Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems

TL;DR

This paper introduces a variational MPO-based method for efficiently finding the steady state of dissipative quantum chains, bypassing the need for full evolution and enabling faster convergence with moderate bond dimensions.

Contribution

The paper proposes a novel variational approach that directly targets the steady state MPO, improving efficiency over traditional evolution-based methods.

Findings

The method converges faster than traditional approaches.

Steady states are well approximated by MPOs with small bond dimensions.

Numerical results demonstrate effectiveness across various models.

Abstract

We present a new variational method, based on the matrix product operator (MPO) ansatz, for finding the steady state of dissipative quantum chains governed by master equations of the Lindblad form. Instead of requiring an accurate representation of the system evolution until the stationary state is attained, the algorithm directly targets the final state, thus allowing for a faster convergence when the steady state is a MPO with small bond dimension. Our numerical simulations for several dissipative spin models over a wide range of parameters illustrate the performance of the method and show that indeed the stationary state is often well described by a MPO of very moderate dimensions.