  We consider the tasks of learning quantum states, measurements and channels
generated by continuous-variable (CV) quantum circuits. This family of circuits
is suited to describe optical quantum technologies and in particular it
includes state-of-the-art photonic processors capable of showing quantum
advantage. We define classes of functions that map classical variables, encoded
into the CV circuit parameters, to outcome probabilities evaluated on those
circuits. We then establish efficient learnability guarantees for such classes,
by computing bounds on their pseudo-dimension or covering numbers, showing that
CV quantum circuits can be learned with a sample complexity that scales
polynomially with the circuit's size, i.e., the number of modes. Our results
show that CV circuits can be trained efficiently using a number of training
samples that, unlike their finite-dimensional counterpart, does not scale with
the circuit depth.
