  We present the detailed process of converting the classical Fourier Transform
algorithm into the quantum one by using QR decomposition. This provides an
example of a technique for building quantum algorithms using classical ones.
The Quantum Fourier Transform is one of the most important quantum subroutines
known at present, used in most algorithms that have exponential speed up
compared to the classical ones. We briefly review Fast Fourier Transform and
then make explicit all the steps that led to the quantum formulation of the
algorithm, generalizing Coppersmith's work.
