Ising machines with strong bilinear coupling

TL;DR

This paper investigates strongly coupled parametric resonator networks, demonstrating their potential as Ising machines and revealing new states and phase transitions relevant for complex optimization tasks.

Contribution

It provides the first experimental and theoretical analysis of strong bilinear coupling in parametrons, expanding understanding of their operation as Ising machines.

Findings

Strong bilinear coupling still allows Ising machine operation.

New mixed symmetry states are generated in the system.

Multiple phase transitions occur in larger networks before reaching the Ising regime.

Abstract

Networks of coupled parametric resonators (parametrons) hold promise for parallel computing architectures. En route to realizing complex networks, we report an experimental and theoretical analysis of two coupled parametrons. In contrast to previous studies, we explore the case of strong bilinear coupling between the parametrons, as well as the role of detuning. We show that the system can still operate as an Ising machine in this regime, even though careful calibration is necessary to ensure that the correct solution space is available. Apart from the formation of split normal modes, new states of mixed symmetry are generated. Furthermore, we predict that systems with $N>2$ parametrons will undergo multiple phase transitions before arriving at a regime that can be equivalent to the Ising problem.