Ross Duncan - Introduction to Categorical Quantum Mechanics

Quantum computing is on the verge of taking over the world. But what about its semantics? What about formal methods for quantum computers? Do we really need to carry around all the machinery of Hilbert spaces, unitary transforms, etc etc in order to work on quantum computing? In fact the answer is no. By analysing the structure of quantum theory in terms of categorical theory we can uncover its essential algebraic structures and thus arrive at a formal theory of quantum computing, which can be presented in a simple graphical language. I’ll present a rational reconstruction of quantum theory in terms of primitive algebraic components inside an abstract monoidal category. (No knowledge of quantum computing or category theory will be required!)