Programmable and reconfigurable photonic simulator for classical XY models

The ability to simulate XY models of classical spins is rather important, since e.g. it is related to solving NP-hard optimization problems. This study uses a photonic simulator to realize XY Hamiltonians with arbitrary spin connections and coupling strengths. The key unit is an optical system for vector-matrix multiplication that can perform arbitrary transformations of complex matrices. The Berezinskii-Kosterlitz-Thouless transition and ground-state search of several XY models are demonstrated experimentally. Thus this Letter provides an effective alternative approach for investigating such models and solving continuous quadratic optimization problems with optical systems.