Temporal Simulations of a Network of Degenerate Optical Parametric Oscillators for Solving Combinational Optimization Problems

We numerically investigate a network of coupled dual-pumped degenerate optical parametric oscillators (DOPOs) with 16 spins built by Kerr microresonators for on-chip coherent Ising machines (CIMs). As a first step, the optical parametric gain in a phase-sensitive amplifier above the oscillation threshold in the silicon nitride cavity is optimized. We aim to emulate a spin glass represented by the bi-phase states with a pi offset during the phase bifurcation of DOPOs. As a result, we achieve the extinction ratio of the phase-sensitive gain over 30 dB with pump power as 10 dBm and detuning as 302 MHz. Besides, the spatially multiplexed spins are then simulated to search for the ground state of the hexadecagon system mapping to feedback. We also study the time evolution of spins. To this end, with three different levels of initial magnetizations, we have obtained an annealing time of up to 45 ns for anti-ferromagnetic and a time of up to 80 ns for ferromagnetic coupling. Notably, the dynamic behavior of the integrated Ising spins for searching minimal Hamiltonian is investigated.