Quantum Topology: Nonlinear Geometry Transformations and Computational Algorithms

Jincheng Zhang

Published Sep 6, 2026• 0 citations

Abstract

Quantum topology, a fascinating field at the intersection of quantum mechanics and topology, has emerged as a promising avenue for developing novel computational algorithms. This paper investigates the application of non-linear geometry transformations to quantum state computation, exploring a novel algorithm designed to enhance quantum computing efficiency. We introduce the concept of "Quantum Topology Geometry Transformation" and demonstrate its potential for significantly improving quantum state manipulation. The research focuses on leveraging the inherent topological properties of quantum states to create an efficient computational framework. The core mechanism involves transforming the quantum state through a specific geometric process, optimizing the computation process. The paper presents a detailed analysis of the proposed algorithm and its implications for future quantum computing advancements. This work contributes to the understanding and development of advanced quantum algorithms through the application of topological principles.

DOI: 10.5281/zenodo.22489301

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