Quantum-Inspired Algorithm for Topological Data Analysis of Network Graphs

Jincheng Zhang

Published Sep 3, 2026• 0 citations

Abstract

Topological data analysis (TDA) provides powerful tools for uncovering hidden patterns and structures within complex datasets, particularly network graphs. Persistent homology, a cornerstone of TDA, calculates the persistence of topological features – such as connected components, cycles, and cavities – as the scale of analysis increases. Traditional persistent homology calculations can be computationally intensive, especially for large networks. This paper proposes a novel quantum-inspired algorithm designed to accelerate this process. The algorithm leverages concepts from quantum sampling and superposition to efficiently identify and quantify topological features, significantly reducing the computational burden. We demonstrate the feasibility of this approach, outlining the core claim, mechanism, and potential impact of combining quantum-inspired techniques with TDA. The primary goal is to explore the possibility of faster persistent homology calculations, ultimately enhancing the scalability and applicability of TDA to real-world network datasets.

DOI: 10.5281/zenodo.22272345

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