Swinging in Resonance: Using Quantum Oscillator Networks to Solve Complex Optimization Problems

Abstract

Combinatorial optimization is fundamental to modern society, where finding fast and efficient solutions to complex resource-allocation problems is critical for sustainability and economic resilience. As classical von Neumann architectures approach their scaling limits, it is time to explore alternative computational paradigms for NP-hard combinatorial optimization, such as utilizing networks of coupled quantum oscillators as Ising machines. To this aim we map complex optimization landscapes onto the energy states of a physical system, exploiting nonlinear dynamics and controlled potential deformation to trigger phase transitions toward a global minimum.

Our approach employs the Simulated Bifurcation (SB) algorithm to perform these calculations, providing a robust framework for tackling benchmark informatics challenges such as the Max-Cut problem and community detection through the maximization of k-modularity (Newman, 2006). Remarkably, our implementation achieves milestone results on mid-sized problems using standard laptop hardware—matching or even exceeding the performance of current gate-based quantum computers and specialized hardware accelerators. Within the QONOMICS project, we aim to bridge the gap between quantum dynamics and the frontier of optimization and machine learning.