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.