Quantum Phase Transitions in Coherent Ising Machines: XY Model for Demonstration

Quantum phase transitions (QPTs) in coherent Ising machines (CIMs) are studied via a spectral mapping between the one-dimensional XY spin model and a network of degenerate optical parametric oscillators (DOPOs). This exact correspondence reveals that the DOPO network faithfully reproduces the quantum critical behavior of the XY model across its anisotropic, isotropic, and transverse-field Ising regimes. The ground-state energy density and its derivatives are analyzed to reveal second-order QPTs characterized by singularities in magnetic susceptibility at critical points. These results show that CIMs do not only serve as powerful platforms for solving combinatorial optimization problems but also provide a versatile optical simulator for studying universal quantum critical phenomena, bridging quantum-spin models and photonic quantum systems.