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Control of a spin qubit in a lateral GaAs quantum dot based on symmetry of gating potential

We study the influence of quantum dot symmetry on the Rabi frequency and phonon induced spin relaxation rate in a single electron GaAs spin qubit. We find that anisotropic dependence on the magnetic field direction is independent of the choice of the gating potential. Also, we discover that relative orientation of the quantum dot, with respect to the crystallographic frame, is relevant in systems with ${\bf C}_{1{\rm v}}$, ${\bf C}_{2{\rm v}}$, or ${\bf C}_{n}$ ($n\neq4r$) symmetry. To demonstrate the important impact of the gating potential shape on the spin qubit lifetime, we compare the effects of an equilateral triangle, square, and rectangular confinement with the known results for the harmonic potential. In the studied cases, enhanced spin qubit lifetime is revealed, reaching almost six orders of magnitude increase for the equilateral triangle gating.