Geometric Topology as Quantum State Representation

Jincheng Zhang

Published Sep 5, 2026• 0 citations

Abstract

Geometric topology, a fascinating field in mathematics, describes the properties of shapes and spaces that are fundamentally different from Euclidean geometry. This research explores the potential of using quantum states to represent and manipulate geometric topology, leveraging quantum entanglement and superposition to enable efficient calculations and simulations within a quantum computing framework. This work proposes a novel approach to geometric topology computation, focusing on building a quantum state representation that can accurately model complex topological structures. We investigate how quantum states can be used to encapsulate geometric topology, and demonstrate the potential for quantum computations to accelerate the analysis and exploration of topological phenomena. The research addresses a key challenge in geometric topology – its complexity – and offers a promising pathway toward harnessing quantum mechanics for advanced mathematical modeling.

DOI: 10.5281/zenodo.22332350

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