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A network of optical parametric oscillators is used to simulate classicalIsing and XY spin chains. The collective nonlinear dynamics of this network,driven by quantum noise rather than thermal fluctuations, seeks out the Ising /XY ground state as the system transitions from below to above the lasingthreshold. We study the behavior of this "Ising machine" for three canonicalproblems: a 1D ferromagnetic spin chain, a 2D square lattice, and problemswhere next-nearest-neighbor couplings give rise to frustration. If the pumpturn-on time is finite, topological defects form (domain walls for the Isingmodel, winding number and vortices for XY) and their density can be predictedfrom a numerical model involving a linear "growth stage" and a nonlinear"saturation stage". These predictions are compared against recent data for a10,000-spin 1D Ising machine.

Topological defect formation in 1D and 2D spin chains realized by network of optical parametric oscillators