Fast-Converging Simulated Annealing for Ising Models Based on Integral Stochastic Computing

Naoya Onizawa, Kota Katsuki, Duckgyu Shin, Warren J. Gross, Takahiro Hanyu

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


Probabilistic bits (p-bits) have recently been presented as a spin (basic computing element) for the simulated annealing (SA) of Ising models. In this brief, we introduce fast-converging SA based on p-bits designed using integral stochastic computing. The stochastic implementation approximates a p-bit function, which can search for a solution to a combinatorial optimization problem at lower energy than conventional p-bits. Searching around the global minimum energy can increase the probability of finding a solution. The proposed stochastic computing-based SA method is compared with conventional SA and quantum annealing (QA) with a D-Wave Two quantum annealer on the traveling salesman, maximum cut (MAX-CUT), and graph isomorphism (GI) problems. The proposed method achieves a convergence speed a few orders of magnitude faster while dealing with an order of magnitude larger number of spins than the other methods.

Original languageEnglish
JournalIEEE Transactions on Neural Networks and Learning Systems
Publication statusAccepted/In press - 2022


  • Combinatorial optimization
  • Computational modeling
  • Convergence
  • graph isomorphism (GI) problem
  • Hamiltonian
  • Integrated circuit modeling
  • Ising model
  • Optimization
  • Probabilistic logic
  • quantum annealing (QA)
  • simulated annealing (SA)
  • stochastic computing
  • Stochastic processes
  • traveling salesman problem (TSP).
  • Urban areas

ASJC Scopus subject areas

  • Software
  • Computer Science Applications
  • Computer Networks and Communications
  • Artificial Intelligence


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