2006/08/21 by Satoshi Morita, Hidetoshi Nishimori
Computer Science · Mathematics · Physics and Astronomy · #Applied mathematics #Ergodicity #Inverse #Ising model #Markov Chains and Monte Carlo Methods #Mathematical optimization #Mathematics #Monte Carlo method #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Monte Carlo #Quantum annealing #Quantum computer #Quantum many-body systems #Quantum mechanics #Simulated annealing #Statistical physics #cond-mat.dis-nn #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.1088/0305-4470/39/45/004
published as J. Phys. A: Math. Gen. 39 (2006) 13903 · 19 pages
arxiv created 2006/08/21 · openalex publication_date 2006/10/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We prove several theorems to give sufficient conditions for convergence of quantum annealing, which is a protocol to solve generic optimization problems by quantum dynamics. In particular the property of strong ergodicity is proved for the path-integral Monte Carlo implementation of quantum annealing for the transverse Ising model under a power decay of the transverse field. This result is to be compared with the much slower inverse-log decay of temperature in the conventional simulated annealing. Similar results are proved for the Green's function Monte Carlo approach. Optimization problems in continuous space of particle configurations are also discussed.