  Universal quantum computation encoded over continuous variables can be
achieved via Gaussian measurements acting on entangled non-Gaussian states.
However, due to the weakness of available nonlinearities, generally these
states can only be prepared conditionally, potentially with low probability.
Here we show how universal quantum computation could be implemented
unconditionally using an integrated platform able to sustain both linear and
quadratic optomechanical-like interactions. Specifically, considering cavity
opto- and electro-mechanical systems, we propose a realisation of a
driven-dissipative dynamics that deterministically prepares the required
non-Gaussian cluster states -- entangled squeezed states of multiple mechanical
oscillators suitably interspersed with cubic-phase states. We next demonstrate
how arbitrary Gaussian measurements on the cluster nodes can be performed by
continuously monitoring the output cavity field. Finally, the feasibility
requirements of this approach are analysed in detail, suggesting that its
building blocks are within reach of current technology.
