Control-target inversion property on Abelian groups - Amini, Massoud (Universiti Putra Malaysia Press, 2009)
We show that the quantum Fourier transform on finite fields used to solve query problems is a special case of the usual quantum Fourier transform on finite Abelian groups. We show that the control-target inversion property holds in general. We apply this to get a sharp query complexity separation between classical and quantum algorithms for a hidden homomorphism problem on finite Abelian groups.