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Generalized Ramsey numbers through adiabatic quantum optimization

Generalized Ramsey numbers through adiabatic quantum optimization Ramsey theory is an active research area in combinatorics whose central theme is the emergence of order in large disordered structures, with Ramsey numbers marking the threshold at which this order first appears. For generalized Ramsey numbers r(G, H), the emergent order is characterized by graphs G and H. In this paper we: (i) present a quantum algorithm for computing generalized Ramsey numbers by reformulating the computation as a combinatorial optimization problem which is solved using adiabatic quantum optimization; and (ii) determine the Ramsey numbers $$r({\mathscr {T}}_{m},{\mathscr {T}}_{n})$$ r ( T m , T n ) for trees of order $$m,n = 6,7,8$$ m , n = 6 , 7 , 8 , most of which were previously unknown. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Generalized Ramsey numbers through adiabatic quantum optimization

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References (24)

Publisher
Springer Journals
Copyright
Copyright © 2016 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
DOI
10.1007/s11128-016-1363-3
Publisher site
See Article on Publisher Site

Abstract

Ramsey theory is an active research area in combinatorics whose central theme is the emergence of order in large disordered structures, with Ramsey numbers marking the threshold at which this order first appears. For generalized Ramsey numbers r(G, H), the emergent order is characterized by graphs G and H. In this paper we: (i) present a quantum algorithm for computing generalized Ramsey numbers by reformulating the computation as a combinatorial optimization problem which is solved using adiabatic quantum optimization; and (ii) determine the Ramsey numbers $$r({\mathscr {T}}_{m},{\mathscr {T}}_{n})$$ r ( T m , T n ) for trees of order $$m,n = 6,7,8$$ m , n = 6 , 7 , 8 , most of which were previously unknown.

Journal

Quantum Information Processing – Springer Journals

Published: Jun 13, 2016

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