The Fast Fourier Transform is described in the Quantum Domain

[.Scott]

TL;DR

The Fast Fourier Transform is described in the Quantum Domain.

In August, "Quantum Information Processing" published an article describing a full FFT in the quantum domain - a so-called QFFT, not to be confused with the simpler QFT.

According to the publication:

The method is applicable to all the problems processed by the conventional FFT. Moreover, the QFFT can simultaneously process multiple data sets which can be generated by U(N) transformations realized by quantum gates as in ["Elementary gates for quantum computation"].