Visibility of noisy quantum dot-based measurements of Majorana qubits

Submission summary

 As Contributors: Torsten Karzig · Aleksei Khindanov · Dmitry Pikulin Arxiv Link: https://arxiv.org/abs/2007.11024v3 (pdf) Date accepted: 2021-05-17 Date submitted: 2021-04-12 07:04 Submitted by: Khindanov, Aleksei Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory Quantum Physics Approach: Theoretical

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.

Published as SciPost Phys. 10, 127 (2021)

Modifications and clarifications addressing the referee reports. See list of changes and referee replies for details.

List of changes

- On page 1, bottom of the left column, added description of what is meant by $\sigma_z$ and $\gamma_{i/j}$.
- On page 2, left column, second paragraph, added description of what is meant by "resonance" and "far-detuned regime".
- On page 2, paragraph after Eq.(2), explained in which case the regime of a single-level QD is appropriate.
- At the end of page 3, added a sentence describing implications of incorrect readout of the Majorana parity on quantum computation.
- On page 4, first full paragraph after Eq.(9), changed "single electron" to "single excess electron".
- On page 4, last paragraph in the left column, rephrased the first sentence such that it is more clear what is meant by "exponentially small" couplings.
- On page 5, first paragraph in the right column, added a sentence which describes the motivation for using $1/f$ noise model.
- At the end of page 5 and beginning of page 6, rewrote discussion on how we treat temperature when calculating expectation values.
- On page 6, paragraph after Eq.(19), added physical motivation for the higher frequency cutoff $\tau_c^{-1}$.
- On page 7, second paragraph in the left column, added reference to Appendix E.
- On page 7, second to last paragraph in the left column, added that the noise-induced term in $S_n$ is perturbative and description of what is meant by that.
- On page 7, first paragraph in the right column, described in more detail what is meant by "smaller coupling".
- Throughout page 7, changed notation from $\bar{t}_-\to |\bar{t}_-|$, $\bar{t}_+\to |\bar{t}_+|$, $\langle C_+\rangle\to C_{\text{diff},+}$ and $\langle n_+ \rangle\to \langle n_{\text{QD},+} \rangle$.