Circuit Complexity in Interacting Quenched Quantum Field Theory

Round 1

Reviewer 1 Report

Dear prof.  Dr. Takayoshi Kobayashi

I have read manuscript number: symmetry-2235628 with the title:" Circuit Complexity in an interacting quenched Quantum Field Theory", and I found that the authors are using the invariant operator method, under a perturbation framework, for computing the ground state of circuit complexity for a quenched quantum field theory having weakly coupled quartic interaction. I would like the authors to consider the following points before I recommend the publication

1-In the introduction, the authors have written in the last two paragraphs "in this work, we:" and they write what they will do in the paper, after this they write "The organization of the paper is as follows:", why?

2-In section II, the authors use scalar field theory with  interaction term without reference and reason.

3-All symbols in equations must be defined.

4-the spelling of some words must be revised for example "organisation" on page 1.

5-The presentation and grammar need improvement. 

Author Response

Response is attached.

Author Response File: Author Response.pdf

Reviewer 2 Report

The authors explore the properties of a quenched state via circuit complexity. I support the publication of this work provided some important points are addressed and improved.

1.  The introduction need serious improvement in a few aspects. i.e. the main bulk of the introduction just talks broadly about previous work and then a sudden shift to what it is done here.

 A. it is necessary justify the results of this work with some argument not just 'motivated by the above...'. Also important concepts are not explained at all, just referenced. Eg. what is circuit complexity? A sharp explanation and motivation will go a long way.

B. The description of "in this work..." it not well thought out! You have 4 points but for example the first point its no novelty whatso ever just starting to explain what you did without reaching some result. Probably this 4 points would be better as a paragraph. Same with the organization of the paper, it fills a bit too long and again the bulletpoints dominate the page for no real reason. Bullet points should be reserved for importnat dinstict points. 

C. Too many citations! 150 in total is too much just by shear number + there are 50 of them bunched up after QCC. this is neither practical to the reader nor fair practice. 

D. I fill the citations also many as they are, tehy only focus to the same topic in some sence. A broader audience can be reached if such solutions are addressed for a broader class of field theories or quantum systems e.g. https://doi.org/10.1103/PhysRevLett.118.240402 and https://doi.org/10.1103/PhysRevB.98.155419

2. Why do you keep calling it a QFT? isnt this too general  you seem to solve the phi^4 theory just mentioned that in section II this general mention of qft feels a bit unprofessional. - do you think it also makes sense to also change the title? again if you are solving for the quatratic interaction just mention that instad of QFT.

3. Section II i feel there are way to many equations bet 2-14, maybe just 'sketch the solution here' and present the results at the end, maybe 1-2 intermetieate equations and the rest move to the appendix. 

4. Same with section III. Are all this long equations necessary they are anyhow mathematica solutions. Try and present the novelty here from the results not from some standard algebraic solution. again more the rest to the appendix. The reader will be able to see clearly without having to work out everysingle details what you have done, and anyone interested in the technical part can find it in the appendix.

5. Section IV is equaiton 48 necessary to be explicitly shown at this point? 

6. Seciton V, i appreciate the results here but i have no idea how you solve 'Numerically' can you please provide a few details? Maybe just name the method and more details in the appendix. 

7. Again in conclusions too many bulletpoints, make proper paragraphs and bullet point the most important consice points. Also your conclusion is too long, just short description of the methodology and then present the novel results maybe also a few side remarks.

Author Response

Response is attached.

Author Response File: Author Response.pdf