quantum Systems with an Absorbing State
• Many-Body Open Quantum Systems
• Creating and concentrating quantum resource states in noisy environments using a quantum neural network
• Building separable approximations for quantum states via neural networks
• Neural-network quantum states at finite temperature
• Machine learning time-local generators of open quantum dynamics
• Machine Learning Quantum States -- Extensions to Fermion-Boson Coupled Systems and Excited-State Calculations
• A scheme for automatic differentiation of complex loss functions
• Quantum and classical correlations in open quantum-spin lattices via truncated-cumulant trajectories
• Dynamical large deviations of two-dimensional kinetically constrained models using a neural-network state ansatz
• Retrieving Quantum Information with Active Learning
• Simulating disordered quantum systems via dense and sparse restricted Boltzmann machines
• Calculating Renyi Entropies with Neural Autoregressive Quantum States
• On the stability of the infinite Projected Entangled Pair Operator ansatz for driven-dissipative 2D lattices
• Mixed State Entanglement Classification using Artificial Neural Networks
• Quantum speed limit for complex dynamics
• Variational Neural-Network Ansatz for Continuum Quantum Field Theory
• Arnoldi-Lindblad time evolution: Faster-than-the-clock algorithm for the spectrum of time-independent and Floquet open quantum systems
• Synchronization of persistent oscillations in spin systems with non-local dissipations
• jVMC: Versatile and performant variational Monte Carlo leveraging automated differentiation and GPU acceleration
• Entanglement Features of Random Neural Network Quantum States
• Dissipative flow equations
• Continuous-mixture Autoregressive Networks for efficient variational calculation of many-body systems
• Machine classification for probe based quantum thermometry
• Benefits of Open Quantum Systems for Quantum Machine Learning
• Time-dependent atomic magnetometry with a recurrent neural network
• Ground state search by local and sequential updates of neural network quantum states
• Quantum gradient descent algorithms for nonequilibrium steady states and linear algebraic systems
• Spin-1/2 kagome Heisenberg antiferromagnet: Machine learning discovery of the spinon pair density wave ground state
• A quantum algorithm for the direct estimation of the steady state of open quantum systems
• Is attention all you need to solve the correlated electron problem?
• Neural-network-based parameter estimation for quantum detection
• Variational Quantum Algorithms for Steady States of Open Quantum Systems
• MLQD: A package for machine learning-based quantum dissipative dynamics
• Artificial-intelligence-based surrogate solution of dissipative quantum dynamics: physics-informed reconstruction of the universal propagator
• Real-time Dynamics of the Schwinger Model as an Open Quantum System with Neural Density Operators
• Quantum Next Generation Reservoir Computing: An Efficient Quantum Algorithm for Forecasting Quantum Dynamics
• Deep learning of many-body observables and quantum information scrambling
• Estimating the Euclidean quantum propagator with deep generative modeling of Feynman paths
• Efficient learning of mixed-state tomography for photonic quantum walk
• Adaptive variational low-rank dynamics for open quantum systems
• Variational approach to the dynamics of dissipative quantum impurity models
• Beating the classical phase precision limit using a quantum neuromorphic platform
• Deep reinforcement learning for preparation of thermal and prethermal quantum states
• Sampling scheme for neuromorphic simulation of entangled quantum systems
• Compact Neural-network Quantum State representations of Jastrow and Stabilizer states
• The unbearable lightness of Restricted Boltzmann Machines: Theoretical Insights and Biological Applications
• Continuous-time dynamics and error scaling of noisy highly-entangling quantum circuits
• Rényi free energy and variational approximations to thermal states
• Deep Neural Networks as Variational Solutions for Correlated Open Quantum Systems
• Nonuniform phases in the geometrically frustrated dissipative XYZ model
• Long-range interaction in an open boundary-driven Heisenberg spin lattice: A far-from-equilibrium transition to ballistic transport
• Exponentially improved efficient machine learning for quantum many-body states with provable guarantees
• Infinite Neural Network Quantum States: Entanglement and Training Dynamics
• Neural-network Quantum States for Spin-1 systems: spin-basis and parameterization effects on compactness of representations
• Machine-learning-inspired quantum optimal control of nonadiabatic geometric quantum computation via reverse engineering
• Invariant Neural Network Ansatz for weakly symmetric Open Quantum Lattices
• Crossover from the discontinuous to continuous phase transitions in dissipative spin system with collective decay
• Casimir effect with machine learning
• Quantum Transport in Open Spin Chains using Neural-Network Quantum States
• Steady-state phases of dissipative spin-1/2 XYZ model with frustrated interaction
• Neural network enhanced hybrid quantum many-body dynamical distributions
• Machine Learning approach to muon spectroscopy analysis
• Inferring Markovian quantum master equations of few-body observables in interacting spin chains
• Sampling asymmetric open quantum systems for artificial neural networks
• Steady-state susceptibility in continuous phase transitions of dissipative systems
• Investigating Network Parameters in Neural-Network Quantum States
• Simulation of Charge Stability Diagrams for Automated Tuning Solutions (SimCATS)
• Non-equilibrium boundary driven quantum systems: models, methods and properties
• Supervised Training of Neural-Network Quantum States for the Next Nearest Neighbor Ising model
• Liouville Space Neural Network Representation of Density Matrices
• Boltzmann machines and quantum many-body problems
• Transfer learning from Hermitian to non-Hermitian quantum many-body physics
• Specialising Neural-network Quantum States for the Bose Hubbard Model
• Quantum many-body solver using artificial neural networks and its applications to strongly correlated electron systems
• Learning quantum dissipation by the neural ordinary differential equation
• Transport in Conductors and Rectifiers: Mean-Field Redfield Equations and Non-Equilibrium Green's Functions
• Accuracy of time-dependent GGE under weak dissipation
• Tensor-network-based variational Monte Carlo approach to the non-equilibrium steady state of open quantum systems
• Differentiable master equation solver for quantum device characterisation
• Variational Neural and Tensor Network Approximations of Thermal States
• Thermalization at Low Temperatures via Weakly-Damped Multi-Site Baths
• Coarse-grained spectral projection (CGSP): a deep learning-assisted approach to quantum unitary dynamics
• Non-Hermitian ultra-strong bosonic clustering through interaction-induced caging
• Bidirectional information flow quantum state tomography
• Neural-network quantum state study of the long-range antiferromagnetic Ising chain
• Dynamics of two-dimensional open quantum lattice models with tensor networks
• Variational Quantum Imaginary Time Evolution for Matrix Product State Ansatz with Tests on Transcorrelated Hamiltonians
• Time-dependent variational principle for open quantum systems with artificial neural networks
• Stochastic Simulation of Emission Spectra and Classical Photon Statistics of Quantum Dot Superluminescent Diodes
• Predicting quantum evolutions of excitation energy transfer in a light-harvesting complex using multi-optimized recurrent neural networks
• A Tensor Network Approach to Finite Markov Decision Processes
• Learning topological defects formation with neural networks in a quantum phase transition
• Full- and low-rank exponential Euler integrators for the Lindblad equation
• Permutationally invariant processes in open multiqudit systems
• Variational Transformer Ansatz for the Density Operator of Steady States in Dissipative Quantum Many-Body Systems
• Many-Body Neural Network Wavefunction for a Non-Hermitian Ising Chain
• Artificial intelligence for representing and characterizing quantum systems
• Learning the dynamics of Markovian open quantum systems from experimental data
• Variational approach to open quantum systems with long-range competing interactions
• Process Tensor Approaches to Non-Markovian Quantum Dynamics
• Multiclass classification of dephasing channels
• Worldline algorithm by oracle-guided variational autoregressive network
• Learning disentangled representation for classical models
• Efficient bit encoding of neural networks for Fock states
• Data-Driven Time Propagation of Quantum Systems with Neural Networks
• Determination of the critical exponents in dissipative phase transitions: Coherent anomaly approach
• Fully differentiable optimization protocols for non-equilibrium steady states
• Machine Learning out of equilibrium correlations in the Bose-Hubbard model