Observing a Phase Transition in a Coherent Ising Machine

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Abstract
The coherent Ising machine (CIM) is known to provide the low-energy states of the Ising model. Here, we investigate how well the CIM simulates the thermodynamic properties of a two-dimensional square-lattice Ising model. Assuming that the spin sets sampled by the CIM can be regarded as a canonical ensemble, we estimate the effective temperature of spins represented by degenerate optical parametric oscillator pulses by using maximum likelihood estimation. With the temperature obtained, we confirm that the thermodynamic quantities obtained with the CIM exhibit phase-transition-like behavior that matches the analytical and numerical results better than the mean field approximation does.

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