2008/06/11 by Satoshi Morita, Hidetoshi Nishimori · 3 citations
Computer Science · Mathematics · Physics and Astronomy · #Adiabatic process #Adiabatic quantum computation #Applied mathematics #Mathematical optimization #Mathematics #Neural Networks and Reservoir Computing #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum algorithm #Quantum annealing #Quantum computer #Quantum dynamics #Quantum mechanics #Quantum operation #Quantum process #Statistical physics #cond-mat.dis-nn #quant-ph
paper · pdf · doi:10.1063/1.2995837
51pages, 8 figures
arxiv created 2008/06/11 · openalex publication_date 2008/12/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Quantum annealing is a generic name of quantum algorithms that use quantum-mechanical fluctuations to search for the solution of an optimization problem. It shares the basic idea with quantum adiabatic evolution studied actively in quantum computation. The present paper reviews the mathematical and theoretical foundations of quantum annealing. In particular, theorems are presented for convergence conditions of quantum annealing to the target optimal state after an infinite-time evolution following the Schrödinger or stochastic (Monte Carlo) dynamics. It is proved that the same asymptotic behavior of the control parameter guarantees convergence for both the Schrödinger dynamics and the stochastic dynamics in spite of the essential difference of these two types of dynamics. Also described are the prescriptions to reduce errors in the final approximate solution obtained after a long but finite dynamical evolution of quantum annealing. It is shown there that we can reduce errors significantly by an ingenious choice of annealing schedule (time dependence of the control parameter) without compromising computational complexity qualitatively. A review is given on the derivation of the convergence condition for classical simulated annealing from the view point of quantum adiabaticity using a classical-quantum mapping.