Fractal Compression of Quantum States

Jincheng Zhang

Published Sep 2, 2026• 0 citations

Abstract

This paper explores a novel approach to quantum state compression leveraging the principles of fractal geometry. Quantum states, particularly those representing complex physical systems, often require significant storage space due to the exponential growth in the Hilbert space dimension. Traditional compression methods struggle with the inherently complex and non-separable nature of quantum information. This work proposes encoding quantum states into a fractal representation, capitalizing on the inherent self-similarity observed at different scales within these states. The core idea is to construct a fractal tree that mirrors the underlying quantum state, enabling efficient data reduction. We present a theoretical framework and mathematical formulation for this fractal compression technique, detailing the encoding and decoding processes. The efficiency of the method is analyzed through theoretical considerations and by examining the relationship between fractal dimension, compression ratio, and the complexity of the original quantum state. The results suggest that fractal compression offers a promising alternative for reducing the storage requirements of quantum information, particularly for states exhibiting significant self-similarity. Further research will focus on developing practical implementations and exploring the technique's applicability to various quantum systems.

DOI: 10.5281/zenodo.22247976

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