A Programmable and Reconfigurable Photonic Simulator for Classical XY Models

The classical spin models attracts growing interests since many optimization problems can be mapped to searching the ground states of these models. However, solving such problems on conventional computers requires exponentially growing resources. In this work, we proposed and experimentally demonstrated a photonic simulator for classical XY models. By encoding the XY spins on the phase term of the input light field, the corresponding XY Hamiltonian could be performed on the output light intensities. The simulator is mainly based on a programmable and reconfigurable optical vector-matrix multiplication system, which can map arbitrary XY models within the dimensionality limit. We first demonstrate the Berezinskii-Kosterlitz-Thouless transition in a two-dimensional XY model, in which the expectation values of some observables are calculated and consistent with the theory. Besides, we performed the ground state search of two 25-spin XY models with different spin connections and coupling strengths. Our proposal paves a new way to investigate the XY spin system.