Tensor-network-based variational Monte Carlo approach to the non-equilibrium steady state of open quantum systems

TL;DR

This paper presents a new tensor-network variational Monte Carlo method for efficiently simulating the non-equilibrium steady states of large open quantum systems with complex interactions, outperforming existing algorithms.

Contribution

It introduces a novel matrix product operator ansatz combined with variational Monte Carlo to simulate non-equilibrium steady states in large, non-local open quantum systems.

Findings

Efficient simulation of large quantum spin chains up to 100 spins.

Improved computational scaling with bond dimension for periodic systems.

Application to dissipative quantum Ising model with complex interactions.

Abstract

We introduce a novel method of efficiently simulating the non-equilibrium steady state of large many-body open quantum systems with highly non-local interactions, based on a variational Monte Carlo optimization of a matrix product operator ansatz. Our approach outperforms and offers several advantages over comparable algorithms, such as an improved scaling of the computational cost with respect to the bond dimension for periodic systems. We showcase the versatility of our approach by studying the phase diagrams and correlation functions of the dissipative quantum Ising model with collective dephasing and long-ranged power law interactions for spin chains of up to $N=100$ spins.