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

  title={A Subexponential-Time Quantum Algorithm for the Dihedral Hidden Subgroup Problem},
  author={Greg Kuperberg},
  journal={SIAM J. Comput.},
  • 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… 

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