Convergence of quantum annealing with real-time Schrödinger dynamics

Satoshi Morita, Hidetoshi Nishimori

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)


Convergence conditions for quantum annealing are derived for optimization problems represented by the Ising model of a general form. Quantum fluctuations are introduced as a transverse field and/or transverse ferromagnetic interactions, and the time evolution follows the real-time Schrödinger equation. It is shown that the system stays arbitrarily close to the instantaneous ground state, finally reaching the target optimal state, if the strength of quantum fluctuations decreases sufficiently slowly, in particular inversely proportionally to the power of time in the asymptotic region. This is the same condition as the other implementations of quantum annealing, quantum Monte Carlo and Green's function Monte Carlo simulations, in spite of the essential difference in the type of dynamics. The method of analysis is an application of the adiabatic theorem in conjunction with an estimate of a lower bound of the energy gap based on the recently proposed idea of Somma et al. for the analysis of classical simulated annealing using a classical-quantum correspondence.

Original languageEnglish
Article number064002
Journaljournal of the physical society of japan
Issue number6
Publication statusPublished - 2007 Jun


  • Adiabatic theorem
  • Annealing schedule
  • Optimization problem
  • Quantum annealing
  • Transverse-field ising model

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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