维度不一致性理论的数学验证

Jincheng Zhang

Published Sep 6, 2026• 0 citations

Abstract

This paper presents a novel theoretical framework for understanding and quantifying dimension mismatch, addressing the longstanding challenge of validating the concept within the realm of mathematical rigor. We propose a model rooted in quantum entanglement to provide a rigorous mathematical basis for analyzing the potential consequences of dimension mismatch in quantum computation. The core claim is that a specific set of dimension mismatch conditions can be demonstrably exploited to yield anomalous computational results through the implementation of a quantum entanglement-driven mechanism. This work aims to provide a solid foundation for future research in quantum computing and its potential for transformative computations.

DOI: 10.5281/zenodo.22508081

Related papers

Quantum Entanglement Computing Models: A Novel Approach to Beyond Classical Computation

Jincheng Zhang

Quantum entanglement, a bizarre phenomenon where two or more particles become linked and share the same fate, holds immense promise for revolutionizing computation. This paper explores the potential of quantum entanglement for novel computation paradigms, focusing on a model designed to transcend the limitations of classical computing. We propose a framework centered around a "纠缠信息编解码" mechanism, which utilizes entanglement as the core foundation for computation. This model aims to enhance quantum computer capabilities, particularly in the realm of complex algorithm implementation and precision simulation. This research will detail the core mechanism, outlining the design of a specialized entanglement coding scheme. The paper will conclude by discussing the challenges and future directions of this research, emphasizing its potential impact on the advancement of quantum computing.

Sep 1, 20260 citations

Quantum Entanglement Analysis and Mitigation

Jincheng Zhang

Quantum entanglement, a cornerstone of quantum mechanics, presents both immense potential and profound challenges for practical applications. This paper investigates the nature of entanglement, focusing on its non-classical properties and exploring a novel theoretical framework—a non-symmetric entanglement model—to analyze and potentially mitigate the influence of spacetime dimensions on entanglement. We propose a method based on this model to develop a quantum computing algorithm that circumvents the inherent challenges posed by non-symmetric entanglement. The core claim is that a rigorous analysis of entanglement's non-symmetric nature, facilitated by this model, will yield a pathway toward significantly enhanced quantum entanglement robustness and security. This work represents a significant step in understanding and potentially harnessing the full capabilities of quantum entanglement.

Aug 31, 20260 citations

基于量子计算的非对称性几何验证

Jincheng Zhang

This paper explores the potential of quantum computing to validate fundamental geometric theorems and uncover novel geometric properties. We propose a novel algorithm leveraging quantum entanglement to simulate geometric transformations and rigorously test the core principles of geometry. The study focuses on utilizing quantum computation to verify geometric theorems and identify subtle geometric relationships not readily apparent through classical methods. This research aims to establish a new avenue for geometric research, potentially leading to breakthroughs in quantum algorithm design and theoretical understanding. The core claim is that quantum computing can provide a more precise and insightful approach to geometric verification, paving the way for new algorithms and a deeper comprehension of geometric concepts.

Sep 4, 20260 citations

拓扑几何与量子纠缠的耦合理论

Jincheng Zhang

This paper explores the intricate coupling between topological geometry and quantum entanglement, proposing a novel computational framework for calculating complex topological structures. We introduce a novel computational paradigm centered around quantum entanglement dynamics, enabling precise calculations based on the inherent properties of entanglement. The core claim is that this approach dramatically expands the potential for quantum computation by leveraging the fundamental link between topological properties and quantum entanglement. This work investigates the potential for utilizing entanglement to precisely model and manipulate topological structures, ultimately paving the way for a significantly enhanced computational capability. The theoretical framework, developed through rigorous mathematical analysis and computational simulations, provides a foundation for future research in quantum topological algorithms. This study underscores the importance of exploring novel computational approaches that integrate the dynamics of quantum entanglement with the geometric properties of topological spaces.

Sep 7, 20260 citations

Quantum Entanglement: A Geometric Analysis of Multi-Dimensional Mathematics

Jincheng Zhang

Quantum entanglement, a cornerstone of quantum mechanics, presents a profound challenge to our classical intuitions about space and time. This paper explores the geometric implications of quantum entanglement, proposing a novel mathematical framework based on multi-dimensional geometry to provide a deeper understanding of entanglement's fundamental properties and potential applications in quantum information and computation. The core mechanism involves transforming entangled states into geometric operations, leveraging the unique properties of multi-dimensional spaces to construct a theoretical model for analyzing entanglement's nature and computational possibilities. The current state of mathematical modeling of quantum entanglement is limited, and this work aims to advance this field by establishing a new geometric perspective that offers a robust foundation for future research.

Sep 4, 20260 citations

拓扑学与量子计算的融合模型

Jincheng Zhang

This paper investigates the potential for a unified model integrating topology and quantum computation, specifically focusing on the analysis of quantum systems and their associated topological structures. We propose a novel framework that combines established topological concepts with quantum mechanical principles to provide a deeper understanding of these intricate phenomena. The core aim is to identify novel applications of quantum computation within the realm of topological physics, exploring how quantum algorithms can be leveraged to uncover and manipulate topological properties. This research aims to advance our understanding of the relationship between topology and quantum mechanics, potentially leading to new theoretical insights and practical applications. The work will examine various aspects of this integration, including the representation of topological phases, quantum algorithms for topological data analysis, and the potential for topological quantum error correction. The paper will conclude by discussing the challenges and future directions of this research.

Sep 4, 20260 citations