中国物理B ›› 2014, Vol. 23 ›› Issue (2): 20306-020306.doi: 10.1088/1674-1056/23/2/020306

• GENERAL • 上一篇    下一篇

Realization of quantum Fourier transform over ZN

付向群, 鲍皖苏, 李发达, 张宇超   

  1. Information Engineering University, Zhengzhou 450004, China
  • 收稿日期:2013-04-21 修回日期:2013-07-04 出版日期:2013-12-12 发布日期:2013-12-12
  • 基金资助:
    Project supported by the National Basic Research Program of China (Grant No. 2013CB338002).

Realization of quantum Fourier transform over ZN

Fu Xiang-Qun (付向群), Bao Wan-Su (鲍皖苏), Li Fa-Da (李发达), Zhang Yu-Chao (张宇超)   

  1. Information Engineering University, Zhengzhou 450004, China
  • Received:2013-04-21 Revised:2013-07-04 Online:2013-12-12 Published:2013-12-12
  • Contact: Bao Wan-Su E-mail:2010thzz@sina.com
  • About author:03.67.Lx; 03.65.Sq; 03.65.Ta; 03.67.-a
  • Supported by:
    Project supported by the National Basic Research Program of China (Grant No. 2013CB338002).

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摘要： Since the difficulty in preparing the equal superposition state of amplitude is 1/√N, we construct a quantile transform of quantum Fourier transform (QFT) over ZN based on the elementary transforms, such as Hadamard transform and Pauli transform. The QFT over ZN can then be realized by the quantile transform, and used to further design its quantum circuit and analyze the requirements for the quantum register and quantum gates. However, the transform needs considerable quantum computational resources and it is difficult to construct a high-dimensional quantum register. Hence, we investigate the design of t-bit quantile transform, and introduce the definition of t-bit semiclassical QFT over ZN. According to probability amplitude, we prove that the transform can be used to realize QFT over ZN and further design its quantum circuit. For this transform, the requirements for the quantum register, the one-qubit gate, and two-qubit gate reduce obviously when compared with those for the QFT over ZN.

关键词: quantum Fourier transform, semiclassical quantum Fourier transform, quantum algorithm

Abstract: Since the difficulty in preparing the equal superposition state of amplitude is 1/√N, we construct a quantile transform of quantum Fourier transform (QFT) over ZN based on the elementary transforms, such as Hadamard transform and Pauli transform. The QFT over ZN can then be realized by the quantile transform, and used to further design its quantum circuit and analyze the requirements for the quantum register and quantum gates. However, the transform needs considerable quantum computational resources and it is difficult to construct a high-dimensional quantum register. Hence, we investigate the design of t-bit quantile transform, and introduce the definition of t-bit semiclassical QFT over ZN. According to probability amplitude, we prove that the transform can be used to realize QFT over ZN and further design its quantum circuit. For this transform, the requirements for the quantum register, the one-qubit gate, and two-qubit gate reduce obviously when compared with those for the QFT over ZN.

Key words: quantum Fourier transform, semiclassical quantum Fourier transform, quantum algorithm

中图分类号:  (Quantum computation architectures and implementations)

  • 03.67.Lx
03.65.Sq (Semiclassical theories and applications) 03.65.Ta (Foundations of quantum mechanics; measurement theory) 03.67.-a (Quantum information)