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Theses

Complexité en requêtes et symétries

Abstract : This work is about the study of the query complexity of symmetric
problems, in both frameworks of quantum and classical randomized
algorithms.

In the quantum case, we show a new application of the so-called
"polynomial" lower bound method to the abelian hidden subgroup problems, via the "symmetrization" technique.

In the case of randomized computing, under a "transitive symmetry"
hypothesis on the considered problems, we give a combinatorial formula allowing us to compute the exact query complexity of the best
nonadaptive algorithm. Moreover, we show that under some symmetry
conditions, this best nonadaptive algorithm is optimal amongst general
algorithms, which gives an expression of the exact query complexity for the corresponding class of problems.
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https://tel.archives-ouvertes.fr/tel-00156762
Contributor : Vincent Nesme <>
Submitted on : Friday, June 22, 2007 - 2:58:07 PM
Last modification on : Wednesday, November 20, 2019 - 3:02:08 AM
Long-term archiving on: : Monday, September 24, 2012 - 10:15:55 AM

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  • HAL Id : tel-00156762, version 1

Citation

Vincent Nesme. Complexité en requêtes et symétries. Mathématiques [math]. Ecole normale supérieure de lyon - ENS LYON, 2007. Français. ⟨tel-00156762⟩

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