The Symmetric Group Defies Strong Fourier Sampling: Part I
Quantum Physics
2007-05-23 v3 Computational Complexity
Abstract
We resolve the question of whether Fourier sampling can efficiently solve the hidden subgroup problem. Specifically, we show that the hidden subgroup problem over the symmetric group cannot be efficiently solved by strong Fourier sampling, even if one may perform an arbitrary POVM on the coset state. Our results apply to the special case relevant to the Graph Isomorphism problem.
Keywords
Cite
@article{arxiv.quant-ph/0501056,
title = {The Symmetric Group Defies Strong Fourier Sampling: Part I},
author = {Cristopher Moore and Alexander Russell and Leonard J. Schulman},
journal= {arXiv preprint arXiv:quant-ph/0501056},
year = {2007}
}
Comments
19 pages; v2 fix typos; v3 adds material on structured permutations