Parallel Solution Search Using a Spatial Photonic Ising Machine Based on Spatial Multiplexing

Solving combinatorial optimization problems is an important task for a broad range of fields including transportation and medical sciences. A spatial photonic Ising machine (SPIM) is an effective way to solve combinatorial optimization problems [1]. By encoding spins that represent the decision variables of a problem into the phase distribution of light, the SPIM enables the calculation of the Ising Hamiltonian obtained from thousands of spins. To solve problems, it is necessary to update a set of spin iteratively based on simulated annealing algorithm. When the number of spins encoding into the SPIM increase, the number of iterations increases rapidly. However, electronic feedback to and switching of a spatial light modulator (SLM) to calculate the Ising Hamiltonian iteratively regulate the processing speed of the SPIM. To reduce the time of the solution-searching process by the SPIM, it is effective to obtain the Ising Hamiltonians simultaneously by using optical parallel processing. In this study, we propose a method of efficient search for optimal solution using the SPIM with parallel processing. The parallel calculation of the multiple Ising Hamiltonians not only reduces the number of the feedback but also updates the set of spins efficiently. To investigate the performance of the proposed method, the number of iterations required to search for optimal solutions are evaluated.