  Hole spin qubits in quasi one-dimensional structures are a promising platform
for quantum information processing because of the strong spin-orbit interaction
(SOI). We present analytical results and discuss device designs that optimize
the SOI in Ge semiconductors. We show that at the magnetic field values at
which qubits are operated, orbital effects of magnetic fields can strongly
affect the response of the spin qubit. We study one-dimensional hole systems in
Ge under the influence of electric and magnetic fields applied perpendicularly
to the device. In our theoretical description, we include these effects
exactly. The orbital effects lead to a strong renormalization of the g-factor.
We find a sweet-spot of the nanowire (NW) g-factor where charge noise is
strongly suppressed and present an effective low-energy model that captures the
dependence of the SOI on the electromagnetic fields. Moreover, we compare
properties of NWs with square and circular cross-sections with ones of
gate-defined one-dimensional channels in two-dimensional Ge heterostructures.
Interestingly, the effective model predicts a flat band ground state for
fine-tuned electric and magnetic fields. By considering a quantum dot (QD)
harmonically confined by gates, we demonstrate that the NW g-factor sweet spot
is retained in the QD. Our calculations reveal that this sweet spot can be
designed to coincide with the maximum of the SOI, yielding highly coherent
qubits with large Rabi frequencies. We also study the effective g-factor of NWs
grown along different high symmetry axes and find that our model derived for
isotropic semiconductors is valid for the most relevant growth directions of
non-isotropic Ge NWs. Moreover, a NW grown along one of the three main
crystallographic axes shows the largest SOI. Our results show that the
isotropic approximation is not justified in Ge in all cases.
