Title: Non-Standard Matrix Decomposition for Quantum State Representation

Jincheng Zhang

Published Sep 7, 2026• 0 citations

Abstract

Quantum state representation is fundamental to quantum computation, requiring efficient methods for manipulation and analysis. Traditional methods often rely on eigenvalue decomposition, which struggles with the intricate correlations inherent in many quantum states, particularly those exhibiting entanglement. This paper introduces a novel matrix decomposition technique, "Quantum Entanglement Matrix Decomposition" (QEMD), designed to explicitly incorporate quantum entanglement and superposition into the core representation of quantum states. This approach significantly enhances computational efficiency and opens new avenues for algorithm design within the quantum realm. The method's core mechanism involves constructing a 'quantum entanglement matrix' that directly represents these correlations, enabling parallel processing and facilitating the development of novel quantum algorithms. We present a comprehensive theoretical analysis and preliminary experimental validation demonstrating the effectiveness of QEMD.

DOI: 10.5281/zenodo.22631702

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