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

TL;DR

This paper demonstrates that coherent Ising machines can simulate quantum phase transitions of the XY model, serving as optical platforms for studying universal quantum critical phenomena and bridging quantum spin models with photonic systems.

Contribution

It establishes an exact spectral mapping between the XY spin model and a network of degenerate optical parametric oscillators, revealing quantum critical behavior in CIMs.

Findings

CIMs reproduce the quantum critical behavior of the XY model.

Second-order QPTs are characterized by singularities in magnetic susceptibility.

CIMs serve as versatile platforms for studying quantum critical phenomena.

Abstract

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.