The Symmetric Group Defies Strong Fourier Sampling: Part I

Moore, Cristopher; Russell, Alexander; Schulman, Leonard J.

The Symmetric Group Defies Strong Fourier Sampling: Part I

Authors

Moore, Cristopher

Russell, Alexander

Schulman, Leonard J.

Description

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.
19 pages; v2 fix typos; v3 adds material on structured permutations