Quantum search algorithm for set operation

Quantum search algorithm for set operation The operations of data set, such as intersection, union and complement, are the fundamental calculation in mathematics. It’s very significant that designing fast algorithm for set operation. In this paper, the quantum algorithm for calculating intersection set $${\text{C}=\text{A}\cap \text{B}}$$ is presented. Its runtime is $${O\left( {\sqrt{\left| A \right|\times \left| B \right|\times \left|C \right|}}\right)}$$ for case $${\left| C \right|\neq \phi}$$ and $${O\left( {\sqrt{\left| A \right|\times \left| B \right|}}\right)}$$ for case $${\left| C \right|=\phi}$$ (i.e. C is empty set), while classical computation needs O (|A| × |B|) steps of computation in general, where |.| denotes the size of set. The presented algorithm is the combination of Grover’s algorithm, classical memory and classical iterative computation, and the combination method decrease the complexity of designing quantum algorithm. The method can be used to design other set operations as well. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Quantum search algorithm for set operation

Loading next page...
 
/lp/springer_journal/quantum-search-algorithm-for-set-operation-p4FiGovxRJ
Publisher
Springer US
Copyright
Copyright © 2012 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/s11128-012-0385-8
Publisher site
See Article on Publisher Site

Abstract

The operations of data set, such as intersection, union and complement, are the fundamental calculation in mathematics. It’s very significant that designing fast algorithm for set operation. In this paper, the quantum algorithm for calculating intersection set $${\text{C}=\text{A}\cap \text{B}}$$ is presented. Its runtime is $${O\left( {\sqrt{\left| A \right|\times \left| B \right|\times \left|C \right|}}\right)}$$ for case $${\left| C \right|\neq \phi}$$ and $${O\left( {\sqrt{\left| A \right|\times \left| B \right|}}\right)}$$ for case $${\left| C \right|=\phi}$$ (i.e. C is empty set), while classical computation needs O (|A| × |B|) steps of computation in general, where |.| denotes the size of set. The presented algorithm is the combination of Grover’s algorithm, classical memory and classical iterative computation, and the combination method decrease the complexity of designing quantum algorithm. The method can be used to design other set operations as well.

Journal

Quantum Information ProcessingSpringer Journals

Published: Mar 24, 2012

References

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
Access to DeepDyve database
Abstract access only
Unlimited access to over
18 million full-text articles
Print
20 pages/month
PDF Discount
20% off