The dihedral hidden subgroup problem

Abstract

We give an exposition of the hidden subgroup problem for dihedral groups from the point of view of the standard hidden subgroup quantum algorithm for finite groups. In particular, we recall the obstructions for strong Fourier sampling to succeed, but at the same time, show how the standard algorithm can be modified to establish polynomial quantum query complexity. Finally, we explain a new connection between the dihedral coset problem and cloning of quantum states.