Liouville Space Neural Network Representation of Density Matrices

Abstract

Neural network quantum states as ansatz wavefunctions have shown a lot of promise for finding the ground state of spin models. Recently, work has been focused on extending this idea to mixed states for simulating the dynamics of open systems. Most approaches so far have used a purification ansatz where a copy of the system Hilbert space is added which when traced out gives the correct density matrix. Here, we instead present an extension of the Restricted Boltzmann Machine which directly represents the density matrix in Liouville space. This allows the compact representation of states which appear in mean-field theory. We benchmark our approach on two different version of the dissipative transverse field Ising model which show our ansatz is able to compete with other state-of-the-art approaches.

13 pages, 9 figures. Updated to published version

References in corpus (41)

• Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) Network
• A computable measure of entanglement
• The density-matrix renormalization group in the age of matrix product states
• Machine learning and the physical sciences
• Efficient classical simulation of slightly entangled quantum computations
• Classical, quantum and total correlations
• QuTiP 2: A Python framework for the dynamics of open quantum systems
• Solving the Quantum Many-Body Problem with Artificial Neural Networks
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• The classical-quantum boundary for correlations: discord and related measures
• Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
• Spectral theory of Liouvillians for dissipative phase transitions
• Quantum Entanglement in Neural Network States
• Generalized Lanczos Algorithm for Variational Quantum Monte Carlo
• Observation of a dissipative phase transition in a one-dimensional circuit QED lattice
• Reconstructing quantum states with generative models
• Neural-Network Approach to Dissipative Quantum Many-Body Dynamics
• Green Function Monte Carlo with Stochastic Reconfiguration
• Deep autoregressive models for the efficient variational simulation of many-body quantum systems
• Feedback-optimized parallel tempering Monte Carlo
• Symmetries and many-body excited states with neural-network quantum states
• Study of the Two-Dimensional Frustrated J1-J2 Model with Neural Network Quantum States
• 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
• Probing a dissipative phase transition via dynamical optical hysteresis
• Neural-Network Quantum States, String-Bond States, and Chiral Topological States
• Unconventional magnetism via optical pumping of interacting spin systems
• Variational principle for steady states of dissipative quantum many-body systems
• Spectral functions in one-dimensional quantum systems at T>0
• Cluster mean-field approach to the steady-state phase diagram of dissipative spin systems
• Constructing neural stationary states for open quantum many-body systems
• Latent Space Purification via Neural Density Operators
• A Matrix-Product-Operator Approach to the Nonequilibrium Steady State of Driven-Dissipative Quantum Arrays
• NetKet: A Machine Learning Toolkit for Many-Body Quantum Systems
• Corner space renormalization method for driven-dissipative 2D correlated systems
• Majorana-Like Modes of Light in a One-Dimensional Array of Nonlinear Cavities
• Quantum correlations in the 1-D driven dissipative transverse field XY model
• Super-resolving the Ising model with convolutional neural networks
• Supplementing Recurrent Neural Networks with Annealing to Solve Combinatorial Optimization Problems
• Neural-network Quantum States for Spin-1 systems: spin-basis and parameterization effects on compactness of representations

Cited by in corpus (4)

• Many-Body Open Quantum Systems
• Deep Neural Networks as Variational Solutions for Correlated Open Quantum Systems
• Tensor-network-based variational Monte Carlo approach to the non-equilibrium steady state of open quantum systems
• Variational Transformer Ansatz for the Density Operator of Steady States in Dissipative Quantum Many-Body Systems