Fig. 3: Electric field sensitivity and coherence dependence on magnetic field orientation.

a, Pulse sequences used to measure the voltage sensitivity of the energy splitting ∂f_Q/∂V_i. A positive (negative) voltage pulse δV_i of varying length t_Z is applied to the test gate electrode i in the first (second) free evolution of a Hahn echo to extract ∣∂f_Q/∂V_i∣. b, Pulse sequences used to infer the sign of ∂f_Q/∂V_i by assessing the shift in the qubit resonance frequency as a result of a voltage pulse δV_i. c, Left: spin-up probability P(t_Z) as reflected by the charge sensor current I_sensor as a function of the pulse length t_Z, where the solid line is a fit to the data points. Right: fast Fourier transform (FFT) of I_sensor, enabling the extraction of ∣∂f_Q/∂V_i∣. d, I_sensor as a function of the drive frequency f_X and δV_i. The shift in the resonance frequency enables the sign of ∂f_Q/∂V_i to be extracted. e, The qubit energy splitting sensitivity to a voltage change on the plunger gate ∂f_Q2/∂V_P2, as a function of different magnetic field orientations ϕ_B and θ_B. B is adapted to keep f_Q2 constant at f_Q2 = 1.36(7) GHz. Data acquisition is hindered for the white areas as a result of limited qubit readout or addressability for these magnetic field orientations (the exact filed orientations of which are given in Supplementary Table 1). f, Hahn coherence time \({T}_{2}^{\,{\rm{H}}}\) as a function of the qubit frequency f_Q2, for different magnetic field orientations indicated by the coloured markers in e. Solid lines correspond to \({T}_{2}^{\,{\rm{H}}}\) as extracted from a pure decay, whereas dotted lines correspond to \({T}_{2}^{\,{\rm{H}}}\) as extracted from the envelope of the nuclear spin-induced collapse and revival. Data indicated by opaque markers are used to fit the power law dependence of \({T}_{2}^{\,{\rm{H}}}\). g, Expected \({T}_{2,{\,{{f}}}_{{{{\rm{Q}}}}2}\, =\, 1\,{{{\rm{GHz}}}}}^{\,{\mathrm{H}}}\) as extracted from a power law fit to the opaque data markers in f as a function of the gate voltage sensitivity (∂f_Q2/∂V_P2)/f_Q2 from e. The coloured markers correspond to the different magnetic field orientations as indicated in e. The solid black line is a fit of \({T}_{2}^{{\mathrm{H}}}=a{x}^{\beta }\) to the data, yielding a scaling factor of a = 2.4 and an exponent of β = −1.04(8).