Ground-state statistics from annealing algorithms: Quantum versus classical approaches

Yoshiki Matsuda, Hidetoshi Nishimori, Helmut G. Katzgraber

Research output: Contribution to journalArticlepeer-review

44 Citations (Scopus)


We study the performance of quantum annealing for systems with ground-state degeneracy by directly solving the Schrödinger equation for small systems and quantum Monte Carlo simulations for larger systems. The results indicate that naive quantum annealing using a transverse field may not be well suited to identify all degenerate ground-state configurations, although the value of the ground-state energy is often efficiently estimated. An introduction of quantum transitions to all states with equal weights is shown to greatly improve the situation, but with a sacrifice in annealing time. We also clarify the relation between the spin configurations in degenerate ground states and the probabilities that those states are obtained by quantum annealing. The strengths and weaknesses of quantum annealing for problems with degenerate ground states are discussed in comparison with classical simulated annealing.

Original languageEnglish
Article number073021
JournalNew Journal of Physics
Publication statusPublished - 2009 Jul 9
Externally publishedYes

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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