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Quantum Topology Adaptive Geometry Topology Transformation

Jincheng Zhang

Published Sep 3, 2026• 0 citations
Publisher

Abstract

Quantum topology, a field of theoretical physics, explores the properties of spacetime that are inherently quantum mechanical. The concept of quantum topology offers a potential framework for understanding and manipulating the geometry of spacetime at the fundamental level. This paper investigates the application of adaptive geometry topology transformations to quantum systems, aiming to enhance the accuracy and efficiency of simulations and calculations. We propose a novel algorithm that dynamically adjusts the underlying topology of a quantum system based on its internal geometric structure, enabling automated optimization and improved simulation results. The core claim centers on the ability of this algorithm to self-correct and refine the topological structure during the simulation process, addressing limitations of traditional topological transformation methods.

DOI
10.5281/zenodo.22278501

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Quantum Geometry explores the intersection of quantum mechanics and geometry, investigating the interplay between quantum states and topological properties. This paper introduces an adaptive topology algorithm designed to address the limitations of traditional topological data analysis, leveraging quantum entanglement to dynamically construct and manipulate topological structures. We propose a novel method that utilizes quantum entanglement to simulate self-learning and evolution within a quantum framework, ultimately enabling efficient and flexible processing of topological information crucial for quantum computation. The core mechanism centers around the application of entangled qubits to iteratively refine and expand topological landscapes, achieving a level of precision and adaptability unattainable with conventional methods. The paper demonstrates the efficacy of this approach through a series of simulations illustrating the algorithm's ability to generate complex topological patterns. We highlight the potential impact of this algorithm on the development of robust quantum algorithms and the exploration of novel topological phenomena.
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