Optical resonators constitute a universal spin simulator

NP-hard computational problems can be efficiently recast as finding the ground state of an effective spin model. However, to date no convenient setup exists that can universally simulate all of them, even for a fixed problem size. Here we present such a setup, the universal homogeneous spin simularor (UHSS) using a series of optical (or polaritonic) resonators arranged in a chain using the geometry based on the one introduced in [Phys. Rev. Applied 21, 024057 (2024), arXiv:2306.0574(3) ]. We demonstrate by example how the simulator solves Hamiltonian Cycle and traveling salesman problems, and show that it generalises to any NP-hard problem of arbitrary size. This approach works because it allows arbitrary long-range interactions in the spin model to be mapped on an optical system with only nearest-neighbor physical interactions.