Numerical Modeling of Integrated Coherent Ising Machine Using Spatially Multiplexed Silicon Nitride Microresonators

Abstract

In this paper, we present mathematical modeling and numerical analysis of an integrated coherent Ising machine (CIM) consisting of a network of coupled add-drop microring resonators. The proposed CIM exploits dual-pumped degenerate optical parametric oscillators (DOPOs) in silicon nitride (SiN), as a CMOS-compatible material, combined with all-optical reconfigurable spatial multiplexing. This approach benefits from the potential of on-chip all-optic computing to solve large-scale NP-hard computational problems, paving the way for a scalable and programmable photonic-based CIMs. We provide design considerations for the optimal phase-sensitive parametric amplifiers by using SiN-based DOPOs to implement a photonic Ising spin as the fundamental building block for CIMs. The binary coherent states of each spin can be optimized by controlling the power of both pumps and their detunings. We also explore the parameter space of optical coupler structures to realize ferromagnetic and antimagnetic coupling between DOPOs, which is required for mapping quadratic unconstrained binary optimization problems (QUBO) to the integrated Ising machine composed of a network of coupled DOPOs. Furthermore, the balanced and unbalanced coupling scenarios between spins are compared for improving spin-state homogeneity. Finally, the time evolution of sixteen coupled microresonators during ground-state search has been investigated as a proof-of-concept under different coupling schemes.