Liouville Space Neural Network Representation of Density Matrices

TL;DR

This paper introduces a novel Liouville space neural network approach using a Restricted Boltzmann Machine to directly represent density matrices, enabling efficient simulation of open quantum systems without purification.

Contribution

It extends neural network quantum states to directly model density matrices in Liouville space, bypassing the need for purification methods.

Findings

Competitively benchmarks on dissipative transverse field Ising models.

Efficiently represents states in mean-field theory.

Outperforms some existing approaches in certain scenarios.

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.