  Control of hyperfine interactions is a fundamental requirement for quantum
computing architecture schemes based on shallow donors in silicon. However, at
present, there is lacking an atomistic approach including critical effects of
central-cell corrections and non-static screening of the donor potential
capable of describing the hyperfine interaction in the presence of both strain
and electric fields in realistically sized devices. We establish and apply a
theoretical framework, based on atomistic tight-binding theory, to
quantitatively determine the strain and electric field dependent hyperfine
couplings of donors. Our method is scalable to millions of atoms, and yet
captures the strain effects with an accuracy level of DFT method. Excellent
agreement with the available experimental data sets allow reliable
investigation of the design space of multi-qubit architectures, based on both
strain-only as well as hybrid (strain+field) control of qubits. The benefits of
strain are uncovered by demonstrating that a hybrid control of qubits based on
(001) compressive strain and in-plane (100 or 010) fields results in higher
gate fidelities and/or faster gate operations, for all of the four donor
species considered (P, As, Sb, and Bi). The comparison between different donor
species in strained environments further highlights the trends of hyperfine
shifts, providing predictions where no experimental data exists. Whilst faster
gate operations are realisable with in-plane fields for P, As, and Sb donors,
only for the Bi donor, our calculations predict faster gate response in the
presence of both in-plane and out-of-plane fields, truly benefiting from the
proposed planar field control mechanism of the hyperfine interactions.
