Abstract
Measurement schemes of Majorana zero modes (MZMs) based on quantum dots (QDs) are of current interest as they provide a scalable platform for topological quantum computation. In a coupled qubit-QD setup we calculate the dependence of the charge of the QD and its differential capacitance on experimentally tunable parameters for both 2-MZM and 4-MZM measurements. We quantify the effect of noise on the measurement visibility by considering 1/f noise in detuning, tunneling amplitudes or phase. We find that on- or close-to-resonance measurements are generally preferable and predict, using conservative noise estimates, that noise coupling to the QDs is not a limitation to high-fidelity measurements of topological qubits.
Highlights
In the present work we identified detuning charge noise as the dominant source of intrinsic noise that affects the measurement visibility of Majorana qubits probed by quantum dots (QDs)
We studied the Hamiltonian for 2-Majorana zero modes (MZMs) and 4-MZM measurements non-perturbatively in the tunnel coupling and emphasized the similarity of their description in the regime of small detunings which in general optimizes signal-to-noise ratio (SNR) in the presence of external noise. 4-MZM measurements require more tuning and more manipulations to bring the system into the optimal measurement regime, but can produce signal of the same order as 2-MZM measurements
We obtain large SNRs 10 for conservative assumptions on the charge noise of the system that is tuned to the optimal measurement regime
Summary
Majorana Zero Modes (MZMs) are explored as a promising platform for topological quantum computation [1,2,3,4,5]. Measurements of the qubits are performed by coupling two (for single qubit measurements, see Fig. 1(a)) or four (for two-qubit measurements, see Fig. 1(b)) MZMs to quantum dots (QDs) while using parity-dependent shifts of the QD charge or capacitance as the readout signal Such QD-based measurements are promising since they can be embedded in scalable designs for the operation of topological qubits [34]. We present details of calculations and treatment of the subleading noise sources – flux and coupling noise
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