  We propose a scheme for entangling the motion of two massive objects in a
hybrid electromechanical architecture. The entanglement is generated due to the
interaction of two mechanical oscillators with a mediating superconducting
qubit. We show that the generated macroscopic entangled states are non-Gaussian
and its lifetime is limited by coherence time of the qubit. The entanglement is
attainable in a wide range of parameters with appropriate control of the qubit.
We confirm performance of our scheme by numerically solving the quantum optical
master equation including sources of noise. The effect of imperfections, such
as asymmetries in the coupling rates as well as mechanical thermal noise are
studied and shown how they affect the amount and lifetime of the entangled
state. Due to the nonlinear nature of the qubit, the initial Gaussian state of
mechanical resonators evolves into a quasi-stationary non-Gaussian state, which
is essential for universal quantum information processing in continuous
variable systems. This work, therefore, provides the first step towards a
universal continuous variable quantum network.
