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Core Claim: Design a quantum computing-based topology-topology analysis algorithm to efficiently compute topological structures and provide more precise topological evolution analysis.

Jincheng Zhang

Published Sep 3, 2026• 0 citations
Publisher

Abstract

This paper explores the application of quantum computing to enhance topology analysis, specifically focusing on the computational complexity of intricate topological structures. The central challenge lies in the inherent difficulty of efficiently representing and manipulating topological data, which often necessitates computationally intensive methods. We propose a novel quantum algorithm framework, leveraging quantum entanglement and superposition to accelerate the analysis of topological phases and their evolution. This framework incorporates a modified version of the Wasserstein distance, adapted for topological data, and utilizes quantum Fourier transforms to efficiently explore the space of possible topological configurations. The algorithm's core mechanism involves quantum-enhanced representation of topological states and the application of a specific quantum operation to determine the order of topological phase transitions. The paper details a preliminary implementation demonstrating the algorithm's potential for improved accuracy and speed compared to classical methods, specifically for analyzing topological landscapes involving complex branching. We present a case study illustrating the algorithm's effectiveness in analyzing a specific topological structure, highlighting the benefits of quantum computation in this area. The paper concludes with a discussion of future research directions, including exploring the algorithm's applicability to more complex topological systems and scaling to larger datasets.

DOI
10.5281/zenodo.22278298

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