Number-theoretic methods in quantum computing

Auteur(s) : SELINGER PETER    28-04-2016  Éditeur(s) : Région PACA   , INRIA (Institut national de recherche en informatique et automatique)   ; INRIA (Institut national de recherche en informatique et automatique), CNRS - Centre National de la Recherche Scientifique, UNS;     Description : An important problem in quantum computing is the so-called approximate synthesis problem: to find a quantum circuit, preferably as short as possible, that approximates a given unitary operator up to given epsilon. Moreover, the solution should be computed by an efficient algorithm. For nearly two decades, the standard solution to this problem was the Solovay-Kitaev algorithm, which is based on geometric ideas. This algorithm produces circuits of size O(log^c(1/epsilon)), where c is approximately 3.97. It was a long-standing open problem whether this exponent c could be reduced to 1. In this talk, I will report on a number-theoretic algorithm that achieves circuit size O(log(1/epsilon)) in the case of the so-called Clifford+T gate set, thereby answering the above question positively. In case the operator to be approximated is diagonal, the algorithm satisfies an even stronger property: it computes the optimal solution to the given approximation problem. The algorithm also generalizes to certain other gate sets arising from number-theoretic unitary groups. This is joint work with Neil J. Ross. Mots-clés libres : Solovay-Kitaev algorithm Classification générale : Mathématiques Informatique Accès à la ressource : http://www.canal-u.tv/video/inria/number_theoretic... rtmpt://fms2.cerimes.fr:80/vod/fuscia/number.theor... http://www.canal-u.tv/video/inria/dl.1/number_theo... Conditions d'utilisation : Droits réservés à l'éditeur et aux auteurs.

DONNEES PEDAGOGIQUES Type pédagogique : cours / présentation Niveau : master, doctorat DONNEES TECHNIQUES Format : video/x-flv Taille : 1.33 Go Durée d'exécution : 1 heure 9 minutes 15 secondes

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