Global Optimization Through Heterogeneous Oscillator Ising Machines

TL;DR

This paper demonstrates that introducing heterogeneity in oscillator Ising machines enhances their ability to reliably find global minima in complex optimization problems by leveraging spectral graph properties.

Contribution

It provides a theoretical analysis linking stability to spectral properties and shows that heterogeneity improves convergence to global optima in OIMs.

Findings

Heterogeneity increases the likelihood of stability in low-energy states.

Spectral analysis explains the stability and convergence behavior.

Numerical results confirm improved global optimization performance.

Abstract

Oscillator Ising machines (OIMs) are networks of coupled oscillators that seek the minimum energy state of an Ising model. Since many NP-hard problems are equivalent to the minimization of an Ising Hamiltonian, OIMs have emerged as a promising computing paradigm for solving complex optimization problems that are intractable on existing digital computers. However, their performance is sensitive to the choice of tunable parameters, and convergence guarantees are mostly lacking. Here, we show that lower energy states are more likely to be stable, and that convergence to the global minimizer is often improved by introducing random heterogeneities in the regularization parameters. Our analysis relates the stability properties of Ising configurations to the spectral properties of a signed graph Laplacian. By examining the spectra of random ensembles of these graphs, we show that the probability of an equilibrium being asymptotically stable depends inversely on the value of the Ising Hamiltonian, biasing the system toward low-energy states. Our numerical results confirm our findings and demonstrate that heterogeneously designed OIMs efficiently converge to globally optimal solutions with high probability.