Convex Optimization for Nonequilibrium Steady States on a Hybrid Quantum Processor

TL;DR

This paper introduces a hybrid quantum algorithm that reformulates the problem of finding steady states of open quantum systems as a semidefinite program, enabling efficient estimation of higher-dimensional steady states and systems with symmetries.

Contribution

It presents a novel quantum-assisted method that overcomes limitations of variational approaches by using semidefinite programming to find steady states of open quantum systems.

Findings

Successfully estimates steady states of higher-dimensional systems

Can identify multiple steady states in symmetric systems

Bypasses issues with variational quantum methods

Abstract

Finding the transient and steady state properties of open quantum systems is a central problem in various fields of quantum technologies. Here, we present a quantum-assisted algorithm to determine the steady states of open system dynamics. By reformulating the problem of finding the fixed point of Lindblad dynamics as a feasibility semidefinite program, we bypass several well-known issues with variational quantum approaches to solving for steady states. We demonstrate that our hybrid approach allows us to estimate the steady states of higher dimensional open quantum systems and discuss how our method can find multiple steady states for systems with symmetries.