Quantum Information Processing, Vol. 6, No. 1, February 2007 (© 2006)
Sure Success Partial Search
Thomas A. Walker,
Samuel L. Braunstein
Received March 16, 2006; accepted June 12, 2006; Published online November 28, 2006
Partial search has been proposed recently for ﬁnding the target block containing a
target element with fewer queries than the full Grover search algorithm which can
locate the target precisely. Since such partial searches will likely be used as sub-
routines for larger algorithms their success rate is important. We propose a par-
tial search algorithm which achieves success with unit probability.
KEY WORDS: Quantum database search; Grover’s algorithm; partial search;
PACS: 03.67.Lx; 03.67.-a.
In 1985 Deutsch designed a quantum algorithm which evaluates whether
the two outputs of a Boolean function are the same or not using only
one function evaluation.
Deutsch and Jozsa generalized this algorithm
for a more general case such as whether a given Boolean function is con-
stant or balanced. This algorithm demonstrated an exponential speed-up
on a quantum machine compared to the best performance on classical
The most important contribution in this ﬁeld was achieved
when Shor discovered a polynomial-time quantum algorithm for factoring
and computing discrete logarithms—yielding an exponentially faster algo-
rithm than the best known classical ones.
After this breakthrough many
researchers started to ﬁnd various applications, especially in cryptanalysis.
On the other hand, Grover discovered the quantum (virtual) database
search algorithm which yields a quadratic speed-up compared to classi-
cal database searches.
Since the database search algorithm is one of
Department of Computer Science, University of York, York, Y010 5DD, UK.
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