Complex Vector Gain-Based Annealer for Minimizing XY Hamiltonians

TL;DR

The paper introduces CoVeGA, an analog computing platform that uses higher-dimensional representations to effectively minimize XY Hamiltonians by overcoming energy barriers and avoiding local minima.

Contribution

CoVeGA employs two complex fields per XY spin and dynamic annealing to improve energy landscape navigation over traditional single-field solvers.

Findings

CoVeGA outperforms single-dimension XY solvers on challenging graph structures.

Higher-dimensional representation helps in overcoming energy barriers.

Benchmark results demonstrate improved minimization success rates.

Abstract

This paper presents the Complex Vector Gain-Based Annealer (CoVeGA), an analog computing platform designed to overcome energy barriers in XY Hamiltonians through a higher-dimensional representation. Traditional gain-based solvers utilizing optical or photonic hardware typically represent each XY spin with a single complex field. These solvers often struggle with large energy barriers in complex landscapes, leading to relaxation into excited states. CoVeGA addresses these limitations by employing two complex fields to represent each XY spin and dynamically evolving the energy landscape through time-dependent annealing. Operating in a higher-dimensional space, CoVeGA bridges energy barriers in this expanded space during the continuous phase evolution, thus avoiding entrapment in local minima. We introduce several graph structures that pose challenges for XY minimization and use them to benchmark CoVeGA against single-dimension XY solvers, highlighting the benefits of higher-dimensional operation.