License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2019.19
URN: urn:nbn:de:0030-drops-101126
URL: https://drops.dagstuhl.de/opus/volltexte/2018/10112/
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Chailloux, André

A Note on the Quantum Query Complexity of Permutation Symmetric Functions

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LIPIcs-ITCS-2019-19.pdf (0.4 MB)

Abstract

It is known since the work of [Aaronson and Ambainis, 2014] that for any permutation symmetric function f, the quantum query complexity is at most polynomially smaller than the classical randomized query complexity, more precisely that R(f) = O~(Q^7(f)). In this paper, we improve this result and show that R(f) = O(Q^3(f)) for a more general class of symmetric functions. Our proof is constructive and relies largely on the quantum hardness of distinguishing a random permutation from a random function with small range from Zhandry [Zhandry, 2015].

BibTeX - Entry

@InProceedings{chailloux:LIPIcs:2018:10112,
  author =	{Andr{\'e} Chailloux},
  title =	{{A Note on the Quantum Query Complexity of Permutation Symmetric Functions}},
  booktitle =	{10th Innovations in Theoretical Computer Science  Conference (ITCS 2019)},
  pages =	{19:1--19:7},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-095-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{124},
  editor =	{Avrim Blum},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/10112},
  URN =		{urn:nbn:de:0030-drops-101126},
  doi =		{10.4230/LIPIcs.ITCS.2019.19},
  annote =	{Keywords: quantum query complexity, permutation symmetric functions}
}

Keywords: quantum query complexity, permutation symmetric functions
Collection: 10th Innovations in Theoretical Computer Science Conference (ITCS 2019)
Issue Date: 2018
Date of publication: 08.01.2019

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