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

Loading next page...
 
/lp/springer_journal/a-desired-state-can-not-be-found-with-certainty-for-grover-s-algorithm-yBwgFusWnN
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.

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve Freelancer

DeepDyve Pro

Price
FREE
$49/month

$360/year
Save searches from Google Scholar, PubMed
Create lists to organize your research
Export lists, citations
Read DeepDyve articles
Abstract access only
Unlimited access to over
18 million full-text articles
Print
20 pages/month
PDF Discount
20% off