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.Comment: 5 pages + 9 pages supplementary materia
