Optimal quantum query bounds for almost all Boolean functions

Open Access
Authors
Publication date 02-2013
Host editors
  • N. Portier
  • T. Wilke
Book title 30th International Symposium on Theoretical Aspects of Computer Science
Book subtitle STACS '13, February 27th to March 2nd, 2013, Kiel, Germany
ISBN (electronic)
  • 9783939897507
Series Leibniz International Proceedings in Informatics
Event 30th International Symposium on Theoretical Aspects of Computer Science
Pages (from-to) 446-453
Publisher Saarbrücken/Wadern: Schloss Dagstuhl - Leibniz-Zentrum für Informatik
Organisations
  • Interfacultary Research - Institute for Logic, Language and Computation (ILLC)
Abstract We show that almost all n-bit Boolean functions have bounded-error quantum query complexity at least n/2, up to lower-order terms. This improves over an earlier n/4 lower bound of Ambainis (A. Ambainis, 1999), and shows that van Dam's oracle interrogation (W. van Dam, 1998) is essentially optimal for almost all functions. Our proof uses the fact that the acceptance probability of a T-query algorithm can be written as the sum of squares of degree-T polynomials.
Document type Conference contribution
Language English
Published at https://doi.org/10.4230/LIPIcs.STACS.2013.446
Other links https://drops.dagstuhl.de/opus/portals/lipics/index.php?semnr=13002
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