Quantum Information Geometry Complexity

Jincheng Zhang

Published Sep 3, 2026• 0 citations

Abstract

Quantum information geometry is a burgeoning field that explores the interplay between quantum mechanics and geometric concepts. This paper investigates the relationship between the complexity of quantum algorithms and the inherent geometric structure of quantum systems, specifically focusing on the potential for optimization through novel approaches. We introduce the concept of "Quantum Multi-Iterations" (QMI) – a framework that leverages quantum entanglement to dynamically modify geometric parameters within quantum algorithms, thereby enhancing efficiency. The core mechanism centers around quantifying and optimizing these geometric transformations, ultimately aiming to improve the performance of quantum algorithms, particularly for high-dimensional geometric problems. We demonstrate the efficacy of the QMI approach through a case study involving a modified version of Grover's search algorithm, showcasing significant improvements in its runtime complexity. The paper concludes with a discussion of the potential implications of this research, including the development of new algorithms and a refined understanding of the fundamental relationship between quantum information and geometric optimization.

DOI: 10.5281/zenodo.22274153

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