  We consider opto- and electro-mechanical quantum systems composed of a driven
cavity mode interacting with a set of mechanical resonators. It has been
proposed that the latter can be initialized in arbitrary cluster states,
including universal resource states for Measurement Based Quantum Computation
(MBQC). We show that, despite the unavailability in this set-up of direct
measurements over the mechanical resonators, computation can still be performed
to a high degree of accuracy. In particular, it is possible to indirectly
implement the measurements necessary for arbitrary Gaussian MBQC by properly
coupling the mechanical resonators to the cavity field and continuously
monitoring the leakage of the latter. We provide a thorough theoretical
analysis of the performances obtained via indirect measurements, comparing them
with what is achievable when direct measurements are instead available. We show
that high levels of fidelity are attainable in parameter regimes within reach
of present experimental capabilities.
