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

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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

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