Adiabatic Quantum Computing

By Tameem Albash, Daniel A. Lidar. Mathematics of Quantum Computing, 2016

404 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/f4bc4c8763f1ebefbbec2fdcbe0df0eb7c3cf55e

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Citations in the corpus

Quantum Approximate Optimization Algorithm: Performance, Mechanism, and Implementation on Near-Term Devices (2018, methodology): “If T is much longer than 1/∆min, where ∆min is the minimum spectral gap, quantum annealing will be able to find the exact solution to MaxCut (ground state of−HC) by the adiabatic theorem [17], and achieve exponentially small fractional error as predicted by Landau-Zener [38].”
Quantum Chemistry in the Age of Quantum Computing. (2018, methodology): “, U(k) MG = Y i2odd G(k) i;i+1 Y i2even G(k) i;i+1: (59) There are N 2 cycles in total, i.e. UNN MG = dM Y2 e k=1 U(k) MG; (60) such that the transformation Wcan be composed as W= UNN MG YM i=1 RZ i: (61) Dallaire-Demers et al.326 suggest that a similar circuit template could be used to create a var”
Shortcuts to adiabaticity: Concepts, methods, and applications (2019, methodology): “There are many works applying the local adiabatic method in the context of adiabatic quantum computation (Albash and Lidar, 2018).”
Combinatorial optimization by simulating adiabatic bifurcations in nonlinear Hamiltonian systems (2019, methodology): “…machines have been developed by various approaches: quantum computers based on quantum annealing ( 8 , 9 ) or quantum adiabatic optimization ( 10 – 12 ) implemented with superconducting circuits ( 13 , 14 ), coherent Ising machines (CIMs) implemented with laser pulses ( 15 – 20 ), and Ising…”
Harnessing the Power of the Second Quantum Revolution (2020, background): “Other continuous-time and thus formally analog models include adiabatic quantum computing [85,101], quantum annealing [102], and Hamiltonian quantum walks [103].”