Guiding Principle for Minor-Embedding in Simulated-Annealing-Based Ising Machines

Tatsuhiko Shirai, Shu Tanaka, Nozomu Togawa

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


We propose a novel type of minor-embedding (ME) in simulated-annealing-based Ising machines. The Ising machines can solve combinatorial optimization problems. Many combinatorial optimization problems are mapped to find the ground (lowest-energy) state of the logical Ising model. When connectivity is restricted on Ising machines, ME is required for mapping from the logical Ising model to a physical Ising model, which corresponds to a specific Ising machine. Herein we discuss the guiding principle of ME design to achieve a high performance in Ising machines. We derive the proposed ME based on a theoretical argument of statistical mechanics. The performance of the proposed ME is compared with two existing types of MEs for different benchmarking problems. Simulated annealing shows that the proposed ME outperforms existing MEs for all benchmarking problems, especially when the distribution of the degree in a logical Ising model has a large standard deviation. This study validates the guiding principle of using statistical mechanics for ME to realize fast and high-precision solvers for combinatorial optimization problems.

Original languageEnglish
Article number9268172
Pages (from-to)210490-210502
Number of pages13
JournalIEEE Access
Publication statusPublished - 2020


  • Annealing machine
  • Ising model
  • graph minor-embedding
  • optimization method
  • simulated annealing
  • statistical mechanics

ASJC Scopus subject areas

  • General Computer Science
  • General Materials Science
  • General Engineering


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