Quantum circuit for the fast Fourier transform

@article{Asaka2020QuantumCF,
  title={Quantum circuit for the fast Fourier transform},
  author={Ryo Asaka and Kazumitsu Sakai and Ryoko Yahagi},
  journal={Quantum Information Processing},
  year={2020},
  volume={19},
  pages={1-20}
}
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… 
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