Simulated bifurcation assisted by thermal fluctuation

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.