Quantum Computing-Based Geometric Topology Analysis

Jincheng Zhang

Published Aug 31, 2026• 0 citations

Abstract

This paper investigates the application of quantum computing to geometric topology, specifically focusing on the analysis of quantum topological phases. We explore how quantum entanglement, a fundamental property of quantum mechanics, can be leveraged to uncover the underlying geometric structure of these phases and ultimately reveal the laws governing them. The core mechanism involves simulating quantum states using quantum algorithms, which allows for the exploration of complex geometric relationships previously inaccessible through classical methods. We present preliminary results demonstrating the potential of this approach to identify key topological features and provide insights into the formation of quantum topological states. The investigation will highlight the benefits of quantum computing in tackling challenges in geometric topology and offers a new theoretical framework for understanding these phenomena.

DOI: 10.5281/zenodo.22202607

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