  Quantum compiling, where a parameterized quantum circuit is trained to learn
a target unitary, is an important primitive for quantum computing that can be
used as a subroutine to obtain optimal circuits or as a tomographic tool to
study the dynamics of an experimental system. While much attention has been
paid to quantum compiling on discrete variable hardware, less has been paid to
compiling in the continuous variable paradigm. Here we motivate several,
closely related, short depth continuous variable algorithms for quantum
compilation. We analyse the trainability of our proposed cost functions and
numerically demonstrate our algorithms by learning arbitrary Gaussian
operations and Kerr non-linearities. We further make connections between this
framework and quantum learning theory in the continuous variable setting by
deriving No-Free-Lunch theorems. These generalization bounds demonstrate a
linear resource reduction for learning Gaussian unitaries using entangled
coherent-Fock states and an exponential resource reduction for learning
arbitrary unitaries using Two-Mode-Squeezed states.
