Quantum annealing in the transverse Ising model

Tadashi Kadowaki, Hidetoshi Nishimori

Research output: Contribution to journalArticlepeer-review

987 Citations (Scopus)


We introduce quantum fluctuations into the simulated annealing process of optimization problems, aiming at faster convergence to the optimal state. Quantum fluctuations cause transitions between states and thus play the same role as thermal fluctuations in the conventional approach. The idea is tested by the transverse Ising model, in which the transverse field is a function of time similar to the temperature in the conventional method. The goal is to find the ground state of the diagonal part of the Hamiltonian with high accuracy as quickly as possible. We have solved the time-dependent Schrödinger equation numerically for small size systems with various exchange interactions. Comparison with the results of the corresponding classical (thermal) method reveals that the quantum annealing leads to the ground state with much larger probability in almost all cases if we use the same annealing schedule.

Original languageEnglish
Pages (from-to)5355-5363
Number of pages9
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Issue number5
Publication statusPublished - 1998
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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