  We propose qubits based on shallow donor electron spins in germanium.
Spin-orbit interaction for donor spins in germanium is in many orders of
magnitude stronger than in silicon. In a uniform bulk material it leads to very
short spin lifetimes. However the lifetime increases dramatically when the
donor is placed into a quasi-2D phononic crystal and the energy of the Zeeman
splitting is tuned to lie within a phonon bandgap. In this situation single
phonon processes are suppressed by energy conservation. The remaining
two-phonon decay channel is very slow. The Zeeman splitting within the gap can
be fine tuned to induce a strong, long-range coupling between the spins of
remote donors via exchange by virtual phonons. This, in turn, opens a very
efficient way to manipulate the quits. We explore various geometries of
phononic crystals in order to maximize the coherent qubit-qubit coupling while
keeping the decay rate minimal. We find that phononic crystals with unit cell
sizes of 100-150 nm are viable candidates for quantum computing applications
and suggest several spin-resonance experiments to verify our theoretical
predictions.
