Quantum and classical physics can be used for mathematical computations that
are hard to tackle by conventional electronics. Very recently, optical Ising
machines have been demonstrated for computing the minima of spin Hamiltonians,
paving the way to new ultra-fast hardware for machine learning. However, the
proposed systems are either tricky to scale or involve a limited number of
spins. We design and experimentally demonstrate a large-scale optical Ising
machine based on a simple setup with a spatial light modulator. By encoding the
spin variables in a binary phase modulation of the field, we show that light
propagation can be tailored to minimize an Ising Hamiltonian with spin
couplings set by input amplitude modulation and a feedback scheme. We realize
configurations with thousands of spins that settle in the ground state in a
low-temperature ferromagnetic-like phase with all-to-all and tunable pairwise
interactions. Our results open the route to classical and quantum photonic
Ising machines that exploit light spatial degrees of freedom for parallel
processing of a vast number of spins with programmable couplings.Comment: https://journals.aps.org/prl/accepted/7007eYb7N091546c41ad4108828a97d5f92006df
