Simulated bifurcation assisted by thermal fluctuation

TL;DR

This paper introduces heated simulated bifurcation, incorporating thermal fluctuations via the Nosé-Hoover method, to enhance the performance of Ising machines in solving large combinatorial optimization problems.

Contribution

The paper proposes a novel heated simulated bifurcation method using thermal fluctuations to improve the escape from local minima in Ising problem solving.

Findings

Performance improved in large-scale Ising problems with up to 2000 spins.

Thermal fluctuations help escape local minima, enhancing solution quality.

Parallel processing can accelerate the proposed method.

Abstract

Various kinds of Ising machines based on unconventional computing have recently been developed for practically important combinatorial optimization. Among them, the machines implementing a heuristic algorithm called simulated bifurcation have achieved high performance, where Hamiltonian dynamics are simulated by massively parallel processing. To further improve the performance of simulated bifurcation, here we introduce thermal fluctuation to its dynamics relying on the Nos\'e-Hoover method, which has been used to simulate Hamiltonian dynamics at finite temperatures. We find that a heating process in the Nos\'e-Hoover method can assist simulated bifurcation to escape from local minima of the Ising problem, and hence lead to improved performance. We thus propose heated simulated bifurcation and demonstrate its performance improvement by numerically solving instances of the Ising problem with up to 2000 spin variables and all-to-all connectivity. Proposed heated simulated bifurcation is expected to be accelerated by parallel processing.