A lambda calculus for density matrices

ALEJANDRO DÍAZ CARO

Buenos Aires

Workshop; Logic and Foundations of Programming Languages Day; 2018

In this talk I will present two flavors of a quantum extension to the lambda calculus. The first one, λρ, follows the approach of classical control/quantum data, where the quantum data is represented by density matrices. We provide an interpretation for programs as density matrices and functions upon them. The second one, λρ°, take advantage of the density matrices presentation in order to follow the mixed trace of programs in a kind of generalised density matrix. Such a control can be seen as a weaker form of the quantum control and data approach. In addition, I will comment on some advances on ongoing works with Malena Ivnisky and Henrán Melgratti (fix point operator), Agustín Borgna (translation to a well-known quantum lambda calculus, and possible extension of the languages), Lucas Romero (polymorphisme) and Alan Rodas and Pablo E. Martínez López (a Haskell implementation).