Rapid fair sampling of the XY spin Hamiltonian with a laser simulator

Coupled oscillators such as lasers, optical parametric oscillators, and Bose-Einstein-condensate polaritons can rapidly and efficiently dissipate into a stable phase-locked state that can be mapped onto the minimal energy (ground state) of classical spin Hamiltonians. However, for degenerate or near-degenerate ground-state manifolds, statistical fair sampling is required to obtain complete knowledge of the minimal-energy state, which needs many repetitions of simulations under identical conditions. We show that with dissipatively coupled lasers such fair sampling can be achieved rapidly and accurately by exploiting the many longitudinal modes of each laser to form an ensemble of identical but independent simulators, acting in parallel. We fairly sampled the ground-state manifold of square, triangular, and kagome lattices by measuring their coherence function and identifying manifolds composed of single, doubly degenerate, and highly degenerate ground states, respectively.