IJPAM: Volume 42, No. 2 (2008)

GENERALIZED TURING QUANTUM MACHINE AND
ITS ALTERNATIVE BULK NMR IMPLEMENTATION

E. Belaga$^1$, K. van Schenk Brill$^2$, J. Grucker$^3$, J. Baudon$^4$, D. Grucker$^5$
$^{1,2}$Institut de Recherche en Mathématiques Avancées
Université Louis Pasteur - CNRS
7, Rue René Descartes, Strasbourg, 67084, FRANCE
$^1$e-mail: belaga@math.u-strasbg.fr
$^2$e-mail: keesvsb@gmail.com
$^{3,4}$Laboratoire de Physique des Lasers
CNRS-Université Paris 13, Villetaneuse, 93430, FRANCE
$^3$e-mail: grucker@galilee.univ-paris13.fr
$^4$e-mail: baudon@galilee.univ-paris13.fr
$^5$Laboratoire de Neuroimagerie in Vivo
CNRS-ULP, Strasbourg Cedex, 67085, FRANCE
e-mail: grucker@ipb.u-strasbg.fr


Abstract.The purpose of the present paper is twofold. First, we introduce the notion of a generalized version of both the classical and quantum Turing computational models, namely, Turing machine able to act in a single step on any finite continuous segment of its band. Second, we produce an alternative bulk NMR implementation of such a generalized Turing machine. The qualifier ``alternative" denominates our new and greatly simplified bulk NMR technique of experimental quantum computational modeling which offers the possibility to work with nuclear magnetic resonance on macroscopic materials, either liquid or solid and as primitive as water or solid xenon.

Received: August 17, 2007

AMS Subject Classification: 68Q05

Key Words and Phrases: quantum computing, NMR, Turing machines, cellular automata

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 42
Issue: 2