Enhancing the Robustness of Dynamical Decoupling Sequences with Correlated Random Phases

Round 1

Reviewer 1 Report

Dear Editor,

The manuscript “Enhancing the robustness of dynamical decoupling sequences with correlated random phases” by Zhen-Yu Wang, Jorge Casanova, and Martin B. Plenio proposes advancement to the random phase dynamical decoupling sequences. In particular, instead of simple random walk in the phase space they suggest to restrict the phase sequence in the way to get total zero phase. Such a method allows reducing the error accumulated during dynamical decoupling procedure. The topic considered in the paper is related to quantum computation. This topic is a fast growing and extremely promising area of quantum physics nowadays. Therefore, the paper is timely and actual. There are many urgent problems in the topic on experimental and theoretical sides. The results presented in the present paper would certainly useful for researchers working in the field. Interestingly, that symmetric phase sequence provides better error suppression than chaotic one. This finding is certainly deserved publication in the Symmetry journal.  

 

However, I suggest introducing some changes in the manuscript prior to publication.

 

1. That would be useful if authors explicitly define fidelity, detuning error and amplitude error (appearing in figures) through initial parameters in their rotation operators.
2. Description of panels c and d in Fig. 2 is somewhat confusing. Is this a difference between fidelity of author’s correlated protocol and uncorrelated protocol. It would be useful to provide fidelity for uncorrelated random phase decoupling as well.
3. When M=6 we have 5 random number. I think that self averaging does not happen in this case. You should have strong fluctuations of the final state and fidelity from try to try. Do you also average your result over many tries?
4. What if the phase is correlated (with zero total change) but is not random (follows a certain law)? Would you get similar results? For example, apply 0 and pi phase one after another.
5. The error coming from the incorrect amplitude and detuning is systematic. Can not it be corrected by adding some constant phase addition at each pulse unit? This phase can be defined from an experiment.
6. For the uncorrelated protocol there is an expression for control errors suppression . Can you also provide similar law for correlated phase error correction?
7. Can authors also provide more details on their numerical simulation or at least give a reference to their previous paper where they describe such simulations. What is “population”? That would be useful (especially for people not working with nitrogen vacancies in diamond) to present description of physical system under consideration. How magnetic field is applied, where is H and C atoms, what is measured …

Author Response

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Author Response File: Author Response.docx

Reviewer 2 Report

The authors present here a small and presumably simple modification (or constraint on phases) to their previous paper on randomized DD pulse sequences (Wang et al., PRL 122, 200403, or Ref. 35).

While seemingly this is a simple increment in terms of scientific value, Wang et al. show that in fact by a proper choice of number of phase-correlated pulses they can (in theory). The effect of correlating the phases of the pulses becomes apparent for large pulse errors (or detuning), which is in real life can be indeed the case.

The presentation of the main idea as well as the calculations supporting it are clear and I believe the reader would grasp the entire message very quickly.

Apart for a few small comments the authors should address (see below), I recommend publication of this manuscript in Symmetry (I see that one of the co-authors is also a guest-editor of this special edition).

 

Comments:

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(1) Fig.1 (c) and (d) (pulse sequence) is the same. This can be compacted to random walk vs. correlated walk (sum 0) sharing the same pulse sequence.

(2) page 3, lines 46-48: I am not the assumption of a static pulse error is a good one for an experimental apparatus. They authors should either justify this (by consulting with an experimentalist) or address the case of a non-static (with some probability distribution) pulse error for consecutive ones.

(3) Figure 3 and the respective text: What is missing is the analytical dependence on G for a given M. Is there an optimal number?

(4) In both figures 2 and 3 the comparison with Ref. 35 is not always clear. I would recommend placing the calculations for both Ref. 35 and the present manuscript side-by-side. The way they are presented here ("increased values of the fidelity") is not entirely intuitive and perhaps the reader would benefit from a simple display of both the original randomized pulses and the correlated-phases one.

Author Response

Please see the attachment.

Author Response File: Author Response.docx