Fig. 4: State transfer from the SC qubit to the electron spin.

The system begins in the excited state of the SC qubit, then evolves according to the master equation Eq. (2). The time-dependent populations of the SC qubit (full blue), the cavity phonon (red dashed), and the electron spin qubit (black dash-dotted) are plotted as a function of time in a. After initializing the system, we apply the series of pulses shown in b, as described in the text, and let the system evolve until the state is transferred to the electron spin. c, e The state-transfer fidelity \({{{\mathcal{F}}}}\), and d, f \({{\mathrm{log}}}\,(1-{{{\mathcal{F}}}})\). Both \({{{\mathcal{F}}}}\), and \({{\mathrm{log}}}\,(1-{{{\mathcal{F}}}})\) are calculated as a function of the phonon-electron-spin coupling g_pe and the electron-spin dephasing rate γ_e. We maximize \({{{\mathcal{F}}}}\) for each pair of parameters [γ_e, g_pe] by adjusting the delays between the respective pulses applied to drive the system dynamics. We consider (c, d) γ_p/(2π) = 10⁻⁷ GHz (corresponding to the mechanical quality factor Q ~ 10⁷) and (e, f) γ_p/(2π) = 10⁻⁴ GHz in the calculations.