  Realising controlled quantum dynamics via the magnetic interactions between
colour centers in diamond remains a challenge despite recent demonstrations for
nanometer separated pairs. Here we propose to use the intrinsic acoustical
phonons in diamond as a data bus for accomplishing this task. We show that for
nanodiamonds the electron-phonon coupling can take significant values that
together with mode frequencies in the THz range, can serve as a resource for
conditional gate operations. Based on these results we analyze how to use this
phonon-induced interaction for constructing quantum gates among the
electron-spin triplet ground states, introducing the phonon dependence via
Raman transitions. Combined with decoupling pulses this offers the possibility
for creating entangled states within nanodiamonds on the scale of several tens
of nanometers, a promising prerequisite for quantum sensing applications.
