Thursday 6 April 2017, 14:00: A lambda calculus for density matrices, Alejandro Díaz-Caro (CONICET, Universidad Nacional de Quilmes).

Density matrices describe quantum systems in mixed state, that is, a statistical set of several quantum states. All the postulates of quantum mechanics can be described in such a formalism, and hence, also quantum computing can be done using density matrices. One advantage of this formalism is that it gives a natural way to reason about the probabilistic outputs of an algorithm.

In this talk we present an extension to lambda calculus for density matrices with a linear type system. Its denotational semantics is the set of density matrices and functions upon them, and so, it is possible to equate programs producing the same density matrices. For example the process of tossing a coin, and according to its result, apply Z or not to a balanced superposition, and the process of tossing a coin and not looking at its result, may look quite different in most quantum programming languages. Yet both processes output the same density matrices thus have the same denotation in our calculus.