High Dimensional Group Theory and Quantum Computing: A Connection

Jincheng Zhang

Published Aug 29, 2026• 0 citations

Abstract

This paper investigates the synergistic relationship between high-dimensional group theory and quantum computing. Traditional quantum computing approaches often lack the structural advantages offered by group theory, leading to limitations in algorithm efficiency and stability. We propose a novel framework based on the principles of group theory to design and optimize quantum algorithms, aiming to significantly enhance their performance. This work explores how the inherent properties of groups can be leveraged to improve the generation and execution of quantum states, thereby reducing computational complexity. The research highlights the potential for a new generation of quantum algorithms that are intrinsically more robust and efficient.

DOI: 10.5281/zenodo.22158833

Related papers

High-Dimensional Topology and Quantum Algorithm Connection

Jincheng Zhang

This paper investigates the synergistic relationship between high-dimensional topology and quantum algorithms. We explore how the inherent properties of high-dimensional topological spaces can be leveraged to enhance the efficiency and stability of quantum algorithms. The core focus is to develop novel optimization strategies predicated on topological constraints, resulting in improved performance compared to traditional approaches. The research utilizes a framework where high-dimensional topology serves as a guiding principle for algorithm design, ultimately aiming to create more robust and computationally effective quantum systems. The investigation will delve into the mathematical underpinnings of this connection, providing a theoretical foundation for practical application. This work contributes to the advancement of quantum algorithm design by offering a new perspective on how topology can impact quantum performance.

Aug 29, 20260 citations

Title: Quantum Topology-Based Algorithms

Jincheng Zhang

This paper explores the potential of quantum topology as a foundation for novel quantum algorithms. Traditional algorithms often focus on classical computations, but quantum topology offers a unique approach to designing quantum algorithms with enhanced capabilities. We propose a new quantum algorithm framework centered around the principles of quantum topology, aiming to optimize algorithm performance and stability through a refined mechanism. This research investigates the inherent properties of quantum topology and how these properties can be leveraged to create a quantum algorithm that surpasses current limitations. The core mechanism involves analyzing the fundamental structure of quantum topology to guide the algorithm's design, ultimately leading to improved efficiency and robustness.

Sep 4, 20260 citations

Topological-Quantum Path Optimization

Jincheng Zhang

This paper investigates the application of topological-quantum path optimization algorithms to enhance quantum computation. Traditional quantum computing relies on classical computers for algorithm design and implementation. We propose a novel approach that leverages the inherent topological properties of quantum systems to guide the optimization of quantum paths, leading to improved efficiency and potentially new quantum algorithms. This research focuses on establishing a framework for optimizing quantum trajectories using topological concepts, aiming to overcome limitations inherent in existing quantum computing methods. The core mechanism involves utilizing topological structures to represent the quantum state and guide the optimization process, ultimately improving the performance of quantum systems.

Sep 3, 20260 citations

Self-Adaptive Geometric Groups: Quantum Algorithm Design

Jincheng Zhang

This paper explores the design of quantum algorithms utilizing self-adaptive geometric groups. We investigate how these groups, leveraging quantum entanglement and geometric properties, can facilitate the development of efficient quantum algorithms. The core mechanism centers on dynamically adjusting the geometric structure of the group to optimize performance. The research focuses on establishing a novel approach to quantum algorithm optimization, emphasizing the synergistic interplay between self-adaptation and quantum mechanics. The paper presents a framework for designing quantum circuits that exhibit enhanced performance through this approach. Specifically, we detail a method for parameterizing the geometric group, enabling the algorithm to adapt to the input data. The work introduces a new optimization strategy based on entanglement and geometric transformations, ultimately aiming to improve the efficiency and robustness of quantum computations. The significance of this research lies in its potential to unlock new possibilities within the field of quantum algorithm design.

Aug 31, 20260 citations

Non-Linear Geometry Topology and Quantum Computation: A Synergistic Approach

Jincheng Zhang

This paper explores the synergistic potential between non-linear geometry topology and quantum computation. Traditional approaches to quantum algorithm design often rely on discrete, deterministic operations, limiting their scalability and efficiency. We propose a novel framework leveraging topological structure to drastically reduce computational complexity within quantum algorithms. This framework utilizes a combination of topological properties and quantum algorithms to guide the design of more efficient quantum computations. We detail the core mechanism, emphasizing the utilization of topological properties to minimize computational burden, offering a fundamentally new perspective on algorithm optimization. This research presents a promising pathway towards the development of more powerful and versatile quantum algorithms.

Aug 31, 20260 citations

Quantum Geometry and Topology: A New Approach to Quantum Computation

Jincheng Zhang

This paper explores the intersection of quantum geometry and topology, investigating its potential to revolutionize quantum computation. We propose a novel framework leveraging quantum geometry to model and manipulate high-dimensional topological structures, thereby offering new tools and algorithms for quantum information processing. The core claim is that this integrated approach, combining quantum geometry with topology information theory, will significantly enhance the capabilities of quantum computers. This research aims to provide a robust and flexible foundation for exploring complex quantum systems and developing advanced quantum algorithms.

Sep 7, 20260 citations