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In recent years there has been a growing interest in optical simulation of lattice spin models for applications in classical computing. Here, we propose optical implementation of a three-state Potts spin model by using networks of coupled parametric oscillators with phase tristability. We first show that the cubic nonlinear process of spontaneous three-photon down-conversion is accompanied by a tristability in the phase of the subharmonic signal between three states with 2��/3 phase contrast. The phase of such a parametric oscillator behaves like a three-state spin system. Next, we show that a network of dissipatively coupled three-photon down-conversion oscillators emulates the three-state planar Potts model. We discuss potential applications of the proposed system for all-optical optimization of combinatorial problems such as graph 3-COL and MAX-3-CUT.


Originally published as: Honari-Latifpour, Mostafa and Mohammad-Ali Miri. "Optical Potts Machine through Networks of Three-Photon Down-Conversion Oscillators." Nanophotonics, 2020,

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