Solving random Ising graphs with nonlinear parametric oscillators

Large networks of parametric oscillators hold the promise to solve a paradigmatic NP-hard problem, namely finding the ground state of frustrated Ising models. Recent theoretical studies and experiments based on linear stability analysis showed that coherent Ising machines necessarily encounters two major obstacles: The system can either be trapped in oscillatory persistent beats, or get stuck in a wrong configuration dictated by the eigenvalues of the coupling matrix. These obstacles make networks of coupled parametric oscillator close to threshold intrinsically not an Ising solver. Here we show that for pump power sufficiently above the threshold the system can find correct Ising solutions. Our study highlights the role of nonlinearities in understanding the dynamics of coupled parametric oscillators and brings hope for their applicability as Ising solvers.