  Central to near-term quantum machine learning is the use of hybrid
quantum-classical algorithms. This paper develops a formal framework for
describing these algorithms in terms of string diagrams: a key step towards
integrating these hybrid algorithms into existing work using string diagrams
for machine learning and differentiable programming. A notable feature of our
string diagrams is the use of functor boxes, which correspond to a
quantum-classical interfaces. The functor used is a lax monoidal functor
embedding the quantum systems into classical, and the lax monoidality imposes
restrictions on the string diagrams when extracting classical data from quantum
systems via measurement. In this way, our framework provides initial steps
toward a denotational semantics for hybrid quantum machine learning algorithms
that captures important features of quantum-classical interactions.
