On mathematical theory of the duality computers

On mathematical theory of the duality computers Recently, Long proposed a new type of quantum computers called duality computers or duality quantum computers. The duality computers based on the general quantum interference principle are much more powerful than an ordinary quantum computer. A mathematical theory for the duality computers has been presented by Gudder. However, he pointed out that a paradoxical situation of the mathematical theory occurs between the mixed state formalism and the pure state formalism. This paper argues for Gudder’s mathematical theory of the duality computers for the mixed state formalism. First, we point out two problems existing in the pure state description of the duality computers. Then, we present a new mathematical theory of the duality computers for the pure state formalism according with Gudder’s mixed state description, generalize the new mathematical theory of the duality computers in the density matrix formalism, and discuss some basic properties of the divider operators and combiner operators of the duality computers. The new mathematical theory can conquer the two problems mentioned above. Finally, we find that the nonunitary operations can be performed on every path of a quantum wave divider of the duality computers. Especially, we discuss in detail that the subwaves interact with environment by a CNOT gate. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

On mathematical theory of the duality computers

Loading next page...
 
/lp/springer_journal/on-mathematical-theory-of-the-duality-computers-8Ma0Zi0DXV
Publisher
Springer US
Copyright
Copyright © 2009 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/s11128-008-0093-6
Publisher site
See Article on Publisher Site

References

  • Mathematical theory of duality quantum computers
    Gudder, S.

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

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches

$49/month

Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.

$588

$360/year

billed annually
Start Free Trial

14-day Free Trial