Quantum algorithms ( CO 781 / CS 867 / QIC 823 , Winter 2011 )

The abelian HSP Recall that in the hidden subgroup problem, we are given a function f : G→ S (for a known group G and a finite set S) satisfying f(x) = f(y) iff x and y are in the same (left) coset of the hidden subgroup H ≤ G. In this lecture we will use additive notation for the group operation of an abelian group, so we have f(x) = f(x) iff x − y ∈ H. The strategy for the general abelian HSP closely follows the algorithm for the discrete log problem, which solves a particular instance of the HSP in ZN × ZN . We begin by creating a uniform superposition over the group,