Abstract
AbstractIn recent years, there has been a growing interest in optical simulation of lattice spin models for applications in unconventional 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 2π/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.
Highlights
Combinatorial optimization deals with minimizing a cost function over a finite and discrete set of objects
It is of great interest to develop novel physical systems that allow for compact embeddings of the cost function of certain optimization problems
We numerically explore the performance of the proposed Potts machine for solving important combinatorial optimization problems such as maximum three-cut (MAX 3-CUT) and graph three-coloring (3-COL)
Summary
Combinatorial optimization deals with minimizing (maximizing) a cost function over a finite and discrete set of objects. It is of great interest to develop novel physical systems that allow for compact embeddings of the cost function of certain optimization problems In this regard, as a generalization of the Ising model, the Potts model is an interesting candidate [18, 19]. The onset of 3PDC oscillations is accompanied with phase tristability of the subharmonic signal By coupling a network of such 3PDC oscillators, one can create a three-state Potts machine as depicted schematically in Figure 1D and E for a two-spin network. We numerically explore the performance of the proposed Potts machine for solving important combinatorial optimization problems such as maximum three-cut (MAX 3-CUT) and graph three-coloring (3-COL)
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