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 2O( √ log N). In this problem an oracle computes a function f on the dihedral group DN which is invariant under a hidden reflection in DN . By contrast, the classical query complexity of DHSP is O( √ 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 transform, which in the… CONTINUE READING
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