  Hole semiconductor nanowires (NW) are promising platforms to host spin qubits
and Majorana bound states for topological qubits because of their strong
spin-orbit interactions (SOI). The properties of these systems depend strongly
on the design of the cross section and on strain, as well as on external
electric and magnetic fields. In this work, we analyze in detail the dependence
of the SOI and $g$ factors on the orbital magnetic field. We focus on magnetic
fields aligned along the axis of the NW, where orbital effects are enhanced and
result in a renormalization of the effective $g$ factor up to $400\,\%$, even
at small values of magnetic field. We provide an exact analytical solution for
holes in Ge NWs and we derive an effective low-energy model that enables us to
investigate the effect of electric fields applied perpendicular to the NW. We
also discuss in detail the role of strain, growth direction, and high energy
valence bands in different architectures, including Ge/Si core/shell NWs,
gate-defined one-dimensional channels in planar Ge, and curved Ge quantum
wells. In core/shell NWs grown along the $[110]$ direction the $g$ factor can
be twice larger than for other growth directions which makes this growth
direction advantageous for Majorana bound states. Also curved Ge quantum wells
feature large effective $g$ factors and SOI, again ideal for hosting Majorana
bound states. Strikingly, because these quantities are independent of the
electric field, hole spin qubits encoded in curved quantum wells are to good
approximation not susceptible to charge noise, significantly boosting their
coherence time.
