  We propose a solid-state hybrid platform based on an array of implanted
nitrogen-vacancy (NV) centers in diamond magnetically coupled to a mechanical
oscillator. The mechanical oscillator and the NV electronic spins both act as a
quantum bus and allow us to induce an effective long-range interaction between
distant nuclear spins, relaxing the requirements on their spatial distance. The
coherent nuclear spin-spin interaction, having the form of an Ising model, can
be maintained in the presence of mechanical damping and spin dephasing via a
pulsed dynamical decoupling of the nuclear spins in addition to the microwave
driving field of the electronic spins. The present hybrid platform provides a
scalable way to prepare multipartite entanglement among nuclear spins with long
coherence times and can be applied to generate graph states that may be used
for universal quantum computing.
