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Visibility of noisy quantum dot-based measurements of Majorana qubits

by Aleksei Khindanov, Dmitry Pikulin, Torsten Karzig

Submission summary

As Contributors: Torsten Karzig · Aleksei Khindanov · Dmitry Pikulin
Arxiv Link: https://arxiv.org/abs/2007.11024v3 (pdf)
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.

Current status:
Editor-in-charge assigned


Author comments upon resubmission

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

List of changes

- Added reference [37, 48-50].
- 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 $\langle n_+ \rangle\to \langle n_{\text{QD},+} \rangle$.
- Added Appendix F.
- On page 7, second paragraph in the right column, added reference to Appendix F.
- On page 8, first paragraph in the right column, clarified that the regime of small detunings optimizes the SNR only in the presence of external noise.

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