Compilation to quantum circuits for a language with quantum data and control

In this paper we further investigate nQML, a functional quantum programming language that follows the “quantum data and control” paradigm. We define a semantics for nQML, which translates programs to quantum circuits in the category FQC of finite quantum computations, following the approach of Altenkirch and Grattage´s QML. This semantics, which coincides with the denotational semantics for nQML over density matrices and unitary transformations, serves as a compiler from nQML programs to quantum circuits. We also provide an implementation of this compiler, written in Haskell, as well as an interpreter for quantum circuits.