Programmable 200 GOPS Hopfield-inspired photonic Ising machine

Ising machines offer a compelling approach to addressing NP-hard problems, but physical realizations that are simultaneously scalable, reconfigurable, fast, and stable remain elusive. Quantum annealers, like D-Wave's cryogenic hardware, target combinatorial optimization tasks, but quadratic scaling of qubit requirements with problem size limits their scalability on dense graphs. Here, we introduce a programmable, stable, room-temperature optoelectronic oscillator (OEO)-based Ising machine with linear scaling in spin representation. Inspired by Hopfield networks, our architecture solves fully-connected problems with up to 256 spins (65,536 couplings), and $>$41,000 spins (205,000+ couplings) if sparse. Our system leverages cascaded thin-film lithium niobate modulators, a semiconductor optical amplifier, and a digital signal processing (DSP) engine in a recurrent time-encoded loop, demonstrating potential $>$200 giga-operations per second for spin coupling and nonlinearity. This platform achieves the largest spin configuration in an OEO-based photonic Ising machine, enabled by high intrinsic speed. We experimentally demonstrate best-in-class solution quality for Max-Cut problems of arbitrary graph topologies (2,000 and 20,000 spins) among photonic Ising machines and obtain ground-state solutions for number partitioning and lattice protein folding - benchmarks previously unaddressed by photonic systems. Our system leverages inherent noise from high baud rates to escape local minima and accelerate convergence. Finally, we show that embedding DSP - traditionally used in optical communications - within optical computation enhances convergence and solution quality, opening new frontiers in scalable, ultrafast computing for optimization, neuromorphic processing, and analog AI.