Quantum search with certainty based on modified Grover algorithms: optimum choice of parameters

In the original Grover algorithm, an exact or almost exact search such that the success probability is unity or infinitesimally close to unity is possible only for certain values of the fraction λ =  M / N where M is the number of marked items that are stored in an unsorted database of N items. Ther...

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Bibliographic Details
Published in:Quantum information processing 2013-05, Vol.12 (5), p.1897-1914
Main Authors: Toyama, F. M., van Dijk, W., Nogami, Y.
Format: Article
Language:English
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Classical and quantum physics: mechanics and fields
Computer science
control theory
systems
Data Structures and Information Theory
Exact sciences and technology
Mathematical Physics
Physics
Physics and Astronomy
Quantum computation
Quantum Computing
Quantum information
Quantum Information Technology
Quantum Physics
Spintronics
Theoretical computing
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Summary:In the original Grover algorithm, an exact or almost exact search such that the success probability is unity or infinitesimally close to unity is possible only for certain values of the fraction λ =  M / N where M is the number of marked items that are stored in an unsorted database of N items. There are various modified algorithms with an adjustable phase or phases such that an exact search can be done for any value of λ by means of a finite number of Grover-type operations. Among them, the algorithm proposed by Long is the simplest in the sense that it has only one adjustable phase and that the phase can be obtained in a closed form. We show that other more general algorithms with additional phases are not more efficient than Long’s version with a single phase.
ISSN:1570-0755
1573-1332
DOI:10.1007/s11128-012-0498-0