I want to add that quantum FFT performs the transform on the amplitudes in the n-qubit state. Thus its output is an n-qubit state with the amplitudes matching the fourier tranforms. We cannot actually directly extract the amplitudes of the resulting state (which is the actual transformed values) from the system, since a measurement collapses the state of the system.
While some people have figured out how to used the result of the quantum FFT to do useful things (e.g. Shor's algorithm), it does not actually provide us with the transformed values in the traditional sense as the classical algorithm does.
While some people have figured out how to used the result of the quantum FFT to do useful things (e.g. Shor's algorithm), it does not actually provide us with the transformed values in the traditional sense as the classical algorithm does.