A new sure-success generalization of Grover iteration and its application to weight decision problem of Boolean functions

A new sure-success generalization of Grover iteration and its application to weight decision... In two recent papers, a sure-success version of the Grover iteration has been applied to solve the weight decision problem of a Boolean function and it is shown that it is quadratically faster than any classical algorithm (Braunstein et al. in J Phys A Math Theor 40:8441, 2007; Choi and Braunstein in Quantum Inf Process 10:177, 2011). In this paper, a new approach is proposed to generalize the Grover’s iteration so that it becomes exact and its application to the same problem is studied. The regime where a small number of iterations is applied is the main focus of this work. This task is accomplished by presenting the conditions on the decidability of the weights where the decidability problem is reduced to a system of algebraic equations of a single variable. Thus, it becomes easier to decide on distinguishability by solving these equations analytically and, if not possible, numerically. In addition, it is observed that the number of iterations scale as the square root of the iteration number of the corresponding classical probabilistic algorithms. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

A new sure-success generalization of Grover iteration and its application to weight decision problem of Boolean functions

Loading next page...
 
/lp/springer_journal/a-new-sure-success-generalization-of-grover-iteration-and-its-rUXHWmAHEs
Publisher
Springer US
Copyright
Copyright © 2013 by Springer Science+Business Media New York
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/s11128-013-0606-9
Publisher site
See Article on Publisher Site

Abstract

In two recent papers, a sure-success version of the Grover iteration has been applied to solve the weight decision problem of a Boolean function and it is shown that it is quadratically faster than any classical algorithm (Braunstein et al. in J Phys A Math Theor 40:8441, 2007; Choi and Braunstein in Quantum Inf Process 10:177, 2011). In this paper, a new approach is proposed to generalize the Grover’s iteration so that it becomes exact and its application to the same problem is studied. The regime where a small number of iterations is applied is the main focus of this work. This task is accomplished by presenting the conditions on the decidability of the weights where the decidability problem is reduced to a system of algebraic equations of a single variable. Thus, it becomes easier to decide on distinguishability by solving these equations analytically and, if not possible, numerically. In addition, it is observed that the number of iterations scale as the square root of the iteration number of the corresponding classical probabilistic algorithms.

Journal

Quantum Information ProcessingSpringer Journals

Published: Jul 2, 2013

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