The dihedral hidden subgroup problem
Quantum Physics
2024-04-11 v2 Computational Complexity
Abstract
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.
Cite
@article{arxiv.2106.09907,
title = {The dihedral hidden subgroup problem},
author = {Imin Chen and David Sun},
journal= {arXiv preprint arXiv:2106.09907},
year = {2024}
}
Comments
19 pages, expanded survey content and additional no-go theorems added