The Quantum Adiabatic Algorithm applied to random optimization problems: the quantum spin glass perspective

TL;DR

This paper reviews recent analytical studies and presents new results on the quantum adiabatic algorithm's effectiveness in solving random optimization problems modeled as quantum spin glasses.

Contribution

It provides a comprehensive review and new insights into how quantum fluctuations influence the quantum adiabatic algorithm's performance on spin glass problems.

Findings

Quantum fluctuations affect the algorithm's efficiency.

Analytical results extend classical spin glass models.

New theoretical insights into quantum optimization performance.

Abstract

Among various algorithms designed to exploit the specific properties of quantum computers with respect to classical ones, the quantum adiabatic algorithm is a versatile proposition to find the minimal value of an arbitrary cost function (ground state energy). Random optimization problems provide a natural testbed to compare its efficiency with that of classical algorithms. These problems correspond to mean field spin glasses that have been extensively studied in the classical case. This paper reviews recent analytical works that extended these studies to incorporate the effect of quantum fluctuations, and presents also some original results in this direction.