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Quantum-Inspired Algorithms for Topological Data Analysis

Jincheng Zhang

Published Aug 31, 2026• 0 citations
Publisher

Abstract

Topological data analysis (TDA) has emerged as a powerful tool for uncovering hidden patterns and structures within complex datasets. However, traditional TDA algorithms can be computationally intensive, particularly when dealing with high-dimensional data. This paper explores the application of quantum-inspired algorithms to enhance TDA, aiming to improve both efficiency and accuracy. We propose a framework that leverages concepts from quantum mechanics, such as entanglement and superposition, to simulate and manipulate topological data structures. The core mechanism involves the use of quantum-inspired simulation techniques to represent and process persistent homology calculations, resulting in a potential acceleration of the algorithm. We demonstrate the theoretical feasibility and outline a potential implementation strategy, suggesting that this approach could unlock new insights within TDA and provide a pathway toward more scalable and robust topological analysis methods. The primary focus is on developing a computational model that mimics aspects of quantum computation without requiring actual quantum hardware, focusing instead on algorithmic design inspired by quantum principles. This work establishes a foundational approach for integrating quantum-inspired techniques into the domain of TDA, paving the way for future research and development in this exciting area.

DOI
10.5281/zenodo.22186498

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