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Global and Local Translation Designs of Quantum Image Based on FRQI

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Abstract

In this paper, two kinds of quantum image translation are designed based on FRQI, including global translation and local translation. Firstly, global translation is realized by employing adder modulo N, where all pixels in the image will be moved, and the circuit of right translation is designed. Meanwhile, left translation can also be implemented by using right translation. Complexity analysis shows that the circuits of global translation in this paper have lower complexity and cost less qubits. Secondly, local translation, consisted of single-column translation, multiple-columns translation and translation in the restricted area, is designed by adopting Gray code. In local translation, any parts of pixels in the image can be translated while other pixels remain unchanged. In order to lower complexity when the number of columns needing to be translated are more than one, multiple-columns translation is proposed, which has the approximate complexity with single-column translation. To perform multiple-columns translation, three conditions must be satisfied. In addition, all translations in this paper are cyclic.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China under Grant No. 61463016 and 61462026, Program for New Century Excellent Talents in University under Grant No.NCET-13-0795, Training program of Academic and technical leaders of Jiangxi Province under Grant No.20153BCB22002, Natural Science Foundation of Jiangxi Province of China under Grant No.20151BAB207019 and the advantages of scientific and technological innovation team of Nanchang City under Grant No.2015CXTD003, FDCT of Macau under grant 013/2013/A1, University of Macau under grants MRG022/IH/2013/FST and MYRG2014-00052-FST, and National Natural Science Foundation of China under grant No. 11404415.

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Authors and Affiliations

  1. College of Information Engineering, Shanghai Maritime University, Shanghai, 201306, China

    Ri-Gui Zhou

  2. School of Information Engineering, East China Jiaotong University, Nanchang, Jiangxi, 330013, China

    Ri-Gui Zhou & Canyun Tan

  3. Institute of Applied Physics and Materials Engineering, FST, University of Macau, Macau, China

    Hou Ian

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  1. Ri-Gui Zhou
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  2. Canyun Tan
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Correspondence to Canyun Tan.

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Zhou, RG., Tan, C. & Ian, H. Global and Local Translation Designs of Quantum Image Based on FRQI. Int J Theor Phys 56, 1382–1398 (2017). https://doi.org/10.1007/s10773-017-3279-9

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