Quantum-Enhanced Constraint Satisfaction Problems via Graph Traversal

Jincheng Zhang

Published Sep 5, 2026• 0 citations

Abstract

Constraint Satisfaction Problems (CSPs) are a fundamental class of computational problems prevalent in various fields, including artificial intelligence, optimization, and cryptography. Traditional CSP solvers often struggle with the exponential complexity associated with large, complex graphs. This research investigates the potential of quantum algorithms, specifically those utilizing quantum walks, to significantly accelerate the solution process for CSPs. We propose a framework that maps CSP instances onto graphs and employs quantum walk algorithms to efficiently traverse the solution space. The core of our approach leverages the quantum superposition principle, enabling the simultaneous exploration of multiple potential solutions. We demonstrate, through theoretical analysis and algorithmic design, that quantum walks can offer a substantial speedup compared to classical algorithms for certain CSP instances, particularly those with high connectivity and large solution spaces. This work contributes a novel approach to tackling computationally intensive CSPs by integrating quantum computing principles with graph traversal techniques, representing a potentially transformative advancement in solving complex optimization challenges.

DOI: 10.5281/zenodo.22317302

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