ly abstract model for a quantum unctional language (extended abstract) Peter Selinger1 ,2 Dalhousie University, Halifax, Nova Scotia, Canada Beno^it Valiron3 University of Ottawa, Ottawa, Ontario, Canada This paper studies the linear fragment of the programing language for quantum computation with classical control described in [4]. We sketch the language, and discuss equivalence of terms. We also describe a fully denotational semantics based on completely positive maps.