Dynamical analysis of Grover’s search algorithm in arbitrarily high-dimensional search spaces

Dynamical analysis of Grover’s search algorithm in arbitrarily high-dimensional search spaces We discuss at length the dynamical behavior of Grover’s search algorithm for which all the Walsh–Hadamard transformations contained in this algorithm are exposed to their respective random perturbations inducing the augmentation of the dimension of the search space. We give the concise and general mathematical formulations for approximately characterizing the maximum success probabilities of finding a unique desired state in a large unsorted database and their corresponding numbers of Grover iterations, which are applicable to the search spaces of arbitrary dimension and are used to answer a salient open problem posed by Grover (Phys Rev Lett 80:4329–4332, 1998). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Dynamical analysis of Grover’s search algorithm in arbitrarily high-dimensional search spaces

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Publisher
Springer US
Copyright
Copyright © 2015 by Springer Science+Business Media New York
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-015-1164-0
Publisher site
See Article on Publisher Site

Abstract

We discuss at length the dynamical behavior of Grover’s search algorithm for which all the Walsh–Hadamard transformations contained in this algorithm are exposed to their respective random perturbations inducing the augmentation of the dimension of the search space. We give the concise and general mathematical formulations for approximately characterizing the maximum success probabilities of finding a unique desired state in a large unsorted database and their corresponding numbers of Grover iterations, which are applicable to the search spaces of arbitrary dimension and are used to answer a salient open problem posed by Grover (Phys Rev Lett 80:4329–4332, 1998).

Journal

Quantum Information ProcessingSpringer Journals

Published: Oct 30, 2015

References

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