  We consider a recently proposed generalisation of the abelian hidden subgroup
problem: the shifted subset problem. The problem is to determine a subset S of
some abelian group, given access to quantum states of the form |S+x>, for some
unknown shift x. We give quantum algorithms to find Hamming spheres and other
subsets of the boolean cube {0,1}^n. The algorithms have time complexity
polynomial in n and give rise to exponential separations from classical
computation.
