# Constructing neural stationary states for open quantum many-body systems

## TL;DR

This paper introduces a neural-network based variational method to efficiently compute stationary states of open quantum many-body systems described by Lindblad equations, using restricted Boltzmann machines.

## Contribution

It presents a novel neural stationary state ansatz and applies variational Monte Carlo to find stationary states, extending neural quantum state techniques to open systems.

## Key findings

- Successfully simulates 1D and 2D transverse-field Ising models
- Efficiently computes stationary states of the XYZ model in 1D
- Demonstrates the method's effectiveness for open quantum systems

## Abstract

We propose a new variational scheme based on the neural-network quantum states to simulate the stationary states of open quantum many-body systems. Using the high expressive power of the variational ansatz described by the restricted Boltzmann machines, which we dub as the neural stationary state ansatz, we compute the stationary states of quantum dynamics obeying the Lindblad master equations. The mapping of the stationary-state search problem into finding a zero-energy ground state of an appropriate Hermitian operator allows us to apply the conventional variational Monte Carlo method for the optimization. Our method is shown to simulate various spin systems efficiently, i.e., the transverse-field Ising models in both one and two dimensions and the XYZ model in one dimension.