Optimal protocols for slowly-driven quantum processes

TL;DR

This paper develops a geometric framework to identify optimal protocols that minimize entropy production in driven quantum systems, with applications to quantum annealing.

Contribution

It extends a classical geometric approach to quantum systems, enabling the calculation of optimal entropy-minimizing protocols in finite-time quantum processes.

Findings

Derived explicit optimal protocols for a two-state quantum system.

Connected geodesic paths on parameter manifolds to entropy minimization.

Applicable to quantum annealing and other driven quantum processes.

Abstract

The design of efficient quantum information processing will rely on optimal nonequilibrium transitions of driven quantum systems. Building on a recently-developed geometric framework for computing optimal protocols for classical systems driven in finite-time, we construct a general framework for optimizing the average information entropy for driven quantum systems. Geodesics on the parameter manifold endowed with a positive semi-definite metric correspond to protocols that minimize the average information entropy production in finite-time. We use this framework to explicitly compute the optimal entropy production for a simple two-state quantum system coupled to a heat bath of bosonic oscillators, which has applications to quantum annealing.