Rapid fair sampling of XY spin Hamiltonian with a laser simulator

TL;DR

This paper demonstrates a rapid and accurate method for fair sampling of the ground state manifold of XY spin Hamiltonians using a laser simulator with multiple longitudinal modes acting in parallel.

Contribution

It introduces a novel approach leveraging multiple laser modes for efficient fair sampling of degenerate ground states in classical spin Hamiltonians.

Findings

Successfully sampled ground states of square, triangular, and Kagome lattices.

Achieved rapid convergence to the minimal energy states.

Demonstrated the method's effectiveness for highly degenerate manifolds.

Abstract

Coupled oscillators such as lasers, OPO's and BEC 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 a 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 identifying manifolds composed of a single, doubly degenerate, and highly degenerate ground states, respectively.