A bounded-error quantum polynomial-time algorithm for two graph bisection problems

A bounded-error quantum polynomial-time algorithm for two graph bisection problems The aim of the paper was to propose a bounded-error quantum polynomial-time algorithm for the max-bisection and the min-bisection problems. The max-bisection and the min-bisection problems are fundamental NP-hard problems. Given a graph with even number of vertices, the aim of the max-bisection problem is to divide the vertices into two subsets of the same size to maximize the number of edges between the two subsets, while the aim of the min-bisection problem is to minimize the number of edges between the two subsets. The proposed algorithm runs in $$O(m^2)$$ O ( m 2 ) for a graph with m edges and in the worst case runs in $$O(n^4)$$ O ( n 4 ) for a dense graph with n vertices. The proposed algorithm targets a general graph by representing both problems as Boolean constraint satisfaction problems where the set of satisfied constraints are simultaneously maximized/minimized using a novel iterative partial negation and partial measurement technique. The algorithm is shown to achieve an arbitrary high probability of success of $$1-\epsilon $$ 1 - ϵ for small $$\epsilon >0$$ ϵ > 0 using a polynomial space resources. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

A bounded-error quantum polynomial-time algorithm for two graph bisection problems

Loading next page...
 
/lp/springer_journal/a-bounded-error-quantum-polynomial-time-algorithm-for-two-graph-ENGsFOHNsh
Publisher
Springer US
Copyright
Copyright © 2015 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/s11128-015-1069-y
Publisher site
See Article on Publisher Site

Abstract

The aim of the paper was to propose a bounded-error quantum polynomial-time algorithm for the max-bisection and the min-bisection problems. The max-bisection and the min-bisection problems are fundamental NP-hard problems. Given a graph with even number of vertices, the aim of the max-bisection problem is to divide the vertices into two subsets of the same size to maximize the number of edges between the two subsets, while the aim of the min-bisection problem is to minimize the number of edges between the two subsets. The proposed algorithm runs in $$O(m^2)$$ O ( m 2 ) for a graph with m edges and in the worst case runs in $$O(n^4)$$ O ( n 4 ) for a dense graph with n vertices. The proposed algorithm targets a general graph by representing both problems as Boolean constraint satisfaction problems where the set of satisfied constraints are simultaneously maximized/minimized using a novel iterative partial negation and partial measurement technique. The algorithm is shown to achieve an arbitrary high probability of success of $$1-\epsilon $$ 1 - ϵ for small $$\epsilon >0$$ ϵ > 0 using a polynomial space resources.

Journal

Quantum Information ProcessingSpringer Journals

Published: Jul 14, 2015

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