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Proceedings Paper

Quantum optimization and maximum clique problems
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Paper Abstract

This paper describes a new approach to global optimization and control uses geometric methods and modern quantum mathematics. Polynomial extremal problems (PEP) are considered. PEP constitute one of the most important subclasses of nonlinear programming models. Their distinctive feature is that an objective function and constraints can be expressed by polynomial functions in one or several variables. A general approach to optimization based on quantum holonomic computing algorithms and instanton mechanism. An optimization method based on geometric Lie - algebraic structures on Grassmann manifolds and related with Lax type flows is proposed. Making use of the differential geometric techniques it is shown that associated holonomy groups properly realizing quantum computation can be effectively found concerning polynomial problems. Two examples demonstrating calculation aspects of holonomic quantum computer and maximum clique problems in very large graphs, are considered in detail.

Paper Details

Date Published: 24 August 2004
PDF: 3 pages
Proc. SPIE 5436, Quantum Information and Computation II, (24 August 2004); doi: 10.1117/12.546845
Show Author Affiliations
Vitaliy Alexeevich Yatsenko, NSAU-NASU Space Research Institute (Ukraine)
Panos M. Pardalos, Univ. of Florida (United States)
Bruno H. Chiarini, Univ. of Florida (United States)

Published in SPIE Proceedings Vol. 5436:
Quantum Information and Computation II
Eric Donkor; Andrew R. Pirich; Howard E. Brandt, Editor(s)

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