  We propose a new typed graphical language for quantum computation, based on
compact categories with biproducts. Our language generalizes existing
approaches such as ZX-calculus and quantum circuits, while offering a natural
framework to support quantum control: it natively supports "quantum tests". The
language comes equipped with a denotational semantics based on linear
applications, and an equational theory. Through the use of normal forms for the
diagrams, we prove the language to be universal, and the equational theory to
be complete with respect to the semantics.
