Boltzmann sampling for an XY model using a non-degenerate optical parametric oscillator network

摘要

We present an experimental scheme of implementing multiple spins in aclassical XY model using a non-degenerate optical parametric oscillator (NOPO)network. We built an NOPO network to simulate a one-dimensional XY Hamiltonianwith 5000 spins and externally controllable effective temperatures. The XY spinvariables in our scheme are mapped onto the phases of multiple NOPO pulses in asingle ring cavity and interactions between XY spins are implemented by mutualinjections between NOPOs. We show the steady-state distribution of opticalphases of such NOPO pulses is equivalent to the Boltzmann distribution of thecorresponding XY model. Estimated effective temperatures converged to thesetting values, and the estimated temperatures and the mean energy exhibitedgood agreement with the numerical simulations of the Langevin dynamics of NOPOphases.