Improving photonic Ising machines by way of a stability analysis of steady states

With increasing computational demands, the importance of efficient computer architectures rises. Photonic Ising machines offer a promising approach to address complex binary optimization problems by leveraging the speed and bandwidth inherent in photonic systems. When the cost function of an optimization problem can be mapped to the energy of an Ising problem, the ground state of the latter will represent the optimal solution. We conduct a stability analysis on this ground state of various benchmark problems. This analysis reveals that some benchmark problems are manageable for all Ising machine implementations. However, there are other problems for which the probability of achieving the ground state depends on the physical implementation. Our analysis shows the reasons for this advantage, leading us to formulate strategies to further enhance Ising machines and pave the way for future research. In future work, we will investigate if photonic Ising machines utilizing a different nonlinearity possess a distinct advantage in this context.