Parity-to-charge conversion in Majorana qubit readout

Abstract

We study the time-dependent effect of Markovian readout processes on Majorana qubits whose parity degrees of freedom are converted into the charge of a tunnel-coupled quantum dot. By applying a recently established effective Lindbladian approximation [Kiršanskas, Franckié, and Wacker, Phys. Rev. B 97, 035432 (2018)2469-995010.1103/PhysRevB.97.035432; Mozgunov and Lidar, Quantum 4, 227 (2020)2521-327X10.22331/q-2020-02-06-227; Nathan and Rudner, arXiv:2004.01469], we obtain a completely positive and trace preserving Lindblad master equation for the combined dot-qubit dynamics, describing relaxation and decoherence processes beyond the rotating-wave approximation. This approach is applicable to a wide range of weakly coupled environments representing experimentally relevant readout devices. We study in detail the case of thermal decay in the presence of a generic Ohmic bosonic bath, in particular for potential fluctuations in an electromagnetic circuit. In addition, we consider the nonequilibrium measurement environment for a parity readout using a quantum point contact capacitively coupled to the dot charge.