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DOI: 10.4230/LIPIcs.STACS.2009.1801
URN: urn:nbn:de:0030-drops-18014
URL: https://drops.dagstuhl.de/opus/volltexte/2009/1801/
Arvind, Vikraman ; Mukhopadhyay, Partha
Quantum Query Complexity of Multilinear Identity Testing
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Abstract
Motivated by the quantum algorithm for testing commutativity of black-box groups (Magniez and Nayak, 2007), we study the following problem: Given a black-box finite ring by an additive generating set and a multilinear polynomial over that ring, also accessed as a black-box function (we allow the indeterminates of the polynomial to be commuting or noncommuting), we study the problem of testing if the polynomial is an \emph{identity} for the given ring. We give a quantum algorithm with query complexity sub-linear in the number of generators for the ring, when the number of indeterminates of the input polynomial is small (ideally a constant). Towards a lower bound, we also show a reduction from a version of the collision problem (which is well studied in quantum computation) to a variant of this problem.
BibTeX - Entry
@InProceedings{arvind_et_al:LIPIcs:2009:1801,
author = {Vikraman Arvind and Partha Mukhopadhyay},
title = {{Quantum Query Complexity of Multilinear Identity Testing}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {87--98},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Susanne Albers and Jean-Yves Marion},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2009/1801},
URN = {urn:nbn:de:0030-drops-18014},
doi = {10.4230/LIPIcs.STACS.2009.1801},
annote = {Keywords: Quantum algorithm, Identity testing, Query complexity, Multilinear polynomials}
}
| Keywords: | Quantum algorithm, Identity testing, Query complexity, Multilinear polynomials | |
| Seminar: | 26th International Symposium on Theoretical Aspects of Computer Science | |
| Issue date: | 2009 | |
| Date of publication: | 19.02.2009 |
