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arXiv:2406.00792 · Physical Review Applied

Qudit-inspired optimization for graph coloring

David Jansen, Timothy Heightman, Luke Mortimer, Ignacio Perito, Antonio Acín

Published Dec 2, 2024• 8 citations
arXivHTMLPDF

Abstract

We introduce a quantum-inspired algorithm for graph coloring problems (GCPs) that utilizes qudits in a product state, with each qudit representing a node in the graph and parameterized by $d$-dimensional spherical coordinates. We propose and benchmark two optimization strategies: qudit gradient descent, initiating qudits in random states and employing gradient descent to minimize a cost function; and qudit local quantum annealing, which adapts the local quantum annealing method to optimize an adiabatic transition from a tractable initial function to a problem-specific cost function. Our approaches are benchmarked against established solutions for standard GCPs, showing that our methods not only rival but frequently surpass the performance of recent state-of-the-art algorithms in terms of solution quality and computational efficiency. The adaptability of our algorithm and its high-quality solutions, achieved with minimal computational resources, point to an advancement in the field of quantum-inspired optimization, with potential applications extending to a broad spectrum of optimization problems.

DOI
10.1103/physrevapplied.22.064002

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