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Quantum State Vector Decomposition (QSVD)

Jincheng Zhang

Published Sep 6, 2026• 0 citations
Publisher

Abstract

Quantum State Vector Decomposition (QSVD) is a novel approach to decomposing complex quantum states into a set of orthogonal vector components, offering significant advantages in quantum state manipulation and measurement. This paper presents a rigorous mathematical framework for identifying and characterizing these orthogonal components, utilizing symmetries and entanglement to achieve a high degree of decomposition. The core claim is that QSVD provides a fundamentally different and potentially more efficient method compared to existing techniques, paving the way for enhanced quantum computations. This research explores the mathematical foundations of QSVD, detailing the method's algorithmic design and demonstrating its potential for practical applications in quantum information processing. The paper concludes with a discussion of the challenges and future directions of this research.

DOI
10.5281/zenodo.22511710

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Quantum State Vector Decomposition (QSVD) is a novel approach to decomposing complex quantum states into a set of orthogonal vector components, offering significant advantages in quantum state manipulation and measurement. This paper presents a rigorous mathematical framework for identifying and characterizing these orthogonal components, utilizing symmetries and entanglement to achieve a high degree of decomposition. The core claim is that QSVD provides a fundamentally different and potentially more efficient method compared to existing techniques, paving the way for enhanced quantum computations. This research explores the mathematical foundations of QSVD, detailing the method's algorithmic design and demonstrating its potential for practical applications in quantum information processing. The paper concludes with a discussion of the challenges and future directions of this research.
Quantum entanglement plays a pivotal role in various quantum algorithms and quantum information processing, offering the potential for enhanced computational capabilities. However, the inherent complexity of entangled states often poses significant challenges, particularly in achieving efficient manipulation and analysis. This paper investigates a novel approach to quantum state decomposition – the Quantum Entanglement Decomposition (QED) algorithm – based on topological self-unfolding. We propose a method that leverages the inherent topological properties of quantum states to transform them into a more structured and interpretable representation, facilitating deeper understanding and computational efficiency. The core mechanism centers around creating a topological manifold within the quantum state, allowing for efficient manipulation and analysis of the underlying entanglement structure. This research introduces a new framework for quantum state decomposition, demonstrating potential advancements in the comprehension and processing of entangled quantum systems. The paper concludes with a discussion of the algorithm's theoretical foundation, experimental validation, and future research directions.
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