Quantum annealing with Jarzynski equality

TL;DR

This paper explores integrating the Jarzynski equality into quantum annealing to potentially overcome the slow sweep speed limitation caused by non-adiabatic transitions in solving combinatorial optimization problems.

Contribution

It introduces a novel approach combining Jarzynski equality with quantum annealing to improve solution efficiency for optimization problems.

Findings

The proposed method may mitigate the impact of non-adiabatic transitions.

It suggests a new pathway to solve optimization problems more efficiently.

The approach could relax the slow sweep requirement in quantum annealing.

Abstract

We show a practical application of the Jarzynski equality in quantum computation. Its implementation may open a way to solve combinatorial optimization problems, minimization of a real single-valued function, cost function, with many arguments. We consider to incorpolate the Jarzynski equality into quantum annealing, which is one of the generic algorithms to solve the combinatorial optimization problem. The ordinary quantum annealing suffers from non-adiabatic transitions whose rate is characterized by the minimum energy gap $\Delta_{\rm min.}$ of the quantum system under consideration. The quantum sweep speed is therefore restricted to be extremely slow for the achievement to obtain a solution without relevant errors. However, in our strategy shown in the present study, we find that such a difficulty would not matter.