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The inability of conventional electronic architectures to efficiently solvelarge combinatorial problems motivates the development of novel computationalhardware. There has been much effort recently toward developing novel,application-specific hardware, across many different fields of engineering,such as integrated circuits, memristors, and photonics. However, unleashing thetrue potential of such novel architectures requires the development of featuredalgorithms which optimally exploit their fundamental properties. We herepresent the Photonic Recurrent Ising Sampler (PRIS), a heuristic methodtailored for parallel architectures that allows for fast and efficient samplingfrom distributions of combinatorially hard Ising problems. Since the PRISrelies essentially on vector-to-fixed matrix multiplications, we suggest theimplementation of the PRIS in photonic parallel networks, which realize theseoperations at an unprecedented speed. The PRIS provides sample solutions to theground state of arbitrary Ising models, by converging in probability to theirassociated Gibbs distribution. By running the PRIS at various noise levels, weprobe the critical behavior of universality classes and their criticalexponents. In addition to the attractive features of photonic networks, thePRIS relies on intrinsic dynamic noise and eigenvalue dropout to find groundstates more efficiently. Our work suggests speedups in heuristic methods viaphotonic implementations of the PRIS. We also hint at a broader class of(meta)heuristic algorithms derived from the PRIS, such as combined simulatedannealing on the noise and eigenvalue dropout levels. Our algorithm can also beimplemented in a competitive manner on fast parallel electronic hardware, suchas FPGAs and ASICs.

Heuristic Recurrent Algorithms for Photonic Ising Machines