基于动态拓扑的自适应几何映射

Jincheng Zhang

Published Sep 7, 2026• 0 citations

Abstract

This paper presents a novel method for geometric mapping based on dynamic topology, specifically incorporating a quantum-inspired approach to achieve complex transformations and enhanced scalability. Traditional geometric mapping techniques often rely on handcrafted parameters, limiting adaptability. We propose a framework utilizing a dynamic topology concept, employing quantum computation to dynamically sculpt the input data into a complex geometric structure. The core mechanism involves mapping data through a 'quantumized' topology, allowing for intricate transformations without requiring manual parameter adjustment. The proposed method offers a promising avenue for solving complex geometric problems with increased flexibility and potential for real-world applicability. This work explores the potential of utilizing dynamic topology and quantum computing to overcome limitations of conventional geometric mapping techniques.

DOI: 10.5281/zenodo.22621315

Related papers

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

Self-Adaptive Topological Modeling

Jincheng Zhang

This paper introduces a novel approach to geometric modeling based on dynamically-constructed topological structures. The method leverages quantum computing to dynamically adjust modeling parameters, enabling a level of precision unattainable through traditional techniques. We propose a framework where input data is mapped to a dynamic topology, and quantum algorithms are employed to refine the model based on the input's inherent geometric characteristics. This offers a significant advancement in modeling accuracy and adaptability, particularly for complex and intricate shapes. The core mechanism centers around a "quantumization" process that transforms the input data into a dynamically evolving topological representation. The paper details the design of the quantum algorithm, its implementation within a computational framework, and a preliminary evaluation of its performance on a set of synthetic and real-world geometric datasets. We demonstrate that this method surpasses existing methods in terms of geometric fidelity and computational efficiency.

Sep 7, 20260 citations

基于量子纠缠的自适应几何映射

Jincheng Zhang

This paper investigates the potential of utilizing quantum entanglement to enable self-adaptive geometric mapping. Traditional geometric mapping methods rely on predefined mapping models, limiting design flexibility. We propose a novel system leveraging quantum entanglement to learn mapping parameters from data, facilitating the creation of complex geometric relationships. The core mechanism centers around establishing entangled states to represent geometric transformations, allowing for a dynamic and adaptable mapping process. This approach offers a fundamentally new pathway for geometric modeling, potentially surpassing the limitations of conventional techniques. The paper details the system's architecture, the quantum entanglement process, and the resulting geometric mappings demonstrated through illustrative examples. We highlight the advantages of this approach in terms of adaptability, efficiency, and the potential for generating intricate geometric structures.

Sep 5, 20260 citations

自适应量子拓扑的自适应几何变换

Jincheng Zhang

This paper investigates the application of self-adaptive quantum topology for achieving complex geometric transformations, offering a novel approach to handle non-linear geometric problems in complex systems. We propose a method leveraging the inherent self-adaptability of quantum topology to dynamically modify geometric parameters, allowing for the creation of intricate transformations without requiring explicit parameter tuning. The core mechanism centers on utilizing the topological properties of quantum systems to facilitate these transformations, addressing limitations of traditional geometric methods. The paper presents a detailed theoretical framework outlining the design of this adaptive technique, including the mathematical formulation of the transformation process and a discussion of its potential applications in various fields, particularly within the context of quantum information processing and advanced geometry. We further explore the advantages and challenges of this approach, highlighting its potential to unlock new capabilities in geometric manipulation. Finally, we outline future research directions to further refine and expand the capabilities of this self-adaptive quantum topology framework.

Aug 31, 20260 citations

基于量子态的自适应几何优化

Jincheng Zhang

This paper introduces a novel approach to geometric optimization leveraging the inherent quantum state properties of the problem. Traditional geometric optimization methods often require manual parameter tuning, limiting precision and requiring significant computational effort. We propose a quantum-inspired algorithm that utilizes quantum state transformations to dynamically adjust parameters during the optimization process, leading to improved geometric accuracy and robustness. The core mechanism involves mapping the problem's objective function to a quantum state space, allowing for efficient exploration of the solution space. We demonstrate the efficacy of this method through a series of numerical experiments, showcasing significant improvements in geometric accuracy compared to standard optimization techniques. The algorithm's ability to adapt to the problem's characteristics makes it a promising tool for complex geometric optimization challenges.

Aug 31, 20260 citations

Quantum Topology Dynamic Topology Mapping

Jincheng Zhang

Quantum Topology Dynamic Topology Mapping is a novel approach to computational geometry, leveraging the principles of quantum topology to achieve unprecedented accuracy and efficiency in geometric transformations. This research introduces a dynamic mapping algorithm based on quantum entanglement and topology, designed to overcome limitations inherent in traditional methods. The core mechanism involves utilizing quantum entanglement to establish a foundational connection between the original geometric structure and the resulting quantum state, thereby enabling the manipulation of complex transformations with significantly reduced computational cost. The algorithm's effectiveness is demonstrated through rigorous analysis and validation of its performance across a range of geometric problems. This work represents a significant advancement in computational geometry, offering a potentially transformative solution for tasks involving intricate geometric calculations.

Aug 31, 20260 citations