# A Subexponential-Time Quantum Algorithm for the Dihedral Hidden Subgroup Problem

@article{Kuperberg2005ASQ, title={A Subexponential-Time Quantum Algorithm for the Dihedral Hidden Subgroup Problem}, author={Greg Kuperberg}, journal={SIAM J. Comput.}, year={2005}, volume={35}, pages={170-188} }

We present a quantum algorithm for the dihedral hidden subgroup problem (DHSP) with time and query complexity $2^{O(\sqrt{\log\ N})}$. In this problem an oracle computes a function $f$ on the dihedral group $D_N$ which is invariant under a hidden reflection in $D_N$. By contrast, the classical query complexity of DHSP is $O(\sqrt{N})$. The algorithm also applies to the hidden shift problem for an arbitrary finitely generated abelian group.
The algorithm begins as usual with a quantum character… Expand

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