Electric g Tensor Control and Spin Echo of a Hole-Spin Qubit in a Quantum Dot Molecule

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.