A quantum lower bound for the query complexity of Simon's problem
Pascal Koiran, Vincent Nesme, Natacha Portier · arXiv (Cornell University) · 2005
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 nontrivial lower bound on the query complexity of a hidden subgroup problem, namely Simon's problem. Our bound is optimal up to a constant factor.