Quantum Information Processing, Vol. 6, No. 4, August 2007 (© 2007)
Quantum Partial Search of a Database with Several
and Vladimir E. Korepin
Received October 12, 2006; accepted February 19, 2007; Published online: August 22, 2007
We consider unstructured database separated into blocks of equal size. Blocks
containing target items are called target blocks. Blocks without target items are
called non-target blocks. We present a fast quantum algorithm, which ﬁnds one
of the target blocks. The algorithm uses the same oracle, which the main Grover
algorithm does. We study the simplest case, when each target block has the same
number of target items. Our algorithm is based on Boyer, Brassard, Hoyer, and
Tapp algorithm of searching database with several target items and on Grover–
Radhakrishnan algorithm of partial search. We minimize the number of queries to
the oracle. We analyze the algorithm for blocks of large size. In next publications
we shall consider more general case when the number of target items is different
in different target blocks.
KEY WORDS: database search; partial search; multiple target blocks; Grover
search; quantum algorithm; optimization.
PACS: 03.67.-a; 03.67.Lx.
Database search has many applications. Search algorithm enters as a
subroutine in many important algorithms. Grover discovered a quantum
algorithm, which searchs faster than classical.
It starts searching from
a uniform superposition of all input states in the database (5). Grover
algorithm was proven to be optimal.
If a database has one target item
Grover algorithm can ﬁnd it in
Department of Electronics Engineering, School of Information and Communication
Engineering, Sungkyunkwan University, Sungkyunkwan, Republic of Korea. E-mail:
C.N. Yang Institute for Theoretical Physics, State University of New York, Stony Brook,
NY 11794-3840, USA. E-mail: firstname.lastname@example.org
To whom correspondence should be addressed.
1570-0755/07/0800-0243/0 © 2007 Springer Science+Business Media, LLC