Algorithms for Quantum Computation: The Derivatives of Discontinuous Functions

Round 1

Reviewer 1 Report

Please see the attached file. 

Comments for author File: Comments.pdf

Author Response

We improved perceived faults in the introduction, to provide more background and include all relevant references. We added the suggested references, even though they do not relate directly to the Problem of Closure. Perhaps the topic can be changed, but we consider that it fits.

We also changed the abstract, put Fig.(1) forward,  improved the English text, provided examples free of physics, and verified the references.

Reviewer 2 Report

Report of Algorithms for quantum computation: the derivatives of discontinuous functions

In this paper, in contrary to conventional assumptions, the author reports that discontinuous functions can be differentiated, which is central to algorithms for quantum computation. The author brings a new point of view on this topic, confirming the opinions of Nicolas Gisin on MRN, and Niels Bohr that physics is not reality, it is a fitting story about reality. The work proposes a solution in mathematics and opens theoretical space for Computer Science and new applications allowing, e. g., the derivative of discontinuous functions and deprecating the mean value theorem. This may sound strange, but new ideas are always welcome to help in difficult fields like the one covered in this paper. However, it would be necessary to clarify more that is being contributed as new.

The author follows a historical tour of what has been contributed so far on the subject, providing relevant examples and references, but it is not clear what his contribution to the subject is.

The authors should correct these aspects:

-        What do the red lines in Fig.1 represent? It is not clear that they are the values of the wave, since in some points the line stops when it reaches the wave and in others it does not. In addition, the figure does not add anything to the text.

-        Model 1 is not sufficiently explained. What is it useful for? It would be necessary to provide the utility of the method.

-        In the second paragraph of the first page, missing parentheses in the formula.

-        In the fourth paragraph of the first page, there is an extra [a] in the fifth line.

If the author had used the journal template, it would have made the review easier. Keep in mind for the future.

Finally, I do not understand the novelty of this paper, and what it contributes to the topic. Actually, a compilation of basic notions of calculation appears with little contribution to the subject in question.

In summary, the author must improve the paper to be published in this journal.

Author Response

We clarified the role of the red lines and named the discrete model, and put forward Eq.(1), to motivate the article. We also revised editorially the text and references, removing the problems noted, and others.

The novelty of this paper, and what it contributes to the topic, is manifold, and has been highlighted, also in the opening of the abstract. We also included examples, without physics or loss of generality.

Round 2

Reviewer 1 Report

This paper can be accepted. 

Author Response

thank you very much

Reviewer 2 Report

The proposed changes have been made by the author, so the article is recommended for publication.