  Silicon hole quantum dots have been the subject of considerable attention
thanks to their strong spin-orbit coupling enabling electrical control. The
physics of silicon holes is qualitatively different from germanium holes and
requires a separate theoretical description. In this work, we theoretically
study the electrical control and coherence properties of silicon hole dots with
different magnetic field orientations. We discuss possible experimental
configurations to optimize the electric dipole spin resonance (EDSR) Rabi time,
the phonon relaxation time, and the dephasing due to random telegraph noise.
Our main findings are: (i) The in-plane $g$-factor is strongly influenced by
the presence of the split-off band, as well as by any shear strain. The
$g$-factor is a non-monotonic function of the top gate electric field, in
agreement with recent experiments. This enables coherence sweet spots at
specific values of the top gate field and specific magnetic field orientations.
(ii) Even a small ellipticity (aspect ratios $\sim 1.2$) causes significant
anisotropy in the in-plane $g$-factor, which can vary by $50\% - 100\%$ as the
magnetic field is rotated in the plane. (iii) EDSR Rabi frequencies are
comparable to Ge, and the ratio between the relaxation time and the EDSR Rabi
time $\sim 10^5$. For an out-of-plane magnetic field the EDSR Rabi frequency is
anisotropic with respect to the orientation of the driving electric field,
varying by $\approx 20\%$ as the driving field is rotated in the plane. Our
work aims to stimulate experiments by providing guidelines on optimizing
configurations and geometries to achieve robust, fast and long-lived hole spin
qubits in silicon.
