# Variational Quantum Monte Carlo Method with a Neural-Network Ansatz for Open Quantum Systems

## TL;DR

This paper introduces a variational Monte Carlo approach using neural networks to efficiently simulate the steady states of large open quantum systems, overcoming exponential complexity in density matrix representation.

## Contribution

It develops a novel neural network-based variational method combined with stochastic reconfiguration to simulate non-equilibrium steady states of open quantum systems.

## Key findings

- Successfully modeled the 2D dissipative XYZ spin model.
- Demonstrated efficiency in handling large system sizes.
- Validated the method against known quantum system behaviors.

## Abstract

The possibility to simulate the properties of many-body open quantum systems with a large number of degrees of freedom is the premise to the solution of several outstanding problems in quantum science and quantum information. The challenge posed by this task lies in the complexity of the density matrix increasing exponentially with the system size. Here, we develop a variational method to efficiently simulate the non-equilibrium steady state of Markovian open quantum systems based on variational Monte Carlo and on a neural network representation of the density matrix. Thanks to the stochastic reconfiguration scheme, the application of the variational principle is translated into the actual integration of the quantum master equation. We test the effectiveness of the method by modeling the two-dimensional dissipative XYZ spin model on a lattice.