  Bosonic continuous-variable Variational quantum circuits (VQCs) are crucial
for information processing in cavity quantum electrodynamics and optical
systems, widely applicable in quantum communication, sensing and error
correction. The trainability of such VQCs is less understood, hindered by the
lack of theoretical tools such as $t$-design due to the infinite dimension of
the physical systems involved. We overcome this difficulty to reveal an
energy-dependent barren plateau in such VQCs. The variance of the gradient
decays as $1/E^{M\nu}$, exponential in the number of modes $M$ but polynomial
in the (per-mode) circuit energy $E$. The exponent $\nu=1$ for shallow circuits
and $\nu=2$ for deep circuits. We prove these results for state preparation of
general Gaussian states and number states. We also provide numerical evidence
that the results extend to general state preparation tasks. As circuit energy
is a controllable parameter, we provide a strategy to mitigate the barren
plateau in continuous-variable VQCs.
