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Quantum Physics

arXiv:1911.03055 (quant-ph)
[Submitted on 8 Nov 2019 (v1), last revised 9 Aug 2020 (this version, v3)]

Title:Quantum circuit for the fast Fourier transform

Authors:Ryo Asaka, Kazumitsu Sakai, Ryoko Yahagi
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Abstract:We propose an implementation of the algorithm for the fast Fourier transform (FFT) as a quantum circuit consisting of a combination of some quantum gates. In our implementation, a data sequence is expressed by a tensor product of vector spaces. Namely, our FFT is defined as a transformation of the tensor product of quantum states. It is essentially different from the so-called quantum Fourier transform (QFT) defined to be a linear transformation of the amplitudes for the superposition of quantum states. The quantum circuit for the FFT consists of several circuits for elementary arithmetic operations such as a quantum adder, subtractor and shift operations, which are implemented as effectively as possible. Namely, our circuit does not generate any garbage bits. The advantages of our method compared to the QFT are its high versatility, and data storage efficiency in terms, for instance, of the quantum image processing.
Comments: 20 pages, typos corrected, published version
Subjects: Quantum Physics (quant-ph)
Cite as: arXiv:1911.03055 [quant-ph]
  (or arXiv:1911.03055v3 [quant-ph] for this version)
  https://doi.org/10.48550/arXiv.1911.03055
Journal reference: Quantum Inf Process 19, 277 (2020)
Related DOI: https://doi.org/10.1007/s11128-020-02776-5

Submission history

From: Kazumitsu Sakai [view email]
[v1] Fri, 8 Nov 2019 05:18:56 UTC (1,747 KB)
[v2] Wed, 29 Apr 2020 13:08:20 UTC (1,599 KB)
[v3] Sun, 9 Aug 2020 09:41:34 UTC (1,599 KB)
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