Convolutional Structure Cuts SPIM Complexity for Dense Problems

Hiroshi Yamashita and Hideyuki Suzuki have proposed a new approach to optimize performance on spatial photonic Ising machines (SPIMs), optical hardware solvers for complex problems. The researchers demonstrate that SPIMs can represent interactions beyond rank-one, clarifying their potential capabilities. They introduce “spatial quadratic unconstrained binary optimization,” or spQUBO, a formulation leveraging spatially convolutional structures that reduces any spQUBO to a two-dimensional version efficiently implementable on SPIMs without multiplexing. The problem size is not directly limited by the number of variables, a characteristic of SPIMs. This advancement promises to broaden the range of solvable problems, including distance-based optimization tasks like placement and clustering, and further our understanding of where SPIMs offer unique computational advantages. The…