Optimizing Quantum Adiabatic Algorithm

TL;DR

This paper investigates how the shape of the adiabatic path affects computational errors in quantum adiabatic algorithms and proposes optimal path designs to minimize these errors, enhancing algorithm efficiency.

Contribution

It introduces a systematic method to optimize adiabatic paths by considering derivatives at path endpoints, improving error reduction in quantum adiabatic algorithms.

Findings

Optimal paths significantly reduce computational errors.

Error depends on derivatives of the adiabatic parameter at start and end.

Method applies generally beyond quantum adiabatic search.

Abstract

In quantum adiabatic algorithm, as the adiabatic parameter $s(t)$ changes slowly from zero to one with finite rate, a transition to excited states inevitably occurs and this induces an intrinsic computational error. We show that this computational error depends not only on the total computation time $T$ but also on the time derivatives of the adiabatic parameter $s(t)$ at the beginning and the end of evolution. Previous work (Phys. Rev. A \textbf{82}, 052305) also suggested this result. With six typical paths, we systematically demonstrate how to optimally design an adiabatic path to reduce the computational errors. Our method has a clear physical picture and also explains the pattern of computational error. In this paper we focus on quantum adiabatic search algorithm although our results are general.