Combinatorial optimization with Kerr solitons.

The challenge of scaling digital computing motivates innovation, especially through the evolution of physical systems that mimic neural networks and combinatorial optimization problems. Light is a hyperefficient information carrier, and if efficient interactions with it could be uncovered, then direct information processing would become far more feasible. We harness an ensemble of hundreds of Kerr microresonator solitons and implement an analog feedback network to create an Ising machine with fully programmable all-to-all interactions. By increasing the feedback for self, on-diagonal interactions, each soliton exhibits a universal spin-like bifurcation, and using this palette of interactions, we solve the canonical Boolean satisfiability problem (SAT). The combination of uniform soliton interactions and the compatibility of our Ising machine with high-speed data interconnects enables rapid and precise solutions of complex SAT problems. The well-established theoretical properties of Kerr solitons bound the trade-off of optical power and time use by the machine at ~0.15 milliwatts per soliton and 1 microsecond for a single feedback step. We performed >10,000 trials on more than 100 randomly generated SAT instances to evaluate the Ising machine, demonstrating the potential to exceed the performance of benchmark digital SAT solvers. Our work highlights the convergence of optical nonlinearity, ultralow loss photonics, and optoelectronic circuits for computation-acceleration tasks.