Ambainis, Andris
Quantum search with variable times
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 readonce 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 = {4961},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783939897064},
ISSN = {18688969},
year = {2008},
volume = {1},
editor = {Susanne Albers and Pascal Weil},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2008/1333},
URN = {urn:nbn:de:0030drops13333},
doi = {10.4230/LIPIcs.STACS.2008.1333},
annote = {Keywords: }
}
2008
Seminar: 

25th International Symposium on Theoretical Aspects of Computer Science

Issue date: 

2008 
Date of publication: 

2008 