Non-Euclidean Vector Space for Quantum State Space Exploration

Jincheng Zhang

Published Sep 5, 2026• 0 citations

Abstract

Quantum state space exploration presents a significant challenge in quantum information science due to the inherent complexity of quantum states. Traditional methods often struggle with the vastness of these spaces, hindering efficient search and analysis. This paper introduces a novel framework for exploring quantum state spaces leveraging non-Euclidean vector spaces, aiming to dramatically improve search efficiency and enable the investigation of complex quantum states. We propose a geometric approach to represent and navigate the state space, utilizing differential geometry to achieve a more efficient and scalable exploration process. This work addresses the limitations of current techniques by providing a fundamentally different perspective on state space representation and navigation. The core mechanism centers around constructing a geometric model of the state space, allowing for the efficient application of techniques from differential geometry to optimize search operations. We demonstrate the effectiveness of this framework through a series of theoretical analyses and preliminary experiments, showcasing significant improvements in search performance compared to existing methods.

DOI: 10.5281/zenodo.22327003

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