Quantum-Enhanced Metric Geometry for Topological Data Analysis

Jincheng Zhang

Published Sep 6, 2026• 0 citations

Abstract

This paper presents a novel approach to topological data analysis (TDA) leveraging quantum-enhanced metric geometry. We introduce a novel quantum algorithm designed to explore the underlying geometric structure of topological data generated from data, employing entanglement to reveal hidden patterns and correlations beyond the capabilities of classical methods. The core mechanism centers on utilizing quantum entanglement to induce a specific geometric transformation, allowing for the detection of previously unobservable topological features. This work addresses limitations in current TDA techniques by offering a fundamentally new methodology with the potential for increased precision and the discovery of complex geometric structures. We outline the algorithm's design, key mathematical components, and preliminary experimental results demonstrating the efficacy of the quantum-enhanced approach in identifying subtle topological patterns.

DOI: 10.5281/zenodo.22494411

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