Accelerating a coherent Ising machine by XY-Ising spin transition

We numerically demonstrate that introducing XY-spin dynamics enabled by phase-insensitive optical parametric gain enhances the performance of coherent Ising machines (CIMs). Whereas conventional CIMs based on phase-sensitive optical parametric gain confine spins to two discrete Ising states, nondegenerate optical parametric oscillators with phase-insensitive gain support continuous-phase XY spins, facilitating spin flips that enable the system to escape local minima. Benchmarking on Wishart-planted problem instances shows that gradually transitioning from XY to Ising spins reduces the time-to-solution by roughly an order of magnitude relative to purely Ising-based dynamics. Furthermore, tailoring the transitions between XY-like and Ising-like regimes yields additional improvements beyond a simple unidirectional XY-to-Ising transition. Our results establish a new framework for engineering CIM dynamics in full phase-quadrature space and point toward fully optical architectures for efficient combinatorial optimization.