License: Creative Commons Attribution-NoDerivs 3.0 Unported license (CC BY-ND 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2013.434
URN: urn:nbn:de:0030-drops-39548
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2013/3954/
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Magnin, Loïck ; Roland, Jérémie

Explicit relation between all lower bound techniques for quantum query complexity

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Abstract

The polynomial method and the adversary method are the two main techniques to prove lower bounds on quantum query complexity, and they have so far been considered as unrelated approaches. Here, we show an explicit reduction from the polynomial method to the multiplicative adversary method. The proof goes by extending the polynomial method from Boolean functions to quantum state generation problems. In the process, the bound is even strengthened. We then show that this extended polynomial method is a special case of the multiplicative adversary method with an adversary matrix that is independent of the function. This new result therefore provides insight on the reason why in some cases the adversary method is stronger than the polynomial method. It also reveals a clear picture of the relation between the different lower bound techniques, as it implies that all known techniques reduce to the multiplicative adversary method.

BibTeX - Entry

@InProceedings{magnin_et_al:LIPIcs:2013:3954,
  author =	{Loick Magnin and J{\'e}r{\'e}mie Roland},
  title =	{{Explicit relation between all lower bound techniques for quantum query complexity}},
  booktitle =	{30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)},
  pages =	{434--445},
  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/2013/3954},
  URN =		{urn:nbn:de:0030-drops-39548},
  doi =		{10.4230/LIPIcs.STACS.2013.434},
  annote =	{Keywords: Quantum computation, lower bound, adversary method, polynomial method}
}

Keywords: Quantum computation, lower bound, adversary method, polynomial method
Collection: 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)
Issue Date: 2013
Date of publication: 26.02.2013

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