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.

中文翻译：

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二面体隐子群问题

我们从有限群的标准隐子群量子算法的角度阐述了二面体群的隐子群问题。特别是，我们回顾了强傅立叶采样成功的障碍，但同时展示了如何修改标准算法以建立多项式量子查询复杂度。最后，我们解释了二面角陪集问题与量子态克隆之间的新联系。