Quantum-Enhanced Fractal Dimension (QFAD)

Jincheng Zhang

Published Sep 5, 2026• 0 citations

Abstract

This paper explores the potential of quantum entanglement to significantly enhance fractal dimension measurements. Traditional fractal dimension estimation relies heavily on computational methods, often susceptible to noise and limitations in representing complex geometries. We propose a novel technique, Quantum-Enhanced Fractal Dimension (QFAD), which utilizes quantum entanglement to create a dynamically evolving map of fractal dimension, leading to enhanced accuracy and robustness. The core mechanism involves manipulating entangled qubits to generate a 'quantum fractal map' which then informs the final fractal dimension calculation. This approach overcomes inherent limitations in classical methods, offering a paradigm shift in fractal dimension analysis, particularly for intricate and high-dimensional datasets. We outline the theoretical framework, experimental setup, and preliminary results demonstrating the efficacy of QFAD. This work represents a significant step towards harnessing quantum phenomena for enhanced data analysis and representation.

DOI: 10.5281/zenodo.22316095

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