Many-body localization enables iterative quantum optimization

TL;DR

This paper introduces an iterative quantum optimization protocol leveraging many-body localization to efficiently find lower energy states in complex landscapes, potentially reaching the global minimum in polynomial time.

Contribution

It proposes a novel quantum algorithm that uses cycling around the localization transition to improve optimization in glassy energy landscapes.

Findings

Algorithm approaches the absolute minimum with polynomial complexity

Cycle parameters are tailored to current optimal states

Performance depends on knowledge of the tricritical point

Abstract

We suggest an iterative quantum protocol, allowing to solve optimization problems with a glassy energy landscape. It is based on a periodic cycling around the tricritical point of the many-body localization transition. This ensures that each iteration leads to a non-exponentially small probability to find a lower local energy minimum. The other key ingredient is to tailor the cycle parameters to a currently achieved optimal state (the "reference" state) and to reset them once a deeper minimum is found. We show that, if the position of the tricritical point is known, the algorithm allows to approach the absolute minimum with any given precision in a polynomial time.