Control-Target Inversion Property on Abelian Groups
Massoud, Amini (2009) Control-Target Inversion Property on Abelian Groups. Malaysian Journal of Mathematical Sciences, 3 (2). pp. 135-146. ISSN 1823-8343
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.
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