Dynamics of the Majorana-Transmon qubit with time-dependent voltage bias.

Hybrid topological-superconducting systems engineered by combining superconducting circuits with 1D Majorana Bound States (MBS) have been proposed as possible platforms for quantum computation. In these systems the topological states are formed by inducing p-wave superconductivity in nanowires in contact with the superconducting leads. Among these proposals there is the recent idea of encoding the quantum information in a basis of fermion parity states originating from an additional hybridization between MBSs of different nanowires placed across a Josephson Junction [1]. Even if the coupling between the two Majorana fermions sacrifices their full topological protection, the system gains a highly anharmonic spectrum and it has been proposed that it can be used for engineering a coherent qubit [2]. Here we focus on the theoretical study of this system's dynamics in the case of time-dependent voltage bias. Within this scenario, we investigate possible protocols for implementing single qubit gates in the system, together with an analysis of the effect of the charge noise on them.
[1] E. Ginossar and E. Grosfeld, Nat. Commun. 5, 4772 (2014); [2] K. Yavilberg, E. Ginossar and E. Grosfeld, Phys. Rev. B 92 (7), 075143 (2015);