Qudit inspired optimization for graph coloring

• URL: http://arxiv.org/abs/2406.00792v1
• Date: Sun, 2 Jun 2024 16:19:55 GMT
• Title: Qudit inspired optimization for graph coloring
• Authors: David Jansen, Timothy Heightman, Luke Mortimer, Ignacio Perito, Antonio Acín,
• Abstract summary: We introduce a quantum-inspired algorithm for Graph Coloring Problems (GCPs) We use qudits in a product state, with each qudit representing a node in the graph and parameterized by d-dimensional spherical coordinates. We benchmark two optimization strategies: qudit gradient descent (QdGD), initiating qudits in random states and employing gradient descent to minimize a cost function.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 (QdGD), initiating qudits in random states and employing gradient descent to minimize a cost function, and qudit local quantum annealing (QdLQA), 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.

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