Partial adiabatic quantum search algorithm and its extensions

Partial adiabatic quantum search algorithm and its extensions In this paper, we again discuss quantum search by partial adiabatic evolution, which was first proposed by Zhang et al. In contrast to previous conclusions, we show that partial adiabatic search does not improve the time complexity of a local adiabatic algorithm. Firstly, we show a variant of this algorithm and find that it is equivalent to the original partial adiabatic algorithm, in the sense of the same time complexity. But we give two alternate viewpoints on this “new” adiabatic algorithm—“global” adiabatic evolution and local adiabatic evolution approaches, respectively. Then, we discuss how global and local adiabatic quantum search can be recast in the framework of partial adiabatic search algorithm. It is found here that the former two algorithms could be considered as special cases of the later one when appropriately tuning the evolution interval of it. Also this implies the flexibility of quantum search based on partial adiabatic evolution. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Partial adiabatic quantum search algorithm and its extensions

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Publisher
Springer US
Copyright
Copyright © 2013 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/s11128-013-0557-1
Publisher site
See Article on Publisher Site

Abstract

In this paper, we again discuss quantum search by partial adiabatic evolution, which was first proposed by Zhang et al. In contrast to previous conclusions, we show that partial adiabatic search does not improve the time complexity of a local adiabatic algorithm. Firstly, we show a variant of this algorithm and find that it is equivalent to the original partial adiabatic algorithm, in the sense of the same time complexity. But we give two alternate viewpoints on this “new” adiabatic algorithm—“global” adiabatic evolution and local adiabatic evolution approaches, respectively. Then, we discuss how global and local adiabatic quantum search can be recast in the framework of partial adiabatic search algorithm. It is found here that the former two algorithms could be considered as special cases of the later one when appropriately tuning the evolution interval of it. Also this implies the flexibility of quantum search based on partial adiabatic evolution.

Journal

Quantum Information ProcessingSpringer Journals

Published: Mar 9, 2013

References

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