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DOI: 10.4230/LIPIcs.STACS.2008.1333
URN: urn:nbn:de:0030-drops-13333
URL: https://drops.dagstuhl.de/opus/volltexte/2008/1333/
Ambainis, Andris
Quantum search with variable times
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Abstract
Since Grover's seminal work, quantum search has been studied in great detail. In the usual search problem, we have a collection of $n$ items $x_1, ldots, x_n$ and we would like to find $i: x_i=1$. We consider a new variant of this problem in which evaluating $x_i$ for different $i$ may take a different number of time steps. Let $t_i$ be the number of time steps required to evaluate $x_i$. If the numbers $t_i$ are known in advance, we give an algorithm that solves the problem in $O(sqrt{t_1^2+t_2^2+ldots+t_n^2)$ steps. This is optimal, as we also show a matching lower bound. The case, when $t_i$ are not known in advance, can be solved with a polylogarithmic overhead. We also give an application of our new search algorithm to computing read-once functions.
BibTeX - Entry
@InProceedings{ambainis:LIPIcs:2008:1333,
author = {Andris Ambainis},
title = {{Quantum search with variable times}},
booktitle = {25th International Symposium on Theoretical Aspects of Computer Science},
pages = {49--61},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-06-4},
ISSN = {1868-8969},
year = {2008},
volume = {1},
editor = {Susanne Albers and Pascal Weil},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2008/1333},
URN = {urn:nbn:de:0030-drops-13333},
doi = {10.4230/LIPIcs.STACS.2008.1333},
annote = {Keywords: }
}
| Seminar: | 25th International Symposium on Theoretical Aspects of Computer Science | |
| Issue date: | 2008 | |
| Date of publication: | 06.02.2008 |
