Quantum Information Processing, Vol. 5, No. 1, February 2006 (© 2006)
Simple Algorithm for Partial Quantum Search
Vladimir E. Korepin
and Lov K. Grover
Received July 14, 2005; accepted October 29, 2005
Quite often in database search, we only need to extract portion of the informa-
tion about the satisfying item. We consider this problem in the following form:
the database of N items is separated into K blocks of size b = N/K elements
each and an algorithm has just to ﬁnd the block containing the item of interest.
The queries are exactly the same as in the standard database search problem. We
present a quantum algorithm for this problem of partial search that takes about
b fewer iterations than the quantum search algorithm.
KEY WORDS: Quantum computation; quantum algorithms; search algorithms.
PACS: 03.67.-a; 03.67.Lx.
Database search is one of the few applications for which a fast quantum
algorithm is known.
The Grover algorithm has been shown to be opti-
mal and cannot be improved even by a single query.
Therefore it is
of great interest to ﬁnd any circumstance under which we can improve
the performance of the quantum search algorithm. The problem of partial
database search is also of independent interest. For example when using
Google to search the internet (which is a large database), we are typically
interested in only some of the attributes of the entity being searched—
e.g. while searching for a grocery store in the neighborhood, we may only
want the address of the store, not its corporate information. Partial search
algorithm search for a block with the target item, not for the target item
itself. It was ﬁrst introduced by Mark Heiligman in,
as a part of algo-
rithm for list matching.
C.N. Yang Institute for Theoretical Physics, State University of New York at Stony Brook,
Stony Brook, NY 11794-3840, USA. E-mail: email@example.com
Bell Laboratories, Lucent Technologies, 600-700 Mountain Avenue, Murray Hill, NJ 07974,
USA. E-mail: firstname.lastname@example.org
1570-0755/06/0200-0005/0 © 2006 Springer Science+Business Media, Inc.