Round 1

Reviewer 1 Report

Topics:

The topic of this article, combining Quantum Computing, Neural Networks, and Value at Risk (VaR) estimation, is highly relevant and interesting, especially in the context of financial risk management.

 

Abstract & Keywords:

The abstract provides a concise overview of the study. It might benefit from a brief mention of the practical applications of improved VaR estimation for readers who are not experts in the field. Keywords are relevant and comprehensive.

 

Article Structure:

The structure of the article follows a logical sequence, making it easy to follow the research process.

 

Introduction:

The introduction effectively introduces the importance of VaR estimation in financial risk management. Consider providing a more in-depth explanation of why traditional methods sometimes fall short in capturing the complexities of financial markets.

 

Monte Carlo VaR Estimation:

The section on Monte Carlo VaR estimation is informative and clear.

 

Linear Approach to Monte Carlo Estimation:

This section provides a good foundation for the later introduction of Quantum Computing.

 

Quantum Computing:

The introduction of Quantum Computing is well-done. However, it's important to remember that readers may have varying levels of familiarity with this topic, so some additional context could be helpful.

 

Neural Networks:

The section on Neural Networks is informative, but consider elaborating on the specific types of neural networks used and their advantages in this context.

 

Research methods:

The methodology section provides a comprehensive overview of the research approach.

 

Research result:

The results section clearly presents the findings. Visual aids, such as graphs or tables, can enhance the understanding of the results.

 

Discussion:

The discussion section effectively analyzes the implications of the findings. Consider discussing potential limitations of the study and how they might have affected the results.

 

Conclusion:

The conclusion summarizes the key findings and their significance well.

 

Recommendation:

Providing recommendations for future research in this area is a valuable addition.

 

References & Citations:

Ensure that all sources are properly cited following the appropriate citation style.

 

Open Problem:

Expanding on the "Open Questions" or "Future Work" section could inspire further research in this domain.

The use of English in this manuscript is quite good.

Author Response

Reviewer 1

Reviewer’s introduction

Topics: The topic of this article, combining Quantum Computing, Neural Networks, and Value at Risk

(VaR) estimation, is highly relevant and interesting, especially in the context of financial risk management.

Authors’ response:

First, we’d like to thank you for taking the time to thoroughly review our work.

Reviewer #1, Concern #1:

Abstract & Keywords: The abstract provides a concise overview of the study. It might benefit from a brief mention of the practical applications of improved VaR estimation for readers who are not experts in the field.

Keywords are relevant and comprehensive.

Authors’ response:

We have extended the abstract, including a brief description of the application of quantum computing for VaR estimations.

Reviewer #1, Concern #2:

Article Structure: The structure of the article follows a logical sequence, making it easy to follow the research process.

Authors’ response:

Thank you. Following the same sequence, we have added a subsection for discussion and another section for related work.

Reviewer #1, Concern #3:

Introduction: The introduction effectively introduces the importance of VaR estimation in financial risk management. Consider providing a more in-depth explanation of why traditional methods sometimes fall short in capturing the complexities of financial markets.

Authors’ response:

We have extended the introduction, explaining the challenges that classical methods face.

Reviewer #1, Concern #4:

Monte Carlo VaR Estimation: The section on Monte Carlo VaR estimation is informative and clear.

Linear Approach to Monte Carlo Estimation: This section provides a good foundation for the later introduction of Quantum Computing.

Authors’ response: Thank you. We have extended both sections to make them clearer.

Reviewer #1, Concern #5:

Quantum Computing: The introduction of Quantum Computing is well-done. However, it’s important to remember that readers may have varying levels of familiarity with this topic, so some additional context could be helpful.

Authors’ response:

As suggested, we have added a brief explanation of what quantum computing is based on.

Reviewer #1, Concern #6:

Neural Networks: The section on Neural Networks is informative, but consider elaborating on the specific types of neural networks used and their advantages in this context.

Authors’ response:

Based on your request, we have elaborated more on the used neural network and why the number of hidden layers is the right choice. Additionally, we have included a table and a figure to better describe the used neural network.

Reviewer #1, Concern #7:

Research methods: The methodology section provides a comprehensive overview of the research approach.

Authors’ response:

Thank you. Following other reviewer comments, we have included further explanations.

Reviewer #1, Concern #8:

Research result: The results section clearly presents the findings. Visual aids, such as graphs or tables, can enhance the understanding of the results.

Authors’ response:

As suggested, we have included more graphics and a table.

Reviewer #1, Concern #9:

Discussion: The discussion section effectively analyzes the implications of the findings. Consider discussing potential limitations of the study and how they might have affected the results.

Authors’ response:

We have included a whole subsection to further discuss the limitations of the study.

Reviewer #1, Concern #10:

Conclusion: The conclusion summarizes the key findings and their significance well.

Authors’ response:

Thank you.

Reviewer #1, Concern #11:

Recommendation: Providing recommendations for future research in this area is a valuable addition.

Authors’ response:

As requested, we have included more future research lines in the conclusions.

Reviewer #1, Concern #12:

References & Citations: Ensure that all sources are properly cited following the appropriate citation style.

Authors’ response:

We have checked that all sources are properly cited. In order to ensure the journal citation style, we use bibtex in this version of the manuscript.

Reviewer #1, Concern #13:

Open Problem: Expanding on the ”Open Questions” or ”Future Work” section could inspire further research in this domain.

Authors’ response:

We hope the new research lines included in the conclusions help to inspire multidisciplinary research, including quantum computing, neural networks, and finance risk modeling.

Reviewer #1, Concern #14:

Comments on the Quality of English Language: The use of English in this manuscript is quite good.

Authors’ response:

Thank you. Based on the comments of other reviewer, we have done a thorough check on the English Language.

Reviewer 2 Report

          This paper studies an interesting problem indeed and, from what I understand, makes a noteworthy contribution towards its solution.

          The organization of the paper is quite good. A minor remark would be that the introduction is somewhat short and the typical “Related Work” section seems to be missing. On the other hand, I got the impression that the authors know this field quite well.

           The rest of the paper is also well-organized. The sections have logical coherence and follow a reasonable pattern of increasing complexity. I think that the Figures are helpful, particularly Figure 6, and facilitate the understanding on behalf of the reader.

          From my personal experience with Qiskit, I agree with their remarks regarding the current capabilities and limitations of Qiskit. Hence, I find their approach utilizing Neural Networks clever and plausible. Ideally, I would have liked a much more extended subsection “5.4 Execution in real quantum computers“, perhaps accompanied by some short of Example, as this is, in my view, one of the pivotal sections of this paper.

          Their command of the English language is quite good.

          In conclusion, I think that this paper has merit and deserves publication, after minor revisions.

Author Response

Reviewer 2

Reviewer’s introduction

This paper studies an interesting problem indeed and, from what I understand, makes a noteworthy contribution towards its solution.

Authors’ response:

First, we’d like to thank you for reviewing our work.

Reviewer #2, Concern #1:

The organization of the paper is quite good. A minor remark would be that the introduction is somewhat short and the typical “Related Work” section seems to be missing. On the other hand, I got the impression that the authors know this field quite well.

Authors’ response:

Thank you. As requested, we have extended the introduction and included a related work section before the conclusions, once our approach has been fully explained.

Reviewer #2, Concern #2:

The rest of the paper is also well-organized. The sections have logical coherence and follow a reasonable pattern of increasing complexity. I think that the Figures are helpful, particularly Figure 6, and facilitate the understanding on behalf of the reader.

Authors’ response:

Thank you. We have further elaborated figure 9 (former figure 6) to make it more readable.

Reviewer #2, Concern #3:

From my personal experience with Qiskit, I agree with their remarks regarding the current capabilities and limitations of Qiskit. Hence, I find their approach utilizing Neural Networks clever and plausible. Ideally, I would have liked a much more extended subsection “5.4 Execution in real quantum computers“, perhaps accompanied by some short of Example, as this is, in my view, one of the pivotal sections of this paper.

Authors’ response:

As suggested, we have extended subsection 5.4 with more details on the execution on real quantum computers.

Reviewer #2, Concern #4:

Comments on the Quality of English Language: Their command of the English language is quite good.

Authors’ response:

Thank you. Anyway, based on the comments of other reviewer, we have done a thorough check on the English Language.

Reviewer #2, Concern #5:

Summary: In conclusion, I think that this paper has merit and deserves publication, after minor revisions.

Authors’ response:

Thank you. We hope our revision meets the expectation.

Reviewer 3 Report

This paper studies the performance of quantum computing by employing neural networks. The topic is timely and suitable for publication in Mathematics. This reviewer has some comments given below

In the Abstract section, the authors should provide a more detail system model, and the solved problem(s), and discuss results with quantities numbers.

The affiliation, and email address of all authors should be given according to the MDPI template.

The introduction must be re-written to motivate and elaborate on which problems are going to be studied and the related works. All related works must be discussed and their advantages and disadvantages too.

In Section II, the detailed system model has to be discussed prudently, which scenarios are considered, which assumptions are taken, etc.

A discussion on the training data should be given, and the mathematical framework of the neural networks should be provided too.

In the numerical results section, more figures, and studies should be given to comprehensively evaluate the proposed approach. Additionally, comparisons with other methods must be given as well.

All uncited references must be removed.

Comments for author File: Comments.pdf

The English can be improved.

Author Response

Reviewer 3

Reviewer’s introduction

This paper studies the performance of quantum computing by employing neural networks. The topic is timely and suitable for publication in Mathematics. This reviewer has some comments given below.

Authors’ response:

Thank you for reviewing our work and comments. We believe the manuscript is now clearer and stronger.

Reviewer #3, Concern #1:

In the Abstract section, the authors should provide a more detail system model, and the solved problem(s), and discuss results with quantities numbers.

Authors’ response:

We have included a brief description of the system, the solved problem and some figures of the obtained results.

Reviewer #3, Concern #2:

The affiliation, and email address of all authors should be given according to the MDPI template.

Authors’ response:

We have carefully checked we are following the MDPI template for affiliation and e-mail addresses.

Reviewer #3, Concern #3:

The introduction must be re-written to motivate and elaborate on which problems are going to be studied and the related works. All related works must be discussed and their advantages and disadvantages too.

Authors’ response:

We have conducted a deep revision of the introduction to better motivate and elaborate the challenges addressed in the paper. We have also included a related work section, providing their advantages and disadvantages with respect to our work.

 

Reviewer #3, Concern #4:

In Section II, the detailed system model has to be discussed prudently, which scenarios are considered, which assumptions are taken, etc.

Authors’ response:

As requested, we have extended Section II, including assumptions and several scenarios (algorithm development and testing).

Reviewer #3, Concern #5:

A discussion on the training data should be given, and the mathematical framework of the neural networks should be provided too.

Authors’ response:

With respect to the neural network and its training data, we have included more information, as well as a table and a figure to better explain it.

Reviewer #3, Concern #6:

In the numerical results section, more figures, and studies should be given to comprehensively evaluate the proposed approach. Additionally, comparisons with other methods must be given as well.

Authors’ response:

We have included some figures related to the errors to better evaluate our approach.

Additionally, as stated before, we have included a new “Related work” section to compare our approach with other methods.

Reviewer #3, Concern #7:

All uncited references must be removed.

Authors’ response:

We have carefully checked that all references were cited in the text. In any case, in this version we use bibtex, so the references are ordered as they appear in the text.

Reviewer #3, Concern #8:

The motivation of choosing log-normal distribution is unclear as well as the percentile threshold. The authors should carefully justify this point since it has a big impact on the problem.

Authors’ response:

We have elaborated the decision of using Log-normal distribution for market modeling in the introduction. With respect to the percentile threshold, it depends on the Central Banks, but we make clear that it is usually in the 1% to 5% span.

Reviewer #3, Concern #9:

In Section 3.1, it is obvious that the accuracy of the Taylor series approximation is constrained by the small argument.

Authors’ response:

We have included the indication that the gain/loss is usually small, so Taylor series approximation fits in VaR calculations.

Reviewer #3, Concern #10:

The PDF in Figure 2 should be normalized to one.

Authors’ response:

We have normalized the axis of the PDF, so its integral is 1.

Reviewer #3, Concern #11:

The motivation and detailed explanation of the amplitude estimation should be provided so that readers can be easily followed.

Authors’ response:

We have moved the comment about the amplitude estimation approach to the related work, as we are not using it in our solution.

Reviewer #3, Concern #12:

All figures quality should be improved.

Authors’ response:

We have further elaborated all figures to improve their quality.

Reviewer #3, Concern #13:

The justifications for the results of VaR = -9441 when 4 qubits and VaR = -9669 when 8 qubits are necessary.

Authors’ response:

We have reviewed all the values used in the examples.

Reviewer #3, Concern #14:

Comments on the Quality of English Language: The English can be improved.

Authors’ response:

Based on your recommendation, we have carefully reviewed the text, to make it more readable.

Round 2

Reviewer 3 Report

The authors have addressed my comments. I have no novel one.

English is readable in the present version.

Author Response

Reviewer #3

Reviewer’s introduction

Comments and Suggestions for Authors: The authors have addressed my comments. I have no novel one.

Authors’ response:

Thank you for reviewing again our work. We believe the manuscript is now clearer and stronger.

Reviewer #3, Concern #1:

Comments on the Quality of English Language: English is readable in the present version.

Authors’ response:

We have carefully reviewed the text and figures again, fixing some typos and making the paper more readable.