The Symmetric Group Defies Strong Fourier Sampling: Part I

Details The Symmetric Group Defies Strong Fourier Sampling: Part I The Symmetric Group Defies Strong Fourier Sampling: Part I

2005-01-12

arxiv.org/abs/quant-ph/0501056v3

Physics

Quantum Physics

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

Scientific paper

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.

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