A convolutional perspective on solving optimization problems with light
Hiroshi Yamashita and Hideyuki Suzuki, “Convolutional formulation of large-scale quadratic unconstrained binary optimization with dense interactions,” Communications Physics 9, 246 (2026).
To use light for combinatorial optimization, we need to express a problem in a form that an optical system can handle. This study focuses on problems in which many variables interact according to a shared rule based on their relative spatial positions.
By expressing this rule as a convolution, we formulated spatial QUBO (spQUBO) as a class of quadratic unconstrained binary optimization (QUBO) problems. We also showed how to transform higher-dimensional, non-periodic problems into two-dimensional periodic systems while preserving their convolutional structure, clarifying their correspondence with spatial photonic Ising machines. Numerical examples of facility location and clustering illustrate applications of the formulation. Together, these results provide a mathematical framework for considering which optimization problems can be represented in optical systems.
