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Marches quantiques généralisées pour l'algorithmique quantique

Abstract : We have studied quantum algorithms with the purpose of calculating a matrix permanent with a quantum computer. After constructing some algorithms, we started to study the quantum equivalent of a random walk. These walks have been introduced hoping to build new quantum algorithms from them. We started by generalizing the existing model of quantum walk and started a classification of the walks defined on Cayley graphs of the simplest groups. We studied then quantum walks over the hypercube and simple lattices in one and two dimensions and we obtained an analytical expression for the wave function, in order to explore numerically quantities such as the hitting time and the variance. Finally, we also extended two existing theorems about the existence of quantum scalar walks and about the weak limit of the walk. These results enable us to consider the classification of more complex graphs with an aim of obtaining structural information on the quantum sub-algorithms that can be constructed.
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https://tel.archives-ouvertes.fr/tel-00169212
Contributor : Olga Lopez Acevedo <>
Submitted on : Sunday, September 2, 2007 - 8:41:36 PM
Last modification on : Thursday, March 5, 2020 - 4:26:40 PM
Long-term archiving on: : Tuesday, September 21, 2010 - 1:32:53 PM

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Olga Lopez Acevedo. Marches quantiques généralisées pour l'algorithmique quantique. Physique mathématique [math-ph]. Université de Cergy Pontoise, 2005. Français. ⟨tel-00169212v2⟩

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