Invariant Neural Network Ansatz for weakly symmetric Open Quantum Lattices

TL;DR

This paper introduces a neural network method that leverages symmetry properties to efficiently find the steady states of weakly symmetric open quantum lattice systems, demonstrated on a dissipative XYZ model.

Contribution

It develops a neural network ansatz that explicitly incorporates system symmetries for efficiently solving steady states in open quantum systems.

Findings

Successfully determines the steady state of a 1D dissipative XYZ model.

Shows that symmetry-aware neural networks reduce computational complexity.

Validates the approach with numerical experiments.

Abstract

We consider $d$-dimensional open quantum lattices whose time evolution is governed by a master equation which is weakly symmetric under the action of a finite group $G$ that is a subgroup of all the possible permutations of the lattice sites. We show that, whenever the steady state is unique, one can introduce a neural network representation for the system density operator that explicitly accounts for the system symmetries and can be efficiently optimized by exploring only a relevant subspace of the parameter space. In particular, as a proof of principle, we demonstrate the validity of our approach by determining the steady state structure of the one dimensional dissipative XYZ model in the presence of a uniform magnetic field.