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Fractal-Dimensional Quantum Information Processing

Jincheng Zhang

Published Sep 3, 2026• 0 citations
Publisher

Abstract

This paper proposes a novel framework for quantum information processing rooted in the principles of fractal geometry. The core claim is that the dimensionality of quantum systems can be inherently linked to fractal structures, offering a fundamentally new approach to data storage and computation. We investigate the utilization of fractal patterns to encode quantum states, exploiting the enhanced information density and computational potential afforded by fractal geometry. Specifically, we explore methods for representing and manipulating quantum states within fractal spaces, utilizing concepts such as self-similarity and non-integer dimensions. The theoretical framework presented demonstrates a potential pathway to significantly increased storage capacity and more efficient quantum algorithms. The key innovation lies in the direct mapping of quantum information onto fractal landscapes, which promises to unlock new possibilities in quantum technologies. The exploration includes examining different fractal types (e.g., Mandelbrot set, Sierpinski triangle) and their suitability for specific quantum information tasks. The research highlights the potential for designing quantum systems with intrinsic fractal properties, leading to enhanced robustness and scalability. Ultimately, this work aims to establish a foundational understanding of how fractal geometry can be leveraged to revolutionize quantum information processing.

DOI
10.5281/zenodo.22270352

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