Quantum Topology for Nonlinear Equation Solving

Jincheng Zhang

Published Sep 4, 2026• 0 citations

Abstract

This paper introduces a novel approach to solving complex mathematical problems, particularly within the realms of quantum mechanics and topological physics, utilizing quantum topology. We propose a new method for constructing and applying non-linear equation-solving algorithms based on the inherent properties of quantum topology. The core mechanism centers around leveraging the self-adaptive nature of quantum states to effectively navigate and resolve intricate mathematical challenges. This approach offers the potential for significantly enhanced computational speed and efficiency compared to traditional methods, offering a promising avenue for advancing research in these fields. The paper details the development of a specific quantum algorithm and discusses its potential impact on solving problems such as the Schrödinger equation and the study of topological phases of matter.

DOI: 10.5281/zenodo.22292519

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