Programmable Photonic Simulator for Spin Glass Models

Abstract

Spin glasses featured by frustrated interactions and metastable states have important applications in chemistry, material sciences and artificial neural networks. However, the solution of the spin glass models (SGMs) is hindered by the computational complexity that exponentially increases with the sample size. Spatial photonic Ising machine (SPIM) based on spatial light modulation can speed up the calculation by obtaining the Hamiltonian from the modulated light intensity. A key challenge in such SPIMs is the large-scale generalization to various spin couplings and higher dimensions. Here, a Fourier-mask method is invented and validated to program the spin couplings in SPIMs, which enables to observe the phase transition of various SGMs and study the critical phenomena with unprecedented sample size. It is also demonstrated that the 3D Ising model, which has not been analytically solved, can be effectively constructed and simulated in 2D Fourier-mask SPIM. This strategy provides a flexible route to tuning couplings and dimensions of statistical spin models, and improves the applicability of SPIMs in neural networks and combinatorial optimization problems.