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DOI: 10.4230/LIPIcs.ITCS.2019.19
URN: urn:nbn:de:0030-drops-101126
URL: https://drops.dagstuhl.de/opus/volltexte/2018/10112/
Chailloux, André
A Note on the Quantum Query Complexity of Permutation Symmetric Functions
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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 | |
| Seminar: | 10th Innovations in Theoretical Computer Science Conference (ITCS 2019) | |
| Issue date: | 2018 | |
| Date of publication: | 08.01.2019 |
