Quantum Representation for Deterministic Push-Down Automata

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this manuscript by Puram, George and Thomas, they studied a specific quantum representation of a special automata called Deterministic Push-Down Automaton (DPDA). It follows a path that begins with classical definitions and culminates in a quantum circuit. Specifically, we start with a Deterministic Pushdown Automaton (DPDA) and present circuits for state transitions and stack operations. These circuits are independent algorithms, with, for instance, the method used for constructing the state transition circuit also applicable to circuits for Boolean matrix functions.

 

I have read through this manuscript, and I have a good opinion of it. The model is well presented, and the background is illustrated clearly. The algorithm is also clear. Overall, it satisfies the scope of electronic journal itself. I would like to recommend it for publication if the authors could edit this version of the manuscript as follows:

     The authors actually illustrated several quantum circuits implementation for various cases throughout the manuscript. But it seems that the size is enormous. Can the authors expand the lines in the results (and other various parts of the manuscript) to further comment on how does the error affect their results on a NISQ-era quantum device in detail?

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The article is written in a way that, after significant effort by the author, is understandable. In terms of content, the article is written correctly. All the considerations contained within are conducted properly. I did not find any errors. Unfortunately, the article is not well-balanced. Almost the entire article is devoted to theoretical considerations, with very little space given to numerical examples. Of course, the article is 20 pages long, but there are ways to reduce the number of pages. For example, improving the figures so that they take up less space. The figures are very simple, and they can easily be reduced by 50%. Improving editorial flaws and redrawing the figures would save a few pages of text.

The editorial aspect is the weakest part of the article. After the Introduction, which I consider excellently written as it introduces the reader to the subject area discussed later and well defines the article's contribution to the field, there are chapters that require much editorial work. The number of errors is so high that I only list a few initial ones. The authors should carefully review the text themselves to catch all deficiencies.

1. Many acronyms are defined multiple times.
2. Not all mathematical symbols are defined (see lines 149, 150).
3. Variables used in mathematical expressions should be written using the appropriate font.
4. In Figure 1 (line 174), symbol "n" should have a specific value.
5. I suggest consistently using apostrophes and quotation marks (line 188).
6. Equation written in line 254 – mixing subscripts with normal font.
7. From section 4.1, symbols in bold font appear. Do they have a different meaning from symbols in regular font?
8. The operation presented in lines 277 and 316 (and further) should be defined.
9. The layout of the figures should be changed. The next reference after Figure 1 is Figure 8 (line 345).
10. There is no need to add a caption after the algorithm, especially if it is defined in the first line of the algorithm.
11. After line 391, I stopped noting remarks on the editorial side. The authors should carefully review the entire text themselves to catch any errors.

What I suggest to the authors:

1. Improve the text in terms of editorial quality.
2. Improve the figures.
3. Add numerical examples.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

I am responding to MDPI request for me to provide you with a report in connection with the submitted manuscript “Quantum Representation for Deterministic Pushdown Automata” by Varun Puram, K M George and Johnson P Thomas. I am pleased to do so.

In this article, the authors have studied a few quntum computing models. More precisely, they have started from a Deterministic Push-Down Automaton (DPDA). They have presented a circuit for state transition and stack operations. The circuits presented can be viewed as independent algorithms. As an example, the approach used to construct the circuit for state transition can be utilized to build the circuit for a function presented as a Boolean matrix. Their research topic is very interesting, the presentation is very good and their results appear to be correct. It would be better if the authors could consider the following comments:

1)     Is it possible, the authors to specify in introduction any physical structure (spin qubits coupled quantum dots, charge qubit coupled quantum dots, squid superconductors etc) which can describe the quantum bit? Please add any reference related to nanostructures.

2)     Do they have in mind any reliable circuit?

3)     Could they specify the role of the control gates and aux0 qubit? The text is very poor.

4)     How do they determine the state |0⟩ and |qi⟩, how many quantum states have they included?

5)     They have written: “Dead states could be added to handle null transitions {∅}.” Please clarify the “dead states”.

6)     Please, explain the state transition matrices or add any reference related to the transition matrices.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

Quantum computing is probably one of the hottest and most fascinating topics for researchers. It was therefore my pleasure to review a manuscript on quantum representation for deterministic pushdown automaton. The authors describe a Deterministic Push-Down Automaton (DPDA), and then a quantum gate based circuit for state transition and stack operations. These circuits can be viewed as independent algorithms. For this reason, we can design the circuit for state transition can be utilized to build the circuit for a function presented as a Boolean matrix. The work is well written and contains readable Fihures. However, there are some shortcomings that should be corrected.

1. There is a lack of affiliations of aurors.

2. The Related Work section is too poor. Only 11 literature sources are listed in the References.

3. There is no confirmation of any attempt to verify the model using any quantum simulation. Was such a simulation ever performed? With what tool?

4. Minor errors:

a) mathematical quantity symbols should be written in italics, which is not the case in some cases, e.g. line 231 q, line 241 K.

b) Figure 3 shows a quantum circuit for control state transition when the current state is 4. A short description of the basic graphic symbols should be added or the tool used to make this drawing (Qiskit or other) should be indicated.

 

c) How do auxiliary qubits work in Figure 4?

 

After correcting the above shortcomings, I will try to quickly make a second review of this interesting manuscript.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Round 2

Reviewer 4 Report

Comments and Suggestions for Authors

Thank you for taking my suggestions into account, which will undoubtedly contribute to a better understanding of the article by the Readers.