Abstract
We analyze a readout scheme for Majorana qubits based on dispersive coupling to a resonator. We consider two variants of Majorana qubits: the Majorana transmon and the Majorana box qubit. In both cases, the qubit-resonator interaction can produce sizeable dispersive shifts in the MHz range for reasonable system parameters, allowing for submicrosecond readout with high fidelity. For Majorana transmons, the light-matter interaction used for readout manifestly conserves Majorana parity, which leads to a notion of quantum nondemolition (QND) readout that is stronger than for conventional charge qubits. In contrast, Majorana box qubits only recover an approximately QND readout mechanism in the dispersive limit where the resonator detuning is large. We also compare dispersive readout to longitudinal readout for the Majorana box qubit. We show that the latter gives faster and higher fidelity readout for reasonable parameters, while having the additional advantage of being manifestly QND, and so may prove to be a better readout mechanism for these systems.
Highlights
Topological phases of matter offer a promising platform for quantum information processing, as qubits encoded into the degenerate ground states of these exotic phases should be extremely robust to errors [1,2,3]
For Majorana transmons, the light-matter interaction used for readout manifestly conserves Majorana parity, which leads to a notion of quantum nondemolition (QND) readout that is stronger than for conventional charge qubits
We compare dispersive readout to longitudinal readout for the Majorana box qubit. We show that the latter gives faster and higher fidelity readout for reasonable parameters, while having the additional advantage of being manifestly QND, and so may prove to be a better readout mechanism for these systems
Summary
Topological phases of matter offer a promising platform for quantum information processing, as qubits encoded into the degenerate ground states of these exotic phases should be extremely robust to errors [1,2,3]. The size of these dispersive shifts directly determine the rate at which one can perform qubit readout by driving the resonator and observing the phase shift of the reflected field [50] It determines the clock frequency in measurement-only approaches to quantum computation with MZMs. Majorana qubits differ from conventional superconducting charge qubits, such as the Cooper pair box and the transmon [51], as a dispersive shift for a Majorana qubit can arise despite the fact that the interaction with the resonator does not induce (virtual) transitions between the two logical qubit states. III and IV we describe in detail the dispersive coupling for a Majorana transmon and a Majorana box qubit, respectively For both qubit variants, we calculate the dispersive frequency shift of a readout resonator from secondorder Schrieffer-Wolff perturbation theory for a range of system parameters using numerical diagonalization. VI we discuss the implications of our results for dispersive readout of Majorana qubits
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