Parity readout in Majorana box qubits from the dispersive to the resonant regime

TL;DR

This paper develops a comprehensive theoretical model for charge reflectometry and capacitive readout of Majorana box qubits, analyzing the crossover from dispersive to resonant regimes and assessing the validity of semiclassical approximations.

Contribution

It provides a unified expression for the parity-dependent susceptibility across regimes and evaluates the accuracy of semiclassical assumptions in different regimes.

Findings

Semiclassical approximation is valid in the dispersive regime.

Deviations in the resonant regime are a few percent.

The model covers the full crossover from dispersive to resonant regimes.

Abstract

We study theoretical models for charge reflectometry and capacitive readout of the Majorana parity degree of freedom in Majorana box qubits, taking into account decoherence channels within the framework of the Lindblad master equation. Noting that a parity-dependent dynamical susceptibility $\chi_z(\omega)$ governs both readout schemes, we provide a general expression for $\chi_z(\omega)$ which covers the full crossover from the resonant regime to the off-resonant dispersive regime. In addition, we re-examine previous results which were obtained under a semiclassical factorization assumption. Using three different error measures, we show that this approximation is quantitatively justified in the dispersive regime. In the resonant regime, however, we find deviations from exact reference data, obtained by numerical solution for the steady state of the full Lindblad equation. These deviations are typically of the order of a few percent in the considered error measures.