# Adiabatic Quantum Computing. (arXiv:1611.04471v2 [quant-ph] UPDATED)

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.