Optimal geometry of lateral GaAs and Si/SiGe quantum dots for electrical control of spin qubits

We investigate the effects of the orientation of the magnetic field and the orientation of a quantum dot, with respect to crystallographic coordinates, on the quality of an electrically controlled qubit realized in a gated semiconductor quantum dot. We find that, due to the anisotropy of the spin-orbit interactions, varying the two orientations it is possible to tune the qubit in the sense of optimizing the ratio of its couplings to phonons and to a control electric field. We find conditions under which such optimal setup can be reached by solely reorienting the magnetic field, and when a specific positioning of the dot is required. We also find that the knowledge of the relative sign of the spin-orbit interactions strengths allows to choose a robust optimal dot geometry, with the dot main axis along [110], or [1$\overline{1}$0], where the qubit can be always optimized by reorienting the magnetic field.