# Variational neural network ansatz for steady states in open quantum systems

## TL;DR

This paper introduces a neural network-based variational method to efficiently find steady states of open quantum lattice systems, demonstrated on the dissipative quantum transverse Ising model.

## Contribution

It develops a neural network ansatz for the steady state density matrix using purification and variational minimization, enabling new computational approaches for open quantum systems.

## Key findings

- Successfully applied to the dissipative quantum transverse Ising model
- Demonstrates the effectiveness of neural network ansatz in open quantum systems
- Provides a scalable method for steady state computation

## Abstract

We present a general variational approach to determine the steady state of open quantum lattice systems via a neural network approach. The steady-state density matrix of the lattice system is constructed via a purified neural network ansatz in an extended Hilbert space with ancillary degrees of freedom. The variational minimization of cost functions associated to the master equation can be performed using a Markov chain Monte Carlo sampling. As a first application and proof-of-principle, we apply the method to the dissipative quantum transverse Ising model.