Quantum Computing and its Calculi

Quantum computing can be thought of in multiple ways. Among those ways, it can be seen as a computational model of quantum mechanics. Studying this model may have implications for our understanding of physics. It can also be seen as a new computational paradigm, with implications for computation, algorithms, and logic. Additionally, it can be viewed as a computational device that requires programming. Therefore, it is necessary to design and study programming languages for this purpose. The study of the foundations of quantum programming languages, type theory, and logic through the Curry-Howard correspondence may shed light on our understanding of quantum mechanics. Furthermore, it may lead to the development of new logics or the understanding of new structures in classical logic. Lastly, implementing these languages will enhance the way we program the new computers when they become widely used.In this project, we propose to study these various aspects of quantum computing, specifically focusing on the foundations of programming languages.