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Quantum Weighted Fractional Fourier Transform

Author

Listed:
  • Tieyu Zhao

    (Information Science Teaching and Research Section, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China)

  • Tianyu Yang

    (Sports Department, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China)

  • Yingying Chi

    (Information Science Teaching and Research Section, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China)

Abstract

Quantum Fourier transform (QFT) is an important part of many quantum algorithms. However, there are few reports on quantum fractional Fourier transform (QFRFT). The main reason is that the definitions of fractional Fourier transform (FRFT) are diverse, while some definitions do not include unitarity, which leads to some studies pointing out that there is no QFRFT. In this paper, we first present a reformulation of the weighted fractional Fourier transform (WFRFT) and prove its unitarity, thereby proposing a quantum weighted fractional Fourier transform (QWFRFT). The proposal of QWFRFT provides the possibility for many quantum implementations of signal processing.

Suggested Citation

  • Tieyu Zhao & Tianyu Yang & Yingying Chi, 2022. "Quantum Weighted Fractional Fourier Transform," Mathematics, MDPI, vol. 10(11), pages 1-13, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1896-:d:829947
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    Cited by:

    1. Fernando L. Pelayo & Mauro Mezzini, 2022. "Preface to the Special Issue on “Quantum Computing Algorithms and Computational Complexity”," Mathematics, MDPI, vol. 10(21), pages 1-3, October.

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