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DOI: 10.4230/LIPIcs.STACS.2013.446
URN: urn:nbn:de:0030-drops-39557
URL: http://drops.dagstuhl.de/opus/volltexte/2013/3955/
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Ambainis, Andris ; Backurs, Arturs ; Smotrovs, Juris ; de Wolf, Ronald

Optimal quantum query bounds for almost all Boolean functions

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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.

BibTeX - Entry

@InProceedings{ambainis_et_al:LIPIcs:2013:3955,
  author =	{Andris Ambainis and Arturs Backurs and Juris Smotrovs and Ronald de Wolf},
  title =	{{Optimal quantum query bounds for almost all Boolean functions}},
  booktitle =	{30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
  pages =	{446--453},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-50-7},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{20},
  editor =	{Natacha Portier and Thomas Wilke},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2013/3955},
  URN =		{urn:nbn:de:0030-drops-39557},
  doi =		{10.4230/LIPIcs.STACS.2013.446},
  annote =	{Keywords: Quantum computing, query complexity, lower bounds, polynomial method}
}

Keywords: Quantum computing, query complexity, lower bounds, polynomial method
Seminar: 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)
Issue Date: 2013
Date of publication: 18.02.2013


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