  The feasibility of high-fidelity single-qubit operations of a hole spin in a
quantum dot molecule by electric g tensor control is demonstrated. Apart from a
constant external magnetic field the proposed scheme allows for an exclusively
electric control of the hole spin. Realistic electric gate bias profiles are
identified for various qubit operations using process-tomography-based optimal
control. They are shown to be remarkably robust against decoherence and
dissipation arising from the interaction of the hole with host-lattice nuclear
spins and phonons, with a fidelity loss of $\approx$ 1 percent for gate
operation times of $\approx 10$ ns. Spin-echo experiments for the hole spin are
modeled to explore dephasing mechanisms and the role of pulse-timing
imperfections on the gate fidelity loss is discussed.
