Mathematical aspects of quantum annealing

Hidetoshi Nishimori, Satoshi Morita

Research output: Contribution to journalArticlepeer-review


Sufficient conditions for convergence of quantum annealing are derived for optimization problems represented by the Ising model. Three different types of time evolution are considered; the real-time Schrödinger equation, the path-integral Monte Carlo method and the Green's function Monte Carlo method. It is proved that the system under each dynamics reaches the target solution in the limit of infinite time if the transverse field, representing the strength of quantum fluctuations, decreases inversely proportionally to the power of time in the asymptotic region.

Original languageEnglish
Article number012021
JournalJournal of Physics: Conference Series
Issue number1
Publication statusPublished - 2008 Jan 1
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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