Detection and Manipulation of Majorana Fermions in Circuit QED

Motivated by recent experimental progress to measure and manipulate Majorana fermions with superconducting circuits, we propose a device interfacing Majorana fermions with circuit quantum electrodynamics. The proposed circuit acts as a charge parity detector changing the resonance frequency of a superconducting \lambda/4 – resonator conditioned on the parity of charges on nearby gates. Operating at both charge and flux sweet-spots, this device is highly insensitive to environmental noise and enables high-fidelity single-shot quantum non-demolition readout of the state of a pair of Majorana fermions. Additionally, the interaction permits the realization of an arbitrary phase gate on the topological qubit, closing the loop for computational completeness. Away from the charge sweet-spot, this device can be used as a highly sensitive charge detector with a sensitivity smaller than 10^{-4} e / \sqrt{Hz} and bandwidth larger than 1 MHz.