Quantum-Enhanced Differential Geometry for Computational Topology

Jincheng Zhang

Published Aug 31, 2026• 0 citations

Abstract

Quantum-Enhanced Differential Geometry (QEDG) presents a novel approach to representing and manipulating differential geometry, offering a pathway to generating highly complex, non-linear topological structures. This paper explores the integration of quantum mechanics into the traditional framework of differential geometry, introducing a 'quantum-induced curvature' mechanism to facilitate the creation of intricate, self-similar topologies. We detail the theoretical underpinnings, demonstrate the practical implementation using a specific mathematical model, and provide an initial analysis of its potential applications within computational topology. The core claim is that QEDG can significantly accelerate the construction of topologically rich landscapes and facilitate the discovery of unexpected topological phenomena.

DOI: 10.5281/zenodo.22185190

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