# Recherche

Pendant mes études doctorales, j'ai fait de la recherche en informatique théorique. Mon thème principal de recherche était l'étude des languages de programmation en informatique quantique, sujet qui m'intéresse toujours. Je suis aussi intéressé par la sémantique de jeux en informatique et en logique de manière générale.

Ma thèse de doctorat Quantum Games as Quantum Types porte sur l'utilisation de jeux quantiques comme types quantiques pour les languages de programmation quantiques. Résultat principal: des sémantiques dénotationelles construites à l'aide de jeux quantiques pour deux $\lambda$-calculs quantiques.

Mes principaux intérêts de recherche sont la sémantique de jeux et l'informatique quantique.

My main research interests are game semantics and quantum computing.

My Ph.D thesis, Quantum Games as Quantum Types discuss the use of quantum games as quantum types for quantum programming languages. Main result: denotational semantics constructed using quantum games for two quantum $\lambda$-calculi.

## Publications

• Thèse de doctorat: Quantum Games as Quantum Types, Université McGill, 2009, sous la direction de Prakash Panangaden.

• Game Semantics for Quantum Data, QPL 2008, B. Coecke, I. Mackie, P. Panangaden, and P. Selinger, editors, Proceedings of the Joint 5th International Workshop on Quantum Physics and Logic and 4th Workshop on Developments in Computational Models (QPL/DCM 2008), Reykjavik. Electronic Notes in Theoretical Computer Science 270(1), 2011.
( vidéo de la présentation lors de QPL 2008

Abstract: This paper presents a game semantics for a simply-typed λ-calculus with qbits constants and associated quantum operations. The resulting language is expressive enough to encode any quantum circuit. The language uses a notion of extended variable, similar to that seen in functional languages with pattern matching, but adapted to the needs of dealing with tensor products. The game semantics is constructed from classical game semantics using quantum interventions as questions and measurements results as answers. A soundness result for the semantics is given.

• Game Semantics for Quantum Stores (with Prakash Panangaden), Proceedings of the 24th Conference on the Mathematical Foundations of Programming Semantics (MFPS XXIV), Electronic Notes in Theoretical Computer Science Volume 218, 22 October 2008, Pages 153-170 (Copyright 2008 Elsevier)

Abstract: This paper presents a game semantics for a simply-typed λ-calculus equipped with quantum stores. The quantum stores are equipped with quantum operations as commands which give the language enough expressiveness to encode any quantum circuits. The language uses a notion of extended variable, similar to that seen in functional languages with pattern matching, but adapted to the needs of dealing with tensor products. These tensored variables are used to refer to quantum stores and to keep track of the size of the states which they contain. The game semantics is constructed from classical game semantics using
intervention operators to encode the effects of the commands. A soundess result for the semantics is given.

• A Quantum Game Semantics for the Measurement Calculus, Prooceedings of the fourth International Workshop on Quantum Programming Languages, Electronic Notes in Theoretical Computer Science (ENTCS) Volume 210, July, Elsevier, 2008, pp. 33-40 (Copyright 2008 Elsevier)

Abstract: In this paper we present a game semantics for a quantum programming language based on a new definition of quantum strategies. The language studied is MCdata, a typed version of the measurement calculus recently introduced by Danos et. al. We give a soundness and adequacy result based on our quantum game semantics. The main contribution is not the semantics of MCdata but rather the development of ideas suitable for a game theoretic treatment of quantum computation in general.

• Information Flow in Game Semantics, GALOP 2005 workshop, ETAPS 2005

Abstract: To successfully model an array of different programing languages, game semantics uses the detailed interactions between a system and its environment. To fine-tune such a model to a particular language, the set of strategies available to the players is limited using various conditions. In many cases these restrictions can be thought as the result of limiting the information available to the players to elaborate their strategies.

The aim of this paper is to study two frameworks to represent this partial knowledge explicitly. The first add to games as defined in game semantics equivalence relations identifying the position that cannot be distinguished by the players. The resulting structure is related to the process of restricting the player’s strategies by a Galois connection. The second framework is based upon a network game representation derived from coloured Petri nets. The games of the first framework are used to study the dynamics of this network game representation, so it can also be connected to game semantics. This relation is then used to give a characterisation of total information games in the network representation. A sketch of the basic constructions needed to define a category of games and strategies using the network representation is given.

• Mémoire de maitrise: Les catégories dérivées, Université de Montréal, 1999, sous la direction d'Abraham Broer

Résumé: L'objectif principal de ce mémoire est de faire une démonstration complète de l'existence des catégories dérivées et de prouver quelques unes de leurs propriétés les plus importantes. Nous présenterons la localisation d'une catégorie par un système multiplicatif et nous démontrerons que la localisation d'une catégorie additive est aussi additive. Nous montrerons à l'aide des cônes que la catégorie des complexes modulo homotopie d'une catégorie abélienne $\mathcal{K}(A)$ est une catégorie triangulée et aussi que la localisation d'une catégorie triangulée par un système multiplicatif compatible avec la structure triangulée est aussi triangulée, ce qui permettra de montrer l'existence des catégories dérivées et le fait qu'elles sont triangulées, en montrant que la famille des quasi-isomorphismes de $\mathcal{K}(A)$ est un système multiplicatif dans $\mathcal{K}(A)$. Nous utiliserons ensuite les catégories dérivées pour définir les foncteurs dérivées d'un foncteur exact à gauche.