Dephasing enhanced transport of spin excitations in a two dimensional lossy lattice

1. Interesting and original methodological approach to the problem of energy transport in dissipative hopping lattices. Potential to apply this approach to other model transport systems.
2. Strong and rigorous analytical results, particularly the bounds on efficiency and transport time and the crucial impact of dephasing in enhancing ( or even allowing) excitations to reach a target site.
3. Numerical results have been carefully obtained and convincingly compared against analytical predictions.
4. To the best of my knowledge the discussion and analysis of system size is potentially novel.
4. Clear and well-presented article, easily accessible to expert and non-expert, alike. The details surrounding the mathematical develop of the numerical monte carlo method and the derivations of the various bounds were particularly welcome.

1. The underlying problem and theory of ENAQT ( or noise-assisted dephasing NAT) is now rather old ( 2008 - ) . The lattice system and model studied in this paper is essentially the same as in the first papers looking at ENAQT in the context of exciton transport in photosynthetic proteins. Consequently, the amount of new qualitative insight into ENAQT is somewhat limited.
2. Introduction focuses a great deal on biological systems, but many relevant citations are missing and some of the presentation of the previous work, particularly w.r.t. this article's contribution, needs to be corrected for the record.
3. Given the single-particle nature of the dynamics, I was surprised by the small lattice sizes used in the numerical simulations, especially given that previous studies have been able to look at much larger and more complex dynamics.
4. The main conclusions seem to repeat a number of general facts that have been known/stated in the ENAQT literature many times before. The conclusion concerning critical antenna (lattice) size might be new, but I think this needs to be checked by looking at some of the 'missing' citations, as mentioned above.

This paper presents an interesting approach to energy transport in models that closely resemble those used to understand the physics of 'light-harvesting' systems, and in particular lattice hopping models used to describe photosynthetic chromophore arrays. The Authors employ monte carlo- based methods for the simulation of quantum walks of on an extended 2D lattice in the presence of dephasing and losses, allowing them to explore the role of the lattice size on the efficiency of excitation capture by a target site. The analytical and numerical parts will be of broad interest across physics and chemistry communities interested in this problem, and I believe that this article could be suitable for publication in SciPosts. However, in order to meet all of the relevant acceptance criteria, I believe that significant revision is required. I set these out, and the reasons behind them, in the next section.

1. The introduction focuses heavily on ENAQT in biological systems such as the FMO complex. Indeed, most of the references relate to studies of this complex, ignoring the vast number of studies on other - typically much larger - complexes such as LHII, LHI, Chlorosomes...given that several of these systems are much closer to the extended 2D lattice considered here, some of these other works should be cited and scanned for any similarities (methods, conclusions concering ENAQT) with the present work. Similarly, an oft-repeated fallacy is that the FMO complex has '100%' efficiency. It can actually be much lower - https://pubs.rsc.org/en/content/articlehtml/2023/cp/d3cp01321a (and refs therein)

As stated, the claims about 'coherence between distant aggregates persist...despite being subjected to noise' isn't true. The Authors should explain carefully what is meant by 'distant', and even by 'coherence ' (do they mean that exciton eigenstates are spread over several monomers, or the coherence between these extended states, as prepared by ultrafast pumping, 'persist'?).

2. The authors should consider/comment if their results are in any way specific to the highly ordered arrangement of dipoles they use in their model. Real biomolecular aggregates often have misaligned dipoles - would random dipole-dipole (anisotropic) interaction make a difference? Also, given the key conclusions of this article revolve around the lattice size scaling, how does this depend on the range of the dipole interaction w.r.t. the lattice site separations?

3. The Authors state some standard results for random walks on page 3. Are these quantum or classical walks? Given the existence in this work of both coherent and classical hopping, this is important. Please add clarifications and citations, particularly for the statement about tree-like networks. It should be noted that dissipative quantum walks on bio-like lattices have been studied before, including speed limits and various types of bound. The authors should check their findings against some of this material. For example ( & non-exhaustively):

https://pubs.rsc.org/en/content/articlelanding/2022/cp/d1cp02727a/unauth
https://iopscience.iop.org/article/10.1088/1367-2630/12/6/065041/meta
https://iopscience.iop.org/article/10.1088/0953-4075/44/18/184012/meta?casa_token=qtWond9LYDcAAAAA:kFyuUxMPjB5SfXpmkGtRuRLD5KUJB61Ryb0ZIS7t_Gu4NrMRJELy9pwZA26Hii-kh-lTkbcFwcctUJbYvIW27WiDLA
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.180601




Minor points:
Intro mentions 'dark states' with explanation or citations. What are these?

Ask for major revision