Quantum Walk-Based Graph Partitioning with Adaptive Step Size

Jincheng Zhang

Published Sep 6, 2026• 0 citations

Abstract

This paper investigates the application of quantum walks for graph partitioning, a computationally challenging problem with significant implications in areas such as network design, data analysis, and optimization. The core idea is to harness the unique properties of quantum mechanics, specifically superposition and interference, to explore the solution space more efficiently than classical algorithms. We propose a novel approach that utilizes a quantum walk on the graph, dynamically adjusting the step size based on local graph density and connectivity. This adaptive step size algorithm is critical to achieving optimal performance, allowing the quantum walk to converge to a near-optimal graph partition with potentially exponential speedup compared to traditional methods. The presented framework offers a promising direction for tackling large and complex graph partitioning problems, and our simulations demonstrate the potential for significant performance improvements. The key innovation lies in the combination of quantum walk dynamics with an adaptive step size strategy, addressing a critical challenge in applying quantum walks to graph problems. We outline the theoretical framework, provide a detailed description of the algorithm, and present initial simulation results that support the viability of this approach.

DOI: 10.5281/zenodo.22448900

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