# 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}
}
• G. Kuperberg
• Published 14 February 2003
• Computer Science
• SIAM J. Comput.
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…
290 Citations

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