基于量子拓扑的动态拓扑几何变形

Jincheng Zhang

Published Sep 4, 2026• 0 citations

Abstract

This paper introduces a novel dynamic topology geometric transformation algorithm based on quantum topology. Traditional topological transformation methods often rely on static transformations, limiting their flexibility and efficiency. We propose a method that dynamically adjusts the topology of a system, leveraging the unique properties of quantum topology to achieve transformative changes. This algorithm aims to provide a more adaptable and powerful approach to complex system manipulation. The core mechanism involves a continuous, iterative process of quantum state manipulation, resulting in significant improvements in the transformation speed and the ability to handle intricate geometric arrangements. We demonstrate the effectiveness of this approach through simulations illustrating the dynamic transformation of a 2D lattice structure.

DOI: 10.5281/zenodo.22289579

Related papers

Quantum Topology Dynamic Geometry Transformation Algorithm

Jincheng Zhang

Quantum topology, a fascinating field of theoretical physics, has recently garnered significant attention for its potential to revolutionize geometric analysis. This paper investigates a novel dynamic geometry transformation algorithm leveraging quantum topology principles to achieve more complex and adaptable geometric transformations. We propose a method that dynamically adjusts the underlying topology of a geometric structure, allowing for intricate and nuanced manipulations that are difficult to achieve with traditional approaches. The core mechanism relies on the inherent properties of quantum topology – specifically, the ability of systems to exist in multiple states simultaneously – which facilitates continuous and self-correcting transformations. The algorithm's potential impact across various fields, including geometry, physics, and computer graphics, is substantial.

Aug 31, 20260 citations

基于量子态的动态拓扑变换算法

Jincheng Zhang

This paper presents a novel dynamic topology transformation algorithm based on quantum state adaptation. Traditional topology transformation algorithms are often static, limiting their efficiency and generalization capabilities. We propose an algorithm that leverages quantum state dynamics to dynamically adjust transformation parameters during optimization, aiming to achieve superior local optima. The core of this approach is the implementation of a quantum-enhanced adaptation mechanism that continuously refines the transformation process, leading to improved solution quality. We demonstrate the effectiveness of this algorithm through a series of illustrative examples, showcasing its ability to overcome limitations of conventional methods. The algorithm's potential impact extends to a wide range of optimization problems, particularly those involving complex geometries and constraints.

Sep 7, 20260 citations

基于动态几何拓扑的自适应量子态生成

Jincheng Zhang

This paper introduces a novel quantum state generation algorithm based on dynamic geometric topology. Traditional quantum state generation methods typically rely on static parameters, but this approach leverages dynamic geometric topology to generate quantum states with complex topological structures, thereby enhancing quantum computation efficiency. The algorithm employs a series of iterative transformations that map initial quantum states into a complex topological space, resulting in a diverse range of quantum states. We demonstrate the effectiveness of this method through simulations and analysis, showcasing improved quantum state diversity and efficiency compared to existing techniques. The core mechanism centers on the construction and manipulation of topological spaces, enabling the generation of highly intricate and controllable quantum states.

Sep 2, 20260 citations

基于量子拓扑的自适应几何模型生成

Jincheng Zhang

This paper introduces a novel method for generating geometric models based on quantum topology, enabling dynamic adaptation to complex data. Traditional geometric modeling techniques often rely on predefined parameters, limiting their flexibility and hindering the ability to capture intricate relationships within data. We propose a framework that leverages quantum topology to dynamically adjust model parameters, allowing the model to learn from data and efficiently represent complex geometric patterns. The core mechanism involves using quantum topology to create a flexible, adaptable representation of the data, enhancing learning and enabling the generation of models that can effectively capture the underlying structure of the input space. The proposed approach offers a significant advancement over static models by providing a mechanism for continuous refinement and adaptation, addressing the challenges of handling high-dimensional and complex datasets.

Aug 31, 20260 citations

基于量子纠缠的自适应几何变换算法

Jincheng Zhang

This paper introduces a novel algorithm based on quantum entanglement to facilitate adaptive geometric transformations. Traditional geometric transformations often rely on fixed parameters and lack the flexibility to handle intricate transformations. We propose a system leveraging quantum entanglement to dynamically adjust geometric parameters, optimizing the transformation process for enhanced efficiency and precision. The core mechanism involves creating and manipulating entangled states to guide the transformation, offering a fundamentally different approach compared to conventional methods. The algorithm demonstrates significant improvements in geometric transformation accuracy and speed through the application of quantum entanglement. This work presents a promising pathway for advancing geometric computation, particularly in scenarios requiring complex transformations and high fidelity.

Sep 4, 20260 citations

基于量子拓扑的几何变换算法的动态调整

Jincheng Zhang

This paper explores the application of quantum topology principles to develop a dynamic adjustment algorithm for geometric transformations. Traditional geometric transformations often suffer from inefficient computational costs, particularly for complex shapes. We propose a novel algorithm leveraging quantum topological properties to automate and dynamically adjust these transformations, aiming to enhance computational efficiency. The algorithm employs a quantum entanglement-based optimization strategy to navigate through the complex space of possible geometric adjustments. We detail the key steps involved in the algorithm's design, including the construction of a quantum state representation and the implementation of a self-correcting mechanism. The core claim focuses on achieving significant improvements in computational speed and flexibility compared to traditional geometric transformation techniques. The paper presents a preliminary demonstration of the algorithm's effectiveness in a specific geometric transformation scenario, highlighting its potential for broader applicability.

Sep 3, 20260 citations