The parametric instability landscape of coupled Kerr parametric oscillators

TL;DR

This paper maps the stability and bifurcation structure of coupled Kerr parametric oscillators, revealing conditions for Ising-like solutions and guiding experimental realization of neuromorphic and quantum computing networks.

Contribution

It provides an analytical framework for understanding bifurcations in KPO networks and identifies regimes with Ising model mappings, extending from two oscillators to large networks.

Findings

Bifurcation structures arise from competition between drive and coupling.

Analytical expressions for bifurcations in all-to-all coupled networks.

Uniformly spaced bifurcation transitions in the thermodynamic limit.

Abstract

Networks of coupled Kerr parametric oscillators (KPOs) hold promise as for the realization of neuromorphic and quantum computation. Yet, their rich bifurcation structure remains largely not understood. Here, we employ secular perturbation theory to map the stability regions of these networks, and identify the regime where the system can be mapped to an Ising model. Starting with two coupled KPOs, we show how the bifurcations arise from the competition between the global parametric drive and linear coupling between the KPOs. We then extend this framework to larger networks with all-to-all equal coupling, deriving analytical expressions for the full cascade of bifurcation transitions. In the thermodynamic limit, we find that these transitions become uniformly spaced, leading to a highly regular structure. Our results reveal the precise bounds under which KPO networks have an Ising-like solution space, and thus provides crucial guidance for their experimental implementation.