Optical resonators constitute a universal spin simulator

TL;DR

The paper introduces a universal optical resonator-based spin simulator capable of efficiently solving NP-hard problems like Hamiltonian Cycle and Traveling Salesman, by mapping long-range interactions onto a chain with only nearest-neighbor interactions.

Contribution

It presents the first universal optical (or polaritonic) spin simulator that can handle all NP-hard problems of arbitrary size using a chain of resonators.

Findings

Successfully demonstrates solving Hamiltonian Cycle and Traveling Salesman problems.

Shows generalization to any NP-hard problem of arbitrary size.

Maps long-range interactions onto a nearest-neighbor optical system.

Abstract

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.