A Kerr soliton Ising machine for combinatorial optimization problems

The growing challenges of scaling digital computing motivate new approaches, especially through the dynamical evolution of physical systems that mimic neural networks and combinatorial optimization problems. While light is a hyper efficient information carrier, intrinsically weak light interactions make direct information processing difficult to implement. Recently, specialized nonlinear photonics have opened new controls over light fields with extraordinary bandwidth, coherence, and the emergence of strong interactions among nonlinear eigenstates like solitons. We harness an ensemble of hundreds of Kerr-nonlinear 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. Using this palette of interactions amongst the entire soliton ensemble, we encode the Ising machine to solve the benchmark 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. Indeed, the soliton properties bound the tradeoff of optical power and time use by the machine at approximately 10 mW and 1 $\mu$s 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, which can be combined for a wide range of computation-acceleration tasks.