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Holonomic implementation of CNOT gate on topological Majorana qubits

by Alessio Calzona, Nicolas P. Bauer, Björn Trauzettel

Submission summary

As Contributors: Alessio Calzona
Preprint link: scipost_202010_00010v1
Code repository:
Date accepted: 2020-12-01
Date submitted: 2020-10-13 13:35
Submitted by: Calzona, Alessio
Submitted to: SciPost Physics Core
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approach: Theoretical


The CNOT gate is a two-qubit gate which is essential for universal quantum computation. A well-established approach to implement it within Majorana-based qubits relies on subsequent measurement of (joint) Majorana parities. We propose an alternative scheme which operates a protected CNOT gate via the holonomic control of a handful of system parameters, without requiring any measurement. We show how the adiabatic tuning of pair-wise couplings between Majoranas can robustly lead to the full entanglement of two qubits, insensitive with respect to small variations in the control of the parameters.

Published as SciPost Phys. Core 3, 014 (2020)

Author comments upon resubmission

Dear Editor,

we would like to resubmit our manuscript "Holonomic implementation of CNOT gate on topological Majorana qubits" for publication in SciPost Physics Core.

We thank the referees for their detailed reports and for their appreciation of the validity and clarity of our paper. They both identify the degree of novelty of our results as the main weakness of our manuscript. While we agree that the possibility to holonomically implement an entangling gate can be expected in view of its formal equivalence with the known measurement-based protocols, we strongly believe in the significance of our work. This is due to two main intertwined reasons. (i) On a practical level, the implementation of our protocols differs from their measurement-only counterparts and it features different experimental challenges (e.g. reaching adiabaticity instead of implementing high-fidelity projective measurements). Given the early stage of experimental development, our results help in broadening and shining light on the spectrum of possible implementations. (ii) To the best of our knowledge, our paper is the first one to explicitly discuss the holonomic implementation of entangling gates on Majorana qubits. This is in sharp contrast with the case of topological single-qubit gates, which have been carefully studied in a plethora of different implementations (despite their formal equivalence). In this respect, our results provide direct and solid answers to questions that are specific to the holonomic implementation (e.g. effects of non-adiabaticity and non-optimal tuning of the couplings).

In the revised version of the manuscript, we better clarify the relationship between our holonomic protocols and the known measurement-based schemes. Moreover, we address the questions and comments raised by the referees. We believe that the new version of the manuscript fulfills all of the acceptance criteria of SciPost Physics Core and we hope that the Referees, and eventually the Editor, will agree with us.

Best regards,
A. Calzona, N. P. Bauer and B. Trauzettel

List of changes

> We have corrected different typos.
> We have added the new Appendix B to better discuss the role of asymmetries in the coupling \chi_y
> We have modified and enriched the paragraph where we discuss the non-adiabatic errors.
> We have added 5 new references ([58-62]) and replaced some arXiv preprints with the published version.
> We have updated the numerical data/codes, which can now be accessed at

Reports on this Submission

Anonymous Report 1 on 2020-11-2 Invited Report

  • Cite as: Anonymous, Report on arXiv:scipost_202010_00010v1, delivered 2020-11-02, doi: 10.21468/SciPost.Report.2138


1- Meets all general acceptance criteria
2- Clarity of exposition
3- Completeness of the analysis


I would like to thank the Authors for their detailed reply to my report. I have reviewed the Authors' reply to both reports as well as the new manuscript.

I find the reply persuasive, and also that the new Appendix B properly fills the gap with respect to question about additional couplings raised in my first report. The additional remarks about the scaling of non-adiabatic corrections are also useful.

Given also that the Authors have followed the suggestion to submit to SciPost Physics Core, I think there are no reasons to further delay publication of this work.

  • validity: high
  • significance: good
  • originality: ok
  • clarity: high
  • formatting: excellent
  • grammar: excellent

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