Adiabatic approximation for the imaginary-time Schrödinger equation and its application to simulated annealing

Kazuya Kaneko, Hidetoshi Nishimori

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

We formulate an adiabatic approximation for the imaginary-time Schrödinger equation. The obtained adiabatic condition consists of two inequalities, one of which coincides with the conventional adiabatic condition for the real-time Schrödinger equation, but the other does not. We apply this adiabatic approximation to the analysis of Markovian dynamics of the classical Ising model, which can be formulated as the imaginary-time Schrödinger equation, to obtain an asymptotic formula for the probability that the system reaches the ground state in the limit of a long annealing time in simulated annealing. Using this form, we amend the theory of Somma, Batista, and Ortiz for a convergence condition for simulated annealing.

Original languageEnglish
Article number094001
Journaljournal of the physical society of japan
Volume84
Issue number9
DOIs
Publication statusPublished - 2015 Sep 15

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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