Quantum algorithm for the asymmetric weight decision problem and its generalization to multiple weights

Quantum algorithm for the asymmetric weight decision problem and its generalization to multiple... As one of the applications of Grover search, an exact quantum algorithm for the symmetric weight decision problem of a Boolean function has been proposed recently. Although the proposed method shows a quadratic speedup over the classical approach, it only applies to the symmetric case of a Boolean function whose weight is one of the pair {0 < w 1 < w 2 < 1, w 1 + w 2 = 1}. In this article, we generalize this algorithm in two ways. Firstly, we propose a quantum algorithm for the more general asymmetric case where {0 < w 1 < w 2 < 1}. This algorithm is exact and computationally optimal. Secondly, we build on this to exactly solve the multiple weight decision problem for a Boolean function whose weight as one of {0 < w 1 < w 2 < · · · < w m  < 1}. This extended algorithm continues to show a quantum advantage over classical methods. Thirdly, we compare the proposed algorithm with the quantum counting method. For the case with two weights, the proposed algorithm shows slightly lower complexity. For the multiple weight case, the two approaches show different performance depending on the number of weights and the number of solutions. For smaller number of weights and larger number of solutions, the weight decision algorithm can show better performance than the quantum counting method. Finally, we discuss the relationship between the weight decision problem and the quantum state discrimination problem. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Quantum algorithm for the asymmetric weight decision problem and its generalization to multiple weights

Loading next page...
 
/lp/springer_journal/quantum-algorithm-for-the-asymmetric-weight-decision-problem-and-its-dIYwYUDtGL
Publisher
Springer Journals
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/s11128-010-0187-9
Publisher site
See Article on Publisher Site

Abstract

As one of the applications of Grover search, an exact quantum algorithm for the symmetric weight decision problem of a Boolean function has been proposed recently. Although the proposed method shows a quadratic speedup over the classical approach, it only applies to the symmetric case of a Boolean function whose weight is one of the pair {0 < w 1 < w 2 < 1, w 1 + w 2 = 1}. In this article, we generalize this algorithm in two ways. Firstly, we propose a quantum algorithm for the more general asymmetric case where {0 < w 1 < w 2 < 1}. This algorithm is exact and computationally optimal. Secondly, we build on this to exactly solve the multiple weight decision problem for a Boolean function whose weight as one of {0 < w 1 < w 2 < · · · < w m  < 1}. This extended algorithm continues to show a quantum advantage over classical methods. Thirdly, we compare the proposed algorithm with the quantum counting method. For the case with two weights, the proposed algorithm shows slightly lower complexity. For the multiple weight case, the two approaches show different performance depending on the number of weights and the number of solutions. For smaller number of weights and larger number of solutions, the weight decision algorithm can show better performance than the quantum counting method. Finally, we discuss the relationship between the weight decision problem and the quantum state discrimination problem.

Journal

Quantum Information ProcessingSpringer Journals

Published: Jul 13, 2010

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 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

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