Implementation of Single-Qubit Gates via Parametric Modulation in the Majorana Transmon

We present a voltage gate-based method for controlling the Majorana transmon, using a sinusoidal modulation of the induced offset charge ng. Working in the transmon regime and in the instantaneous eigenstates basis, we find the time evolution under this protocol that realizes tunable X-Z rotations. We optimize the parameters of the system for different single-qubit gates in both the laboratory frame and the qubit rotating frame, obtaining qubit control errors 1-F smaller than about 2×10-4. In addition to this, we conduct an analysis of the effects of the charge noise, assuming wide-band 1/f additive noise in ng, both for the free and the driven evolutions. For the free evolution, the relaxation and dephasing rates are calculated perturbatively, obtaining long dephasing times of the order of milliseconds at the system's sweet spots. For the driven case, the average fidelity for the X gate is obtained via a numerical simulation, demonstrating remarkable resilience.