The quantum query complexity of the abelian hidden subgroup problem

Authors:
Pascal Koiran;Vincent Nesme;Natacha Portier
Affiliations:
Laboratoire de lInformatique du Parallélisme, École Normale Supérieure de Lyon, 46, allée dItalie, 69364 Lyon, Cedex 07, France;Laboratoire de lInformatique du Parallélisme, École Normale Supérieure de Lyon, 46, allée dItalie, 69364 Lyon, Cedex 07, France;Laboratoire de lInformatique du Parallélisme, École Normale Supérieure de Lyon, 46, allée dItalie, 69364 Lyon, Cedex 07, France
Venue:
Theoretical Computer Science
Year:
2007

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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.