  Continuous-Variable (CV) devices are a promising platform for demonstrating
large-scale quantum information protocols. In this framework, we define a
general quantum computational model based on a CV hardware. It consists of
vacuum input states, a finite set of gates - including non-Gaussian elements -
and homodyne detection. We show that this model incorporates encodings
sufficient for probabilistic fault-tolerant universal quantum computing.
Furthermore, we show that this model can be adapted to yield sampling problems
that cannot be simulated efficiently with a classical computer, unless the
polynomial hierarchy collapses. This allows us to provide a simple paradigm for
short-term experiments to probe quantum advantage relying on Gaussian states,
homodyne detection and some form of non-Gaussian evolution. We finally address
the recently introduced model of Instantaneous Quantum Computing in CV, and
prove that the hardness statement is robust with respect to some experimentally
relevant simplifications in the definition of that model.
