From the journal Digital Discovery Peer review history

28-Dec-2022

Dear Dr Ghosh:

Manuscript ID: DD-ART-09-2022-000094
TITLE: Classical and quantum machine learning applications in spintronics

Thank you for your submission to Digital Discovery, published by the Royal Society of Chemistry. I sent your manuscript to reviewers and I have now received their reports which are copied below.

I have carefully evaluated your manuscript and the reviewers’ reports, and the reports indicate that major revisions are necessary.

Please submit a revised manuscript which addresses all of the reviewers’ comments. Further peer review of your revised manuscript may be needed. When you submit your revised manuscript please include a point by point response to the reviewers’ comments and highlight the changes you have made. Full details of the files you need to submit are listed at the end of this email.

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I look forward to receiving your revised manuscript.

Yours sincerely,
Linda Hung
Associate Editor
Digital Discovery
Royal Society of Chemistry

************

Respected Editors/ Reviewers,

We are grateful for the reviewing the manuscript and comprehensive feedback. We are attaching the following documents as a response to the decision letter.

1. Revised manuscript (Revised_manuscript.pdf).
2. Response to Referees (Referee_response.docx)
3. LaTeX and other supplementary files (Revised_manuscript.zip).
4. Data Availability Statement (Data_Availability_Statement .pdf)
5. Table of Contents Entry (A_table_of_contents_entry.docx)

Regards,
Kumar Ghosh and Sumit Ghosh.

This text has been copied from the Microsoft Word response to reviewers and does not include any figures, images or special characters:

We would like to thank the editor and the three referees for their valuable comments to improve our manuscripts. Here, we have listed their comments, our response, and changes made in the revised version. Changes are highlighted.

Referee 1:

Recommendation:
The manuscript shows a machine learning approach to predicting conductances and spin response function using random forests. The work is timely and could simplify quantum mechanical simulations. I recommend that the manuscript can be accepted after the authors address my comments below.

Comments:
1) In The authors mention the difficulty of training Machine Learning models due to the large amount of data that needs to be used. However, the first model trained just consists of 17 input parameters and is trained in 5 seconds which seems like a small model compared to state-of-the-art AI models with billions of parameters that need months tom train. Can the he authors comment on this disconnect?

Response: The main objective of this paper is to demonstrate the feasibility of applying machine learning algorithm in spintronics to predict different physical observable. The method we presented here is not limited by the number of parameters or datapoint. With sufficient computational resource, one can use a larger set of input parameters with larger dataset to predict the behaviour of larger system. The referee is right to point that the with months of training the state-of-the art AI models can handle billions of parameters. However, for most physical problem the challenge is to express the physical observable as a function of minimum number of parameters. Considering the highly non-linear outcome, as we show in our results, this is a highly non-trivial task. Besides, experimentally one can obtain only few features of a system and therefore for practical use one requires a method which can predict a highly nonlinear outcome from fewer input parameter.


2) How many parameters are part of the ML model that is used for the classical and quantum approach? Are the model parameters the same for both models?

Response: For classical ML model we consider 17 input parameters. First 16 inputs are the spin configuration of 16 magnetic sites (1 for ↑ spin and -1 for ↓ spin) and the 17th input is the energy at which the physical observables are calculated. In section 2.3 we describe the data and respective parameter in details.

For quantum machine learning we consider 2 input parameters and one output parameter. Here we keep a fixed spin configuration and choose the strength of Rashba spin-orbit interaction (tR) and the transmission energy (E) as the input parameter. The output parameter is the sign of onsite non-equilibrium Sx,y component. Due to limitation of resources, it is not possible to handle large number of input parameter or classes with QML at this point, however, with sufficient resource, our approach is applicable to larger parameter space and dataset. In section 3.3 we describe the data and respective parameter for quantum machine learning in details.


3) The authors mention that the ML approach is a favorable alternative compared to quantum mechanical calculations. Can the authors comment on why one would expect the quantum model to perform better. Is there an intuitive answer?

Response: Quantum mechanical calculations require exact description of the full system which makes them computationally very demanding. The physical observables on the other hand depends on a smaller subset of parameters. In quantum mechanical calculation it is usually not possible to trace out the relevant variables from the whole system and reduce the dimensionality of the problem. With a suitable choice of these parameters, ML approach provides a better alternative in this case by obtaining an effective response from the finite training data. For quantum mechanical system with exponentially large number of possible configurations, ML therefore is far more suitable option compared to the brute force quantum mechanical calculation.

The quantum machine learning models are powerful in terms of their scalability over the classical counterparts. For e.g., the overall complexity of the quantum SVM is O(log(NM)), compared to its classical counterpart O(M2(M+N)), where N is the dimension of the feature space and M is the number of training vectors. Also, in Ref 13 (arXiv:2112.08869 [quant-ph], 2021), the authors have shown that using a classical-quantum hybrid autoencoder (a type of quantum neural network) leads to a performance enhancement (compared to its classical counterpart) in terms of precision, recall, and F1 scores for standard anomaly detection. In the last paragraph of section 2.3 we describe complexity of quantum models compared to its classical counterparts.


4) Usually there is a training, validation and test set when a machine learning model is trained. The test set is only used in the last phase of testing after all optimisations are finished. In this manuscript, only a test set is used. What optimisations have been performed to reduce the test error? Is it clear that the the model is not overfitted to the test sets?

Response: We divide the whole dataset into different train and test dataset 50 times and took an average over the accuracy. The accuracy and standard deviation are also calculated by averaging over 50 different train-test cycles (see Table 1 and first paragraph of section 3.2). The 50-fold cross validation ensures the model to be free from overfitting.

5) Minor comments:
I have indicated some revisions below:
On page one the word spin is used twice in a row: "on manipulating spin spin degree of freedom and has been"
Rewrite this sentence: "In the ML approach these limited parameters are used to construct..."
Typo: "By discretising the continuous..."
Typo in Keywords: "Quantum transport, spintronics"

Response: In the revised manuscript, we have corrected all the typos and grammatical mistakes.




Referee 2:

Recommendation:
The authors use classical ML techniques to train and predict (conductance, spin density) properties of a multi-site spin system. They also introduce quantum ML approaches to study the system with limited feature set and analyze the viability of quantum ML over classical ML approaches.

Comments:
1) The code accompanying the paper is available on a public data repository (GITHUB). There are some issues with the documentation of the code on GITHUB that need to be fixed:

• A README file is needed to describe the dataset and the codes in the repository.
• Apart from README file in the repository, a brief description of the organization of the dataset and important parts of the code should also be mentioned in the paper.

Response: A README file is added in the GitHub describing the dataset and relevant files containing the classical and quantum ML codes. Organization of the dataset is mentioned in the paper in section 2.3 and the relevant codes are mentioned in Appendix A.


2) A better description of how the problem is treatable as a classification is needed. A visual illustration showing the inputs and the output (classes) may improve the readability of the manuscript.

Response: A visual illustration of data structure (inputs and output classes) and data analysis is presented in Fig. 5.

3) Some typos and grammatical errors in the manuscript should be corrected:
• Page 2 -“By DISCRETISE the continuous outcome”
• Page 2 – “The onsite energies ARE also consist of both”
• Page 6 – “the quantum classifier is performing better than IT'S classical counterparts”

Response: In the revised manuscript, we have corrected all the typos and grammatical mistakes.


Referee 3:

In this article, the authors have successfully illustrated by using modeling of a two terminal device with magnetic impurity how Random Forest ML algorithm, chosen as the best among three training algorithms, is capable of predicting the highly non-linear nature of conductance and the non-equilibrium spin response function for any random magnetic configuration relevant to their simplified model. The authors have claimed that quantum ML has the capability to handle a large configuration space and their approach is applicable for solid state devices as well as for designing molecular device systems which require much sizable configuration space for predicting their physical quantities.

As the authors have stated in the article, quantum ML algorithms will be powerful in terms of their scalability over the classical counterparts. Indeed, the authors’ method is generic and seems equally applicable to a large class of systems, especially molecular device models with rather simple electronic-structural parameters, but the method is essentially phenomenological. In this context, the application to realistic molecular systems won’t be straightforward. The authors have referred to the methodological easiness of the extension to molecular model systems without giving any tips. The article lacks this point. The last part of the conclusion seems overstated with this lack.


Comments:

1) The authors have intended to consistently prepare the article in British English, but they have given the American English spelling for some important words. And there are many typos and some grammatical errors, unfortunately.

Response: In the revised manuscript, we have corrected all the typos and grammatical mistakes.

07-Feb-2023

Dear Dr Ghosh:

Manuscript ID: DD-ART-09-2022-000094.R1
TITLE: Classical and quantum machine learning applications in spintronics

Thank you for your submission to Digital Discovery, published by the Royal Society of Chemistry. I sent your manuscript to reviewers and I have now received their reports which are copied below.

After careful evaluation of your manuscript and the reviewers’ reports, I will be pleased to accept your manuscript for publication after revisions.

Please revise your manuscript to fully address the reviewers’ comments. One of the reviewers has noted that there are some typos and grammatical errors in the manuscript. Although these will be checked when we prepare your manuscript for publication, please attempt to address these if possible.

When you submit your revised manuscript please include a point by point response to the reviewers’ comments and highlight the changes you have made. Full details of the files you need to submit are listed at the end of this email.

Digital Discovery strongly encourages authors of research articles to include an ‘Author contributions’ section in their manuscript, for publication in the final article. This should appear immediately above the ‘Conflict of interest’ and ‘Acknowledgement’ sections. I strongly recommend you use CRediT (the Contributor Roles Taxonomy, https://credit.niso.org/) for standardised contribution descriptions. All authors should have agreed to their individual contributions ahead of submission and these should accurately reflect contributions to the work. Please refer to our general author guidelines https://www.rsc.org/journals-books-databases/author-and-reviewer-hub/authors-information/responsibilities/ for more information.

Please submit your revised manuscript as soon as possible using this link :

*** PLEASE NOTE: This is a two-step process. After clicking on the link, you will be directed to a webpage to confirm. ***

https://mc.manuscriptcentral.com/dd?link_removed

(This link goes straight to your account, without the need to log in to the system. For your account security you should not share this link with others.)

Alternatively, you can login to your account (https://mc.manuscriptcentral.com/dd) where you will need your case-sensitive USER ID and password.

You should submit your revised manuscript as soon as possible; please note you will receive a series of automatic reminders. If your revisions will take a significant length of time, please contact me. If I do not hear from you, I may withdraw your manuscript from consideration and you will have to resubmit. Any resubmission will receive a new submission date.

The Royal Society of Chemistry requires all submitting authors to provide their ORCID iD when they submit a revised manuscript. This is quick and easy to do as part of the revised manuscript submission process.   We will publish this information with the article, and you may choose to have your ORCID record updated automatically with details of the publication.

Please also encourage your co-authors to sign up for their own ORCID account and associate it with their account on our manuscript submission system. For further information see: https://www.rsc.org/journals-books-databases/journal-authors-reviewers/processes-policies/#attribution-id

I look forward to receiving your revised manuscript.

Yours sincerely,
Linda Hung
Associate Editor
Digital Discovery
Royal Society of Chemistry

************

Reviewer 1

I very much appreciate the thoughtful responses of the authors.

However, it is not clear to me that the all answers to my points raised have been changed and highlighted in the paper in case a future reader will have the same questions. I recommend that the authors do the relevant changes to the manuscript and link the responses to the pages/lines in the manuscript. They could for example copy the changed lines under the response paragraphs.

The authors should also comment in the manuscript about what challenges and barriers would need to be overcome for their machine learning approach to be scaled up physically to 1000+ parameters/magnetic sites. Would you need a quantum computer to see the advantages of quantum machine learning or can the techniques be efficiently run on a classical computer?

Reviewer 2

The authors’ responses to the comments from Reviewer 3 have been given in a reasonable manner, except for the corrections in terms of the language rules. It seems that the authors have not seriously considered the reviewer’s comment on the language rules, and unfortunately there remain so many typos and grammatical errors including misspelling in British English, hoping that they will be corrected during the editing processes.

Reviewer 3

The authors have addressed my previous comments. So, I recommend the publication of this work.

We would like to thank the editor and the three referees for their valuable comments to improve our manuscript. We are attaching the revised manuscript, the referee response, and other supplementary files.

This text has been copied from the Microsoft Word response to reviewers and does not include any figures, images or special characters:

Referee 1:

Comments: I very much appreciate the thoughtful responses of the authors. However, it is not clear to me that the all answers to my points raised have been changed and highlighted in the paper in case a future reader will have the same questions. I recommend that the authors do the relevant changes to the manuscript and link the responses to the pages/lines in the manuscript. They could for example copy the changed lines under the response paragraphs.

Response: We have added additional texts in the manuscript (highlighted in yellow). Here we also provide a brief list of relevant modifications which answers the referee’s earlier comments.

1. The reason for choosing a small number of input parameters is given in the second paragraph of section 3 (page 5).
2. Description of input parameters is given in first paragraph of section 3 (page 4). Parameters for quantum classifier is defined in Sec3.3 (page 6).
3. The scaling of different methods is described in the last paragraph of Sec 2.3 (page 4).
4. Remarks on cross validation is provided on the first paragraph of Sec 3.2 (page 5).


Comments: The authors should also comment in the manuscript about what challenges and barriers would need to be overcome for their machine learning approach to be scaled up physically to 1000+ parameters/magnetic sites. Would you need a quantum computer to see the advantages of quantum machine learning or can the techniques be efficiently run on a classical computer?

Response: Considering the scalability of the quantum machine learning algorithms over their classical counter parts we shall obtain a significant enhancement in terms of the performance for a larger configuration space and data size (mentioned in conclusion section and Sec. 2.3). For example, the parameter space of a system containing 1000+ magnetic sites will be significantly large; therefore, QML will be the best viable option in that regime.

Referee2:

Comments:

The authors have addressed my previous comments. So, I recommend the publication of this work.

Response: We thank the referee for the positive comment.

Referee3:

Comments:

The authors’ responses to the comments from Reviewer 3 have been given in a reasonable manner, except for the corrections in terms of the language rules. It seems that the authors have not seriously considered the reviewer’s comment on the language rules, and unfortunately there remain so many typos and grammatical errors including misspelling in British English, hoping that they will be corrected during the editing processes.

Response: In the revised manuscript, we have corrected the typos and grammatical mistakes.

22-Feb-2023

Dear Dr Ghosh:

Manuscript ID: DD-ART-09-2022-000094.R2
TITLE: Classical and quantum machine learning applications in spintronics

Thank you for submitting your revised manuscript to Digital Discovery. I am pleased to accept your manuscript for publication in its current form. I have copied any final comments from the reviewer(s) below.

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Associate Editor
Digital Discovery
Royal Society of Chemistry

Reviewer 1

The authors addressed my concerns. I recommend to accept the manuscript.