A desired state can not be found with certainty for Grover’s algorithm in a possible three-dimensional complex subspace

A desired state can not be found with certainty for Grover’s algorithm in a possible... Using an accurate method, we prove that no matter what the initial superposition may be, neither a superposition of desired states nor a unique desired state can be found with certainty in a possible three-dimensional complex subspace, provided that the deflection angle Φ is not exactly equal to zero. By this method, we derive such a result that, if N is sufficiently large (where N denotes the total number of the desired and undesired states in an unsorted database), then corresponding to the case of identical rotation angles, the maximum success probability of finding a unique desired state is approximately equal to cos2 Φ for any given $${\Phi\in\left[0,\pi/2\right)}$$ . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

A desired state can not be found with certainty for Grover’s algorithm in a possible three-dimensional complex subspace

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Publisher
Springer US
Copyright
Copyright © 2010 by Springer Science+Business Media, LLC
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/s11128-010-0209-7
Publisher site
See Article on Publisher Site

Abstract

Using an accurate method, we prove that no matter what the initial superposition may be, neither a superposition of desired states nor a unique desired state can be found with certainty in a possible three-dimensional complex subspace, provided that the deflection angle Φ is not exactly equal to zero. By this method, we derive such a result that, if N is sufficiently large (where N denotes the total number of the desired and undesired states in an unsorted database), then corresponding to the case of identical rotation angles, the maximum success probability of finding a unique desired state is approximately equal to cos2 Φ for any given $${\Phi\in\left[0,\pi/2\right)}$$ .

Journal

Quantum Information ProcessingSpringer Journals

Published: Nov 4, 2010

References

  • Experimental NMR realization of a generalized quantum search algorithm
    Long, G.L.; Yan, H.Y.; Li, Y.S.; Tu, C.C.; Tao, J.X.; Chen, H.M.; Liu, M.L.; Zhang, X.; Luo, J.; Xiao, L.; Zeng, X.Z.

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