Fig. 2: The qubit Zeeman splitting.

Comparison of the qubit Zeeman splitting between Schrieffer-Wolff transformation (to the third order) and exact numerical diagonalization for four different configurations. When the gate electric field is turned off, the qubit Zeeman splitting g₀μ_BB ≈ 110 μeV. In all these figures, the out-of-plane magnetic field is B = 0.1 T. We can notice that the sweet spot does not change much as a function of the quantum dot radius, but the size of the qubit Zeeman splitting will be smaller for a larger quantum dot size. In all of these plots, we have \(\hbar\)ω_l ≫ g₀μ_BB. Numerical diagonalization is the red curve, Schrieffer-Wolff method is the blue curve. a d = 11 nm, a₀ = 50 nm. b d = 11 nm, a₀ = 60 nm. c d = 15 nm, a₀ = 50 nm. d d = 15 nm, a₀ = 60 nm.