Experimental Observation of Phase Transitions in Spatial Photonic Ising Machine
Abstract
Statistical spin dynamics plays a key role to understand the working principle for novel optical Ising machines. Here we propose the gauge transformations for spatial photonic Ising machine, where a single spatial phase modulator simultaneously encodes spin configurations and programs interaction strengths. Thanks to gauge transformation, we experimentally evaluate the phase diagram of high-dimensional spin-glass equilibrium system with 100 fully-connected spins. We observe the presence of paramagnetic, ferromagnetic as well as spin-glass phases and determine the critical temperature Tc and the critical probability pc of phase transitions, which agree well with the mean-field theory predictions. Thus the approximation of the mean-field model is experimentally validated in the spatial photonic Ising machine. Furthermore, we discuss the phase transition in parallel with solving combinatorial optimization problems during the cooling process and identify that the spatial photonic Ising machine is robust with sufficient many-spin interactions, even when the system is associated with the optical aberrations and the measurement uncertainty.