Qudit-inspired optimization for graph coloring

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 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.