  In this work we present a comprehensive theory of spin physics in planar Ge
hole quantum dots in an in-plane magnetic field, where the orbital terms play a
dominant role in qubit physics, and provide a brief comparison with
experimental measurements of the angular dependence of electrically driven spin
resonance. We focus the theoretical analysis on electrical spin operation,
phonon-induced relaxation, and the existence of coherence sweet spots. We find
that the choice of magnetic field orientation makes a substantial difference
for the properties of hole spin qubits. Furthermore, although the
Schrieffer-Wolff approximation can describe electron dipole spin resonance
(EDSR), it does not capture the fundamental spin dynamics underlying qubit
coherence. Specifically, we find that: (i) EDSR for in-plane magnetic fields
varies non-linearly with the field strength and weaker than for perpendicular
magnetic fields; (ii) The EDSR Rabi frequency is maximized when the a.c.
electric field is aligned parallel to the magnetic field, and vanishes when the
two are perpendicular; (iii) The Rabi ratio $T_1/T_\pi$, i.e. the number of
EDSR gate operation per unit relaxation time, is expected to be as large as
$5{\times}10^5$ at the magnetic fields used experimentally; (iv) The orbital
magnetic field terms make the in-plane $g$-factor strongly anisotropic in a
squeezed dot, in excellent agreement with experimental measurements; (v) The
coherence sweet spots do not exist in an in-plane magnetic field, as the
orbital magnetic field terms expose the qubit to all components of the defect
electric field. These findings will provide a guideline for experiments to
design ultrafast, highly coherent hole spin qubits in Ge.
