基于自适应量子拓扑的自适应几何优化算法

Jincheng Zhang

Published Aug 31, 2026• 0 citations

Abstract

This paper introduces a novel adaptive geometric optimization algorithm based on quantum topology. Traditional geometric optimization methods often rely on fixed parameter settings, limiting their ability to effectively address complex geometric problems. This paper proposes a new algorithm that dynamically adjusts geometric optimization parameters based on the problem's characteristics, enabling more efficient optimization. We leverage the inherent adaptability of quantum topology to achieve this dynamic adjustment. The core mechanism involves utilizing quantum topological properties to iteratively refine geometric parameters, leading to improved solutions compared to conventional methods. We demonstrate the effectiveness of our algorithm through several illustrative examples, showcasing its ability to handle challenging geometric configurations.

DOI: 10.5281/zenodo.22183800

Related papers

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

基于量子拓扑的非线性几何优化算法 (Non-linear Geometric Optimization Algorithm Based on Quantum Topology)

Jincheng Zhang

This paper introduces a novel non-linear geometric optimization algorithm based on quantum topology. Traditional optimization methods often rely on predefined models, limiting their ability to effectively handle complex systems. This algorithm leverages the inherent adaptability of quantum topology to dynamically optimize system structures, enabling efficient numerical simulations. We propose a framework that utilizes the principles of quantum entanglement and superposition to guide the optimization process, resulting in improved performance compared to conventional approaches. The core mechanism involves mapping the system's structure and objective function into a quantum state space, allowing for parallel exploration of multiple solution spaces. The algorithm's effectiveness is demonstrated through a series of illustrative examples, showcasing its capability to optimize complex geometric structures with high efficiency.

Sep 2, 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

Core Claim: We propose a novel adaptive quantum topology-based geometric optimization method that leverages the inherent properties of quantum topology to optimize complex geometric structures, enabling more efficient geometric design.

Jincheng Zhang

Quantum topology, a fascinating area of physics, offers the potential to manipulate space in ways that are fundamentally difficult to achieve classically. This research explores the application of quantum topology to geometric optimization, presenting a new approach that dynamically adapts to the problem's geometry. The core mechanism involves utilizing the self-adaptive nature of quantum topology to generate and refine optimization strategies, ultimately leading to improved geometric design. This paper details the proposed method, highlights its advantages, and provides a comprehensive analysis of its potential impact on geometric problem-solving. The study focuses on a specific geometric optimization task, demonstrating its efficacy through a series of illustrative examples. The analysis also considers the inherent challenges and potential limitations of this approach. We conclude with a discussion of future research directions and the broader implications of this work on the field of geometric optimization.

Aug 31, 20260 citations

Quantum Topology Simulation Adaptive Optimization

Jincheng Zhang

This paper introduces a novel adaptive optimization algorithm based on quantum topology simulation, designed to dynamically adjust optimization parameters based on the specific characteristics of the problem being addressed. The core mechanism leverages the unique properties of quantum topology – a mathematical framework that describes the robustness of geometric structures – to generate a simulated environment where the optimization process is inherently influenced by the underlying problem's topology. We demonstrate the effectiveness of this approach through a series of simulations and preliminary experiments, showcasing enhanced optimization efficiency compared to traditional optimization techniques. The paper provides a detailed explanation of the quantum topology simulation process, the adaptive parameter adjustment strategy, and the resulting benefits for various optimization problems.

Sep 4, 20260 citations

拓扑量子算法的自适应参数优化

Jincheng Zhang

This paper presents a novel approach to quantum algorithm optimization utilizing the principles of topological quantum algorithms. Traditional optimization methods often rely on fixed parameters, limiting the algorithm's adaptability. We propose a method that dynamically adjusts quantum system parameters based on the system's inherent topology, allowing for automated optimization and enhanced algorithm performance. The core mechanism involves constructing a topological representation of the quantum system and iteratively refining this representation to guide the algorithm towards optimal solutions. This approach offers a significant advancement in the field, addressing the limitations of conventional optimization techniques by leveraging the inherent properties of quantum systems. The work details the design of a robust parameter adjustment strategy and provides a preliminary assessment of its efficacy through theoretical analysis and simulated results.

Sep 2, 20260 citations