Quantum Adiabatic Brachistochrone

TL;DR

This paper introduces a geometric framework for adiabatic quantum computation, optimizing evolution time by finding geodesics on a control parameter manifold, which improves performance and clarifies the roles of entanglement and curvature.

Contribution

It formulates a time-optimal approach to AQC using a Riemannian metric, providing a geometric perspective and practical improvements.

Findings

Geodesic-based control improves AQC efficiency

Entanglement and curvature influence algorithm performance

Demonstrated with two example cases

Abstract

We formulate a time-optimal approach to adiabatic quantum computation (AQC). A corresponding natural Riemannian metric is also derived, through which AQC can be understood as the problem of finding a geodesic on the manifold of control parameters. This geometrization of AQC is demonstrated through two examples, where we show that it leads to improved performance of AQC, and sheds light on the roles of entanglement and curvature of the control manifold in algorithmic performance.