Stability Analysis of Photonic Ising Machines

Photonic Ising machines are a promising tool for solving NP-hard optimisation problems, claiming both a smaller time-to-solution and energy consumption than CPUs used today [1]. They are based on the principle that a natural system automatically settles in the lowest energy state. When the cost function of a certain optimisation problem can be mapped to the energy of a natural system, the ground state of that system can be translated to the optimal solution to the problem. This ground state however, is not always reached as the system can get stuck in local minima, resulting in sub-optimal solutions. It turns out that the success rate of finding the optimal solution is heavily dependent on the problem at hand [2]. Understanding why the Ising machine fails to find the ground state for certain problems and how to avoid these difficulties, is essential to increase their efficiency. To tackle these questions, we perform an analytical stability analysis of the fixed points and use it to predict regions in parameter space with higher success rate.