Rydberg gates in donors in silicon*

We predict a new variant of the Rydberg blockade gate which - considering the interaction to be the limiting parameter and not the Rabi frequency - we demonstrate theoretically to have an order of magnitude improvement in fidelities and speed over existing protocols. We do this using a Lindblad equation to model the noise characteristics of the Rydberg entangling gate proposed by Levine et al. Applying our new gate protocol to donors in silicon, we show that it would help overcome the strenuous requirements on atomic precision donor placement and substantial gate tuning, which so far has hampered scaling in this platform. We calculate multivalley Rydberg interactions for several donor species using the Finite Element Method, and show that induced electric dipole and Van der Waals interactions, calculated here for the first time, are important even for low-lying excited states. We show that Rydberg gate operation is possible within the lifetime of donor excited states with 99.9% fidelity for the creation of a Bell state in the presence of decoherence.