  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.
