Adiabatic Quantum Computing

TL;DR

Adiabatic quantum computing (AQC) is a versatile approach to quantum computation that has evolved from solving optimization problems to a universal model, with significant theoretical developments, algorithmic examples, and complexity insights.

Contribution

This review comprehensively covers the theoretical foundations, variants, and computational complexity aspects of AQC, highlighting recent advances and open challenges.

Findings

Several variants of the adiabatic theorem are presented.

Explicit AQC algorithms demonstrating quantum speedup are discussed.

Obstructions to success in Stoquastic AQC and potential resolutions are analyzed.

Abstract

Adiabatic quantum computing (AQC) started as an approach to solving optimization problems, and has evolved into an important universal alternative to the standard circuit model of quantum computing, with deep connections to both classical and quantum complexity theory and condensed matter physics. In this review we give an account of most of the major theoretical developments in the field, while focusing on the closed-system setting. The review is organized around a series of topics that are essential to an understanding of the underlying principles of AQC, its algorithmic accomplishments and limitations, and its scope in the more general setting of computational complexity theory. We present several variants of the adiabatic theorem, the cornerstone of AQC, and we give examples of explicit AQC algorithms that exhibit a quantum speedup. We give an overview of several proofs of the universality of AQC and related Hamiltonian quantum complexity theory. We finally devote considerable space to Stoquastic AQC, the setting of most AQC work to date, where we discuss obstructions to success and their possible resolutions.