Dispersive readout of Majorana qubits

TL;DR

This paper explores dispersive readout techniques for Majorana qubits, demonstrating high-fidelity, potentially quantum nondemolition measurements, and compares different qubit types and readout methods for optimal performance.

Contribution

It introduces a dispersive readout scheme for Majorana qubits, analyzing its effectiveness and comparing it with longitudinal readout to identify the most promising approach.

Findings

Dispersive shifts in the MHz range enable fast, high-fidelity readout.

Majorana transmons allow for quantum nondemolition readout conserving parity.

Longitudinal readout offers faster, higher fidelity, and QND advantages for Majorana box qubits.

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.