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.