Approches Graphiques en Informatique Quantique
Résumé
Quantum computing is a fast-growing research area. A quantum computer can solve problems which are out of reach of the classical computers. It is essential to understand the fundamental structures of quantum information processing in order to develop specific and effective tools. In this habilitation thesis we consider several examples of graphical approaches for quantum computing : first of all the graph state formalism, the measurement-based model of quantum computing and the quantum secret sharing protocol. We then explore in depth the ZX-calculus, a category theory based diagrammatic language for quantum reasoning. This language is equipped with an equational theory to transform any diagram into an equivalent diagram. The language is said to be complete if, for any pair of diagrams representing the same quantum evolution,
there exists a transformation from one to the other using the rules of the language. We show the completeness of ZX-calculation for several fragments of quantum mechanics.
Origine : Fichiers produits par l'(les) auteur(s)
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