Quantum Computing and the Connection to Topological Groups

Jincheng Zhang

Published Aug 31, 2026• 0 citations

Abstract

Quantum computing represents a paradigm shift in computational power, offering the potential to solve complex problems intractable for classical computers. The fundamental principles of quantum mechanics, particularly superposition and entanglement, underpin this transformative capability. However, harnessing the full potential of quantum computers necessitates a deeper understanding of their underlying mathematical structures. This paper explores the intriguing connection between quantum computing and topological groups, focusing on leveraging their unique properties to optimize quantum algorithms and design novel quantum systems capable of tackling previously insurmountable computational challenges. We propose a novel approach that utilizes the inherent structure of topological groups to enhance quantum computation, potentially unlocking significant advancements in both theoretical understanding and practical application.

DOI: 10.5281/zenodo.22186636

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