Title: Non-Euclidean Geometry via Quantum Entanglement

Jincheng Zhang

Published Sep 3, 2026• 0 citations

Abstract

This paper presents a novel approach to geometry, moving beyond the limitations of Euclidean space through the utilization of quantum entanglement. We propose a framework termed "Quantum Mapping" that converts geometric primitives into entangled quantum states, allowing for the generation of dynamically evolving shapes. The core mechanism centers around a unique mapping technique that leverages entanglement to manipulate these states, ultimately leading to the creation of geometrically complex and dynamically evolving shapes. The proposed method offers a fundamentally different perspective on shape construction, potentially unlocking new possibilities in areas such as fractal geometry, complex forms, and the exploration of non-intuitive spatial relationships. The paper details the Quantum Mapping technique, its mathematical underpinnings, and the resulting geometric constructions, demonstrating the potential of this approach to revolutionize geometric modeling.

DOI: 10.5281/zenodo.22264974

Related papers

Title: Quantum Entanglement Geometry Evolution Model

Jincheng Zhang

Quantum entanglement offers a unique pathway to explore complex geometric topologies, enabling simulations that are beyond the capabilities of classical methods. This paper proposes a novel geometric topology evolution model based on quantum entanglement, utilizing entanglement to dynamically generate and evolve geometric structures. We present a framework that leverages the inherent properties of quantum entanglement to create highly accurate geometric models, offering a fundamentally new approach to computational geometry. The model's core mechanism focuses on simulating entanglement-induced topological transformations, providing precise geometric representations of evolving structures. This research aims to advance our understanding of geometric evolution and explore potential applications in areas such as fractal geometry and topological data analysis.

Sep 3, 20260 citations

Title: Non-Euclidean Quantum State Space Description

Jincheng Zhang

Quantum state space description is a fundamental concept in quantum mechanics, but its application to practical algorithms is limited by the inherent geometric constraints of the Hilbert space. This paper explores a novel approach to quantum state space representation, leveraging non-Euclidean geometry to provide a geometrically-aligned framework for quantum algorithms. We propose a method for constructing quantum states and performing computations that directly reflects the properties of a non-Euclidean space, potentially unlocking new algorithmic possibilities. The core mechanism centers around establishing a mapping between quantum states and geometric primitives, allowing for the creation of algorithms that are inherently more robust and adaptable to non-Euclidean geometries. This work introduces a new methodology for quantum state representation and computation, aiming to overcome the limitations of traditional geometric approaches and facilitate the development of fundamentally new quantum algorithms.

Sep 6, 20260 citations

Title: Non-Euclidean Geometry and Quantum Entanglement

Jincheng Zhang

This paper explores the potential for unifying geometric properties with quantum phenomena through the development of a novel framework, termed "resonant geometry." We propose a mathematical model wherein geometric shapes exhibit emergent quantum behavior, driven by a dynamically adjustable operator that mimics the quantum state of the shape. The core claim is to establish a bridge between discrete quantum systems and continuous space, potentially unveiling new physics and offering a deeper understanding of fundamental geometric concepts. The paper details the introduction of a new mathematical operator and outlines a preliminary exploration of its effects on geometric transformations and quantum entanglement. We argue that this approach represents a significant departure from traditional geometric methods and opens avenues for investigating the interplay between space, quantum mechanics, and geometry.

Sep 3, 20260 citations

Title: Non-Local Quantum Entanglement for Computational Geometry

Jincheng Zhang

Quantum entanglement, a cornerstone of quantum mechanics, offers an unprecedented capability for manipulating complex systems. This research explores the application of this phenomenon to computational geometry, specifically focusing on generating and manipulating geometric primitives within a dynamically evolving holographic space. We propose a novel quantum algorithm that leverages a dynamically responsive "quantum foam" layer to accelerate geometric computations, potentially revolutionizing CAD and simulation workflows. The core mechanism involves adjusting the entanglement network based on geometric properties, allowing for parallel processing and the creation of intricate 3D models. This paper details the algorithmic framework, demonstrates preliminary results through simplified geometric examples, and discusses the implications of this approach for advanced computational geometry.

Sep 2, 20260 citations

Title: Adaptive Geometry Transformation Generation based on Quantum Computing

Jincheng Zhang

This paper explores the potential of quantum computing to revolutionize geometry generation, addressing the computational challenges inherent in creating complex geometric transformations. We propose a novel paradigm leveraging quantum computation to design and optimize geometric transformations, aiming to surpass the limitations of classical methods. The core mechanism centers around quantum algorithms for generating and refining geometric primitives, offering a fundamentally different approach to complex shape creation. This research investigates the feasibility of quantum computing for handling geometric transformations with increased efficiency and precision, ultimately leading to a new generation of computational tools for geometric modeling and design. Specifically, we detail the design of a quantum algorithm for generating and manipulating geometric transformations, emphasizing its potential to overcome the computational bottlenecks encountered in traditional approaches. The paper concludes with a discussion of the challenges and future directions of this research.

Sep 3, 20260 citations

Title: Non-Euclidean Geometry as a Framework for Quantum Entanglement

Jincheng Zhang

Quantum entanglement, a phenomenon where two or more particles become linked in such a way that they share the same fate no matter how far apart they are, remains a cornerstone of quantum mechanics. However, standard interpretations often struggle to fully capture its paradoxical nature and the complexities of its measurement. This paper investigates the potential of non-Euclidean geometry as a novel framework for understanding and manipulating entanglement, proposing a geometric representation that explicitly incorporates the 'non-Euclidean' property. We aim to move beyond traditional interpretations by providing a mathematically rigorous foundation for exploring entanglement's properties and offering a pathway towards novel quantum information processing techniques. This investigation centers on the hypothesis that entanglement's correlations are inherently linked to the underlying geometric structure, and that non-Euclidean geometry offers a more profound and nuanced understanding of this connection. The paper explores the conceptual implications of this framework, detailing the mathematical constructs that would be necessary to represent and manipulate entangled states within this context. We will discuss the potential benefits of this approach, including a potential resolution to the measurement problem and a deeper understanding of quantum phenomena.

Aug 31, 20260 citations