The quantum query complexity of the abelian hidden subgroup problem

Abstract: Simon, in his FOCS’94 paper, was the first to show an exponential gap between classical and quantum computation. The problem he dealt with is now part of a well-studied class of problems, the hidden subgroup problems. We study Simon’s problem from the point of view of quantum query complexity and give here a first non-trivial lower bound on the query complexity of a hidden subgroup problem, namely Simon’s problem. More generally, we give a lower bound which is optimal up to a constant factor for any abelian group. [Copyright &y& Elsevier]