Title: Fractal Self-Similarity for Quantum Algorithm Design

Jincheng Zhang

Published Sep 3, 2026• 0 citations

Abstract

Fractal self-similarity, a ubiquitous phenomenon in nature, presents a compelling and potentially transformative concept for quantum algorithm design. This paper explores the application of this principle to optimize quantum circuit construction, focusing on the development of novel algorithms that harness repeating patterns at different scales. We propose a new approach predicated on identifying and exploiting fractal self-similarity within quantum circuits, resulting in enhanced computational performance and novel algorithmic capabilities. This work investigates the mathematical foundations of fractal self-similarity and demonstrates its practical implementation within a specific quantum algorithm framework. The paper will outline the core mechanism, detailing the process of defining a 'Fractal Scale' and utilizing iterative algorithms to exploit self-similarity. The ultimate goal is to leverage fractal self-similarity to unlock new possibilities in quantum computing, pushing the boundaries of what's currently achievable.

DOI: 10.5281/zenodo.22268182

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