Simulated bifurcation for higher-order cost functions

TL;DR

This paper extends the simulated bifurcation algorithm to handle higher-order cost functions, demonstrating its effectiveness and potential advantages over existing methods for complex combinatorial optimization problems.

Contribution

The authors develop a higher-order simulated bifurcation method and show it outperforms second-order SB and simulated annealing on third-order cost functions.

Findings

Higher-order SB outperforms second-order SB with additional spins

Higher-order SB surpasses simulated annealing on third-order problems

Results suggest practical usefulness of higher-order SB

Abstract

High-performance Ising machines for solving combinatorial optimization problems have been developed with digital processors implementing heuristic algorithms such as simulated bifurcation (SB). Although Ising machines have been designed for second-order cost functions, there are practical problems expressed naturally by higher-order cost functions. In this work, we extend SB to such higher-order cost functions. By solving a problem having third-order cost functions, we show that the higher-order SB can outperform not only the second-order SB with additional spin variables, but also simulated annealing applied directly to the third-order cost functions. This result suggests that the higher-order SB can be practically useful.