Neural-Network Approach to Dissipative Quantum Many-Body Dynamics

TL;DR

This paper introduces a machine learning-based method using neural networks, specifically restricted Boltzmann machines, to efficiently simulate the dynamics of open quantum many-body systems described by Markovian master equations.

Contribution

It develops a variational Monte Carlo algorithm employing neural networks to model mixed quantum states, enabling effective simulation of dissipative quantum systems.

Findings

Accurately simulates dissipative spin lattice systems

Demonstrates neural network approach matches traditional methods

Provides a scalable framework for open quantum system 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.