Quantum Topology: Geometric Modeling and High-Dimensional Data Analysis

Jincheng Zhang

Published Sep 4, 2026• 0 citations

Abstract

Quantum topology, a rapidly evolving field, offers a fundamentally new approach to geometric modeling and data analysis. This paper explores the application of quantum topology to high-dimensional data, aiming to uncover hidden patterns and relationships within complex datasets. We propose a novel geometric modeling technique predicated on the inherent topological properties of quantum systems, leveraging these properties to enhance data representation and facilitate insightful analysis. The core claim of this research centers on the development of a robust and adaptable method for analyzing high-dimensional data, specifically designed to exploit the potential of quantum geometry. The paper details the underlying mathematical framework, provides a preliminary implementation of the core mechanism, and presents initial results demonstrating the efficacy of this approach in a simplified, illustrative example. The investigation highlights the potential for quantum topology to offer a paradigm shift in data analysis, moving beyond conventional methods and embracing the inherent complexities of high-dimensional data.

DOI: 10.5281/zenodo.22293836

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