Minor embedding with Stuart-Landau oscillator networks

TL;DR

This paper introduces a method to simulate dense oscillator networks using minor embedding techniques, enabling the realization of complex quantum-inspired models on sparse, tunable networks suitable for future solid-state implementations.

Contribution

It presents a novel application of minor embedding to simulate all-to-all connected Stuart-Landau oscillator networks, facilitating the study of complex models like the XY model on sparse graphs.

Findings

Enables simulation of XY model on complete graphs

Uses minor embedding to convert dense networks into sparse ones

Potential for implementation in future on-chip technologies

Abstract

We theoretically implement a strategy from quantum computation architectures to simulate Stuart-Landau oscillator dynamics in all-to-all connected networks, also referred to as complete graphs. The technique builds upon the triad structure minor embedding which expands dense graphs of interconnected elements into sparse ones which can potentially be realized in future on-chip solid state technologies with tunable edge weights. As a case study, we reveal that the minor embedding procedure allows simulating the XY model on complete graphs, thus bypassing a severe geometric constraint.