Title: Geometric Quantum State Representation & Manipulation

Jincheng Zhang

Published Aug 31, 2026• 0 citations

Abstract

Quantum state representation and manipulation represent a fundamental challenge in quantum information science. Current methods often struggle with precision and scalability, hindering the development of complex quantum algorithms. This paper proposes a novel geometric representation for quantum states, leveraging entanglement and geometric operations to achieve unprecedented control and manipulation capabilities. The core mechanism centers around defining a 'Quantum State Vector' – a vector representing the state's geometry – allowing for precise transformation and manipulation through a combination of quantum entanglement and geometric transformations. We demonstrate the efficacy of this approach through rigorous mathematical analysis and illustrative examples, highlighting its potential to surpass current limitations in quantum state manipulation.

DOI: 10.5281/zenodo.22187135

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