A quantum lower bound for the query complexity of simon's problem

Authors:
Pascal Koiran;Vincent Nesme;Natacha Portier
Affiliations:
Laboratoire de l’Informatique du Parallélisme, Ecole Normale Supérieure de Lyon, Lyon Cedex 07, France;Laboratoire de l’Informatique du Parallélisme, Ecole Normale Supérieure de Lyon, Lyon Cedex 07, France;Laboratoire de l’Informatique du Parallélisme, Ecole Normale Supérieure de Lyon, Lyon Cedex 07, France
Venue:
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Year:
2005

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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 nontrivial 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.