Strong Fourier Sampling Fails over $G^n$
Gorjan Alagic; Cristopher Moore; Alexander Russell · 2005 · arXiv
WASTE classifies this as Negative / Null Result Report · AI classification, approximate
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Abstract (excerpt)
We present a negative result regarding the hidden subgroup problem on the powers $G^n$ of a fixed group $G$. Under a condition on the base group $G$, we prove that strong Fourier sampling cannot distinguish some subgroups of $G^n$. Since strong sampling is in fact the optimal measurement on a coset state, this shows that we have no hope of efficiently solving the hidden subgroup problem over these groups with separable measurements on coset states (that is, using any polynomial number of single-register coset state experiments). Base groups satisfying our condition include all nonabelian simpl
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Metadata source: arXiv