Adversary lower bounds for nonadaptive quantum algorithms

Authors:
Pascal Koiran;Jürgen Landes;Natacha Portier;Penghui Yao
Affiliations:
LIP,11UMR 5668 ENS Lyon, CNRS, UCBL associée à l'INRIA. Work done when Landes and Yao were visiting LIP with financial support from the Mathlogaps program. Ecole Normale Supérieure ...;School of Mathematics, University of Manchester, UK;LIP,11UMR 5668 ENS Lyon, CNRS, UCBL associée à l'INRIA. Work done when Landes and Yao were visiting LIP with financial support from the Mathlogaps program. Ecole Normale Supérieure ...;State Key Laboratory of Computer Science, Chinese Academy of Sciences, China
Venue:
Journal of Computer and System Sciences
Year:
2010

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Abstract

We present two general methods for proving lower bounds on the query complexity of nonadaptive quantum algorithms. Both methods are based on the adversary method of Ambainis. We show that they yield optimal lower bounds for several natural problems, and we challenge the reader to determine the nonadaptive quantum query complexity of the ''1-to-1 versus 2-to-1'' problem and of Hidden Translation. In addition to the results presented at Wollic 2008 in the conference version of this paper, we show that the lower bound given by the second method is always at least as good (and sometimes better) as the lower bound given by the first method. We also compare these two quantum lower bounds to probabilistic lower bounds.