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The quantum Fourier transform based on quantum vision representation

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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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Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant No. 61462026, No. 61762012, No. 61763014 and No. 61762014, the Fund for Distinguished Young Scholars of Jiangxi Province under Grant No. 2018ACB21013, the key research project of Guangxi Normal University Grant No. 2016ZD008 and an award of China Scholarship Council, Science and technology research project of Jiangxi Provincial Education Department under Grant No. GJJ170382, Project of International Cooperation and Exchanges of Jiangxi Province under Grant No. 20161BBH80034, Project of Humanities and Social Sciences in colleges and universities of Jiangxi Province under Grant No. JC161023.

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Correspondence to Hai-ying Xia.

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Li, HS., Fan, P., Xia, Hy. et al. The quantum Fourier transform based on quantum vision representation. Quantum Inf Process 17, 333 (2018). https://doi.org/10.1007/s11128-018-2096-2

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