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.

References in corpus (29)

• Deep Learning with Coherent Nanophotonic Circuits
• Ising formulations of many NP problems
• Quantum annealing with more than one hundred qubits
• Network of Time-Multiplexed Optical Parametric Oscillators as a Coherent Ising Machine
• A Coherent Ising Machine Based On Degenerate Optical Parametric Oscillators
• Generalized spatial differentiation from spin Hall effect of light
• Large-scale photonic Ising machine by spatial light modulation
• Engineering Ising-XY spin models in a triangular lattice via tunable artificial gauge fields
• Realizing the $XY$ Hamiltonian in polariton simulators
• Observation of topological phenomena in a programmable lattice of 1,800 qubits
• A Photonic Crystal Slab Laplace Differentiator
• Large-scale Ising spin network based on degenerate optical parametric oscillators
• Phase Transition in the Number Partitioning Problem
• Analog computing by Brewster effect
• Heuristic Recurrent Algorithms for Photonic Ising Machines
• Nanophotonic spin-glass for realization of a coherent Ising machine
• Optical phase mining by adjustable spatial differentiator
• Noise-enhanced spatial-photonic Ising machine
• Phase diagram and complexity of mode-locked lasers: from order to disorder
• Persistent coherent beating in coupled parametric oscillators
• Scalable spin-glass optical simulator
• Simulating Ising and Potts models and external fields with non-equilibrium condensates
• Rapid Phase Retrieval by Lasing
• Large-scale Ising Emulation with Four-Body Interaction and All-to-All Connection
• Realizing spin-Hamiltonians in nanoscale active photonic lattices
• Theory of coupled parametric oscillators beyond coupled Ising spins
• Controllable Josephson junction for photon Bose-Einstein condensates
• Optical computation of a spin glass dynamics with tunable complexity
• Mapping the XY Hamiltonian onto a Network of Coupled Lasers

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