t-bit semiclassical quantum Fourier transform |
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Authors: | XiangQun Fu WanSu Bao Chun Zhou Zhen Song |
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Institution: | Institute of Electronic Technology, The PLA Information Engineering University, Zhengzhou 450004, China |
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Abstract: | Because of the difficulty of building a high-dimensional quantum register, this paper presents an implementation of the high-dimensional
quantum Fourier transform (QFT) based on a low-dimensional quantum register. First, we define the t-bit semiclassical quantum Fourier transform. In terms of probability amplitude, we prove that the transform can realize quantum
Fourier transformation, illustrate that the requirement for the two-qubit gate reduces obviously, and further design a quantum
circuit of the transform. Combining the classical fixed-window method and the implementation of Shor’s quantum factorization
algorithm, we then redesign a circuit for Shor’s algorithm, whose required computation resource is approximately equal to
that of Parker’s. The requirement for elementary quantum gates for Parker’s algorithm is O(⌈ log N⌉3, and the quantum register for our circuit requires t−1 more dimensions than Parker’s. However, our circuit is t
2 times as fast as Parker’s, where t is the width of the window. |
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Keywords: | semiclassical quantum Fourier transform Shor's quantum algorithm window method |
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