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 $T_c$ and the critical probability $p_c$ 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.

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• 20736-node Weighted Max-Cut Problem Solving by Quadrature Photonic Spatial Ising Machine
• Universal classical optical computing inspired by quantum information process
• An optical Ising spin glass simulator with tuneable short range couplings
• Spin Hamiltonians in the Modulated Momenta of Light
• A Programmable and Reconfigurable Photonic Simulator for Classical XY Models
• Singular transport in non-equilibrium strongly internal-coupled 1D tilted field spin-1/2 chain
• Dense Associative Memory in a Nonlinear Optical Hopfield Neural Network
• Spatial Optical Simulator for Classical Statistical Models
• A spatial-photonic Ising machine to solve the two-way number-partitioning problem