Readout of Majorana Qubits

Abstract

Schemes for topological quantum computation with Majorana bound states rely heavily on the ability to measure products of Majorana operators projectively. Here, we employ Markovian quantum measurement theory, including the readout device, to analyze such measurements. Specifically, we focus on the readout of Majorana qubits via continuous charge sensing of a tunnel-coupled quantum dot by a quantum point contact. We show that projective measurements of Majorana products $\prod_i\hat{\gamma}_i$ can be implemented by continuous charge sensing under quite general circumstances. Essential requirements are that a combined local parity $\hat{\pi}$, involving the quantum dot charge along with the Majorana product of interest, be conserved, and that the two eigenspaces of the combined parity $\hat{\pi}$ generate distinguishable measurement signals. We find that qubit readout may have to rely on measuring noise correlations of the quantum-point-contact current. The average current encodes the qubit readout only transiently for fine-tuned parameters or in the presence of relaxation processes. We also discuss the corresponding measurement and decoherence times and consider processes such as residual Majorana hybridizations which are detrimental to the measurement protocol. Finally, we emphasize that the underlying mechanism -- which we term symmetry-protected readout -- is quite general and has further implications for both, Majorana and non-Majorana systems.