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Z. Le, . De-raisonner, and . Calculer-en-quantique, Un aspect des plus importants du langage est sa complétude :Étant donnés deux diagrammes qui représentent la mêmeévolution quantique, puis-je transformer l'un en l'autre en utilisant seulement les règles graphiques permises par le langage ? Si c'est le cas, cela veut dire que le langage graphique capture entièrement la mécanique quantique. Le langage est connu commeétant complet pour une sous-classe (ou fragment) particulière d'évolutions quantiques, appelée Cli ord. Malheureusement, celle-ci n'est pas universelle : on ne peut pas représenter, ni même approcher, certainesévolutions. Dans ce e thèse, nous proposons d'élargir l'ensemble d'axiomes pour obtenir la complétude pour des fragments plus grands du langage, qui en particulier sont approximativement universels, voire universels. Pour ce faire, dans un premier temps nous utilisons la complétude d'un autre langage graphique et transportons ce résultat au ZX-Calculus. A n de simpli er ce e fastidieuseétape, nous introduisons un langage intermédiaire, intéressant en lui-même car il capture un fragment particulier mais universel de la mécanique quantique : To oli-Hadamard. Nous dé nissons ensuite la notion de diagramme linéaire, qui permet d'obtenir une preuve uniforme pour certains ensembles d'équations, Nous dé

, Grâceà cela, nous reprouvons les résultats de complétude précédents, mais ce e fois sans utiliser de langage tiers, et nous en dérivons de nouveaux, pour d'autres fragments. Lesétats contrôlés, utilisés pour la dé nition de forme normale, s'avèrent en outre utiles pour réaliser des opérations non-triviales telles que la somme

. Mots-clés, Mécanique antique Catégorique, ZX-Calculus, Complétude, Universalité, Formes Normales