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| Number-theoretic methods in quantum computing (en Anglais) | |||
Droits : Droits réservés à l'éditeur et aux auteurs Auteur(s) : SELINGER Peter Éditeur(s) : Région PACA ,INRIA (Institut national de recherche en informatique et automatique) 28-04-2016 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 | TECHNIQUE Type : image en mouvement Format : video/x-flv Source(s) : rtmpt://fms2.cerimes.fr:80/vod/fuscia/number.theoretic.methods.in.quantum.computing_21621/peter.selinger.28.avril.2016.720.a.2500kbits.mp4 | ||
Entrepôt d'origine : Canal-u.fr Identifiant : oai:canal-u.fr:21621 Type de ressource : Ressource documentaire | |||
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| Number-theoretic methods in quantum computing (en Anglais) | |||||||||
Identifiant de la fiche : 21621 Schéma de la métadonnée : LOMv1.0, LOMFRv1.0 Droits : libre de droits, gratuit Droits réservés à l'éditeur et aux auteurs. Auteur(s) : SELINGER PETER 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 28-04-2016 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
| PEDAGOGIQUE Type pédagogique : cours / présentation Niveau : master, doctorat TECHNIQUE Type de contenu : image en mouvement Format : video/x-flv Taille : 1.33 Go Durée d'exécution : 1 heure 9 minutes 15 secondes RELATIONS Cette ressource fait partie de : | ||||||||
Entrepôt d'origine : Canal-u.fr Identifiant : oai:canal-u.fr:21621 Type de ressource : Ressource pédagogique | |||||||||
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