Lifetime of Majorana qubits in Rashba nanowires with nonuniform chemical potential

We study the lifetime of topological qubits based on Majorana bound states hosted in a one-dimensional Rashba nanowire (NW) with proximity-induced superconductivity and nonuniform chemical potential needed for manipulation and readout. If nearby gates tune the chemical potential locally so that part of the NW is in the trivial phase, Andreev bound states (ABSs) can emerge which are localized at the interface between topological and trivial phases with energies significantly less than the gap. The emergence of such subgap states decreases the Majorana qubit lifetime at finite temperatures due to local perturbations that can excite the system into these ABSs. Using the Keldysh formalism, we study such excitations caused by fluctuating charges in capacitively coupled gates and calculate the corresponding Majorana lifetimes due to thermal noise, which are shown to be reduced in comparison with those in NWs with uniform chemical potential.