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In the realm of quantum computing, circuit description languages represent avalid alternative to traditional QRAM-style languages. They indeed allow forfiner control over the output circuit, without sacrificing flexibility normodularity. We introduce a generalization of the paradigmatic lambda-calculusProto-Quipper-M, itself modeling the core features of the quantum circuitdescription language Quipper. The extension, called Proto-Quipper-K, is meantto capture a very general form of dynamic lifting. This is made possible by theintroduction of a rich type and effect system in which not only computations,but also the very types are effectful. The main results we give for theintroduced language are the classic type soundness results, namely subjectreduction and progress.

On Dynamic Lifting and Effect Typing in Circuit Description Languages (Extended Version)