Qudit-inspired optimization for graph coloring
David Jansen, Timothy Heightman, Luke Mortimer, Ignacio Perito, and, Antonio Ac\'in

TL;DR
This paper presents a quantum-inspired algorithm using qudits for graph coloring, employing gradient descent and quantum annealing strategies that outperform some existing methods in solution quality and efficiency.
Contribution
It introduces a novel qudit-based optimization approach for graph coloring, combining gradient descent and quantum annealing techniques with benchmarking results.
Findings
Our methods often outperform state-of-the-art algorithms.
The algorithms achieve high-quality solutions with minimal resources.
Benchmarking shows competitive or superior performance.
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…
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