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Quantum Information Processing
Published in: Quantum Information Processing 12/2018

01-12-2018

The quantum Fourier transform based on quantum vision representation

Authors: Hai-Sheng Li, Ping Fan, Hai-ying Xia, Shuxiang Song, Xiangjian He

Published in: Quantum Information Processing | Issue 12/2018

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Abstract

Quantum Fourier transform (QFT) plays a key role in many quantum algorithms, but the existing circuits of QFT are incomplete and lacking the proof of correctness. Furthermore, it is difficult to apply QFT to the concrete field of information processing. Thus, we firstly investigate quantum vision representation (QVR) and develop a model of QVR. Then, we design four complete circuits of QFT and inverse QFT and describe the functions of their components. Meanwhile, we prove the correctness of the four complete circuits using formula derivation. Next, 2D QFT and 3D QFT based on QVR are proposed for the first time. Experimental results with simulation show the proposed QFTs are valid and useful in processing quantum images and videos. In conclusion, this paper develops a complete framework of QFT based on QVR and provides a feasible scheme for QFT to be applied in quantum vision information processing.
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Metadata
Title
The quantum Fourier transform based on quantum vision representation
Authors
Hai-Sheng Li
Ping Fan
Hai-ying Xia
Shuxiang Song
Xiangjian He
Publication date
01-12-2018
Publisher
Springer US
Published in
Quantum Information Processing / Issue 12/2018
Print ISSN: 1570-0755
Electronic ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-018-2096-2

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