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Analysis and improvement of the quantum Arnold image scrambling

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Abstract

We investigate the quantum Arnold image scrambling proposed by Jiang et al. (Quantum Inf Process 13(5):1223–1236, 2014). It is aimed to realize Arnold and Fibonacci image scrambling in quantum computer. However, the algorithm does not perceive the particularities of “mod \(2^{n}\),” multiply by 2, and subtraction in binary arithmetic. In this paper, a possible simplified version is presented based on 3 theorems and a corollary which represent the particularities of binary arithmetic. The theoretical analysis indicates that the network complexity is dropped from 140n \(\sim \)168n to 28n \(\sim \)56n and the unitarity of circuits is not destroyed.

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Authors and Affiliations

  1. College of Computer, Beijing University of Technology, Beijing,  100124, China

    Nan Jiang & Luo Wang

Authors
  1. Nan Jiang
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  2. Luo Wang
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Corresponding author

Correspondence to Nan Jiang.

Additional information

This work is supported by the Beijing Municipal Education Commission Science and Technology Development Plan under Grant no. KM201310005021, and the Graduate Technology Fund of BJUT under Grant No. YKJ-2013-10282.

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Jiang, N., Wang, L. Analysis and improvement of the quantum Arnold image scrambling. Quantum Inf Process 13, 1545–1551 (2014). https://doi.org/10.1007/s11128-014-0749-3

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  • DOI: https://doi.org/10.1007/s11128-014-0749-3

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