Quantum Information Processing, Vol. 5, No. 3, June 2006 (© 2006)
Quest for Fast Partial Search Algorithm
Vladimir E. Korepin
and Jinfeng Liao
Received January 18, 2006; Accepted April 6, 2006; Published online May 10, 2006
The Grover quantum algorithm can ﬁnd a target item in a database faster than
any classical algorithm. In partial search, one trades accuracy for speed, and a
part of the database (a block) containing the target item can be found even
faster. We consider different partial search algorithms and argue that the
algorithm originally suggested by Grover and Radhakrishnan and modiﬁed by
Korepin is the optimal one. The efﬁciency of an algorithm is measured by the
number of queries to the oracle.
KEY WORDS: Quantum algorithms, searching and sorting, Groves algorithm,
PACS: 03.67.-a, 03.67.Lx.
Database searches have many applications and are used widely. They
occur as subroutines in many important algorithms, including NP com-
plete ones. Grover discovered a quantum algorithm that searches faster
than any classical algorithm.
It consists of a repetition of the Grover
, which operates on the computational quantum states. For
a database with a large number of entries N the number of repetitions
N . (1)
C.N. Yang Institute for Theoretical Physics, State University of New York at
Stony Brook, Stony Brook, NY 11794-3840, USA.
Department of Physics and Astronomy, State University of New York at Stony Brook,
Stony Brook, NY 11794-3840, USA.
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1570-0755/06/0600-0209/0 © 2006 Springer Science+Business Media, Inc.