Circuit of Quantum Fractional Fourier Transform

被引:1
作者
Zhao, Tieyu [1 ]
Chi, Yingying [2 ]
机构
[1] Northeastern Univ Qinhuangdao, Informat Sci Teaching & Res Sect, Qinhuangdao 066004, Peoples R China
[2] Northeastern Univ Qinhuangdao, Coll Marxism, Qinhuangdao 066004, Peoples R China
关键词
quantum fractional Fourier transform; quantum Fourier transform; quantum phase estimation; quantum computing; IMAGE ENCRYPTION; REPRESENTATION;
D O I
10.3390/fractalfract7100743
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In this paper, we first use the quantum Fourier transform (QFT) and quantum phase estimation (QPE) to realize the quantum fractional Fourier transform (QFrFT). As diverse definitions of the discrete fractional Fourier transform (DFrFT) exist, the relationship between the QFrFT and a classical algorithm is then established; that is, we determine the classical algorithm corresponding to the QFrFT. Second, we observe that many definitions of the multi-fractional Fourier transform (mFrFT) are flawed: when we attempt to propose a design scheme for the quantum mFrFT, we find that there are many invalid weighting terms in the definition of the mFrFT. This flaw may have very significant impacts on relevant algorithms for signal processing and image encryption. Finally, we analyze the circuit of the QFrFT and the reasons for the observed defects.
引用
收藏
页数:15
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