  We introduce witnesses for the average channel fidelity between a known
target gate and an arbitrary unknown channel, for continuous-variable (CV)
systems. These are observables whose expectation value yields a tight lower
bound to the average channel fidelity in question, thus constituting a
practical tool for certification of experimental CV gates. Our framework
applies to a broad class of target gates. Here, we focus on three specific
types of targets: multi-mode Gaussian unitary channels, single-mode coherent
state amplifiers, and the single-mode (non-Gaussian) cubic phase gate, which is
a crucial ingredient for CV universal quantum computation. Our witnesses are
experimentally-friendly as they rely exclusively on Gaussian measurements, even
for the non-Gaussian-target case. Moreover, in all three cases, they can be
measured efficiently in the estimation error $\epsilon$ and failure probability
$\Delta$, as well as in the number of modes $m$ for the Gaussian-target case.
To end up with, our approach for the Gaussian-target case relies on an improved
measurement scheme for Gaussian state-fidelity witnesses, which is polynomially
and exponentially more efficient in $m$ and $\Delta$, respectively, than
previous schemes. The latter constitutes an interesting byproduct result on its
own. Our findings are relevant to the experimental validation of many-body
quantum technologies.
