Geometric Topology for Quantum State Representation

Jincheng Zhang

Published Aug 31, 2026• 0 citations

Abstract

This paper explores the application of geometric topology to quantum state representation, aiming to develop a novel framework that leverages topological properties to enhance the analysis and manipulation of quantum information. We introduce a 'topological geometric transformation' – a mathematical operation that maps quantum states to a higher-dimensional space – as a core mechanism for achieving this goal. This transformation preserves essential topological invariants, offering a significant advancement over existing methods. The paper details the design of this transformation, its mathematical formulation, and its potential impact on quantum state representation, highlighting its advantages in terms of efficiency and representation capabilities.

DOI: 10.5281/zenodo.22194654

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