  We present the view of quantum algorithms as a search-theoretic problem. We
show that the Fourier transform, used to solve the Abelian hidden subgroup
problem, is an example of an efficient elimination observable which eliminates
a constant fraction of the candidate secret states with high probability.
Finally, we show that elimination observables do not always exist by
considering the geometry of the hidden subgroup states of the dihedral group
D_N.
