Quantum-Inspired Graph Clustering using Amplitude Estimation

Jincheng Zhang

Published Sep 5, 2026• 0 citations

Abstract

Graph clustering, the process of grouping nodes in a graph based on their relationships, is a cornerstone of numerous data analysis applications, including social network analysis, bioinformatics, and anomaly detection. Traditional graph clustering algorithms often struggle with scalability and computational complexity, particularly when dealing with large graphs. This paper proposes a novel approach to graph clustering that leverages quantum-inspired amplitude estimation techniques. By mimicking the probabilistic nature of quantum algorithms, we approximate the probability distribution of node assignments within clusters, significantly accelerating the clustering process. Our method utilizes a modified version of the Lloyd-Max algorithm, incorporating amplitude estimation to reduce the number of iterations required to converge to a stable clustering solution. We demonstrate, through theoretical analysis and algorithmic design, that this approach can achieve comparable or superior clustering performance compared to conventional methods, while exhibiting a markedly reduced computational footprint. The core contribution lies in adapting amplitude estimation principles – originally developed for quantum computing – to a classical graph clustering context, offering a potentially transformative solution for tackling computationally intensive graph clustering problems. The efficiency gains are particularly pronounced in scenarios with high-dimensional node feature spaces.

DOI: 10.5281/zenodo.22332821

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