Estimation of Convex Polytopes for Automatic Discovery of Charge State Transitions in Quantum Dot Arrays

Round 1

Reviewer 1 Report

This manuscript presents a novel method for iterative detection of quantum dot state transitions for automatic recognition of the occupancy of multi-dot systems. The study seems fairly complete, encompassing both simulated and real device data to show the accuracy of the method. This study is differentiated from other similar automated tuning schemes across the field in how the transitions are detected and how the states are determined (based on geometry). However, I have several minor and major concerns, which I outline below.

1. There are several claims throughout the manuscript that this method is uniquely capable of scaling beyond 2 or 3 dots. While I believe this may be the only manuscript which shows 3/4 dot state identification, it may be unjustified to claim this, as done in line 25. For instance, the automated tuning techniques at HRL have been shown to tune 6 quantum dots in a row (https://www.youtube.com/watch?v=H1ouyV4nbyg). On this note, line 29 claims four quantum dots is "outside the scope of human tuning capabilities", which while 4D plots would be impossible to interpret, 4 quantum dots have certainly been tuned up by humans. 

2. I have some confusion regarding the distinction made between "state identification" and "state transitions" from lines 70-80. It's my understanding that state identification refers to the description of the number of quantum dots in an array which are occupied, or their specific occupation. State transitions are the borders (or facets) between these states. While I understand the point being made that certain state transitions, such as a polarization line, can be small and difficult to resolve, claiming the methods cited in lines 67-77 "are not easily transferred to the task of finding state transitions" seems not generally true. In the discussion section on line 409, you claim this is the "first automatic discovery of state transitions". I'm not sure I agree with that, there are many ways to automatically detect transition lines, such as a Hough transformation (https://arxiv.org/pdf/1911.11651.pdf). I think this claim need clarity.

3. An assumption made for this work is that the boundaries (facets) of states are linear (not curved), which is not always the case in real systems. This is partially discussed in the discussion section regarding "device instabilities", however I would note that well functioning devices may have curved transitions due to intentionally and desired high coupling between dots. The constant interaction model used to describe the dots does not account for this, which may be why others opt for semi-classical Thomas-Fermi calculations (COMSOL). 

4. SGD (stochastic gradient descent?) on line 124 and i.i.d (independent and identically distributed?) on line 130 are not defined. These may not be familiar to the broader experimental quantum dot audience.

5. Throughout the notation section, there is a term "T" in the exponent. I don't see this defined and I'm not sure what it is.

6. From how I understand it, this technique aims to determine the "true" polytope shape / number of facets from a finite number of border point pairs. A system with a defined number of occupied interacting quantum dots will be described by a polytope with a specific number of facets. This method then aims to correlate the measurements with a "ground truth" polytope. The results section seems to say it can correctly identify that the experimental system is in a [1,1,1] state. It's my understanding, however, that any number of electrons in each dot (such as [2, 3, 1]) will have the same overall number of facets / overall polytope shape. While distinguishing between occupied and un-occupied states is certainly valuable and comparable with other methods (such as the ray-based classification method by Zwolak, et al), it's not clear to me that this manuscript sufficiently describes the goals and limitations of the classification.

7. The notation section defines the polytope as finite. However, for states with one or more unoccupied dots (such as [1,1,0]), the polytope will have an "open" face, that extends towards infinity in negative (for electrons) voltage direction. How does this method account for that?

8. I'm not sure I fully understand Figure 4. I think further explanation of how the errors present themselves in the slices would be helpful. 

9. In general, some clarity about the exact purpose of this technique would be helpful. No single technique aims to tune a quantum dot device from start to qubits (nor should it). Is this method used to determine how many dots are occupied, or how many electrons are in each dot, or where each facet is, or something else?

I think this is an interesting alternative technique for state classification to what has been published. However, I think it would be aided by some general clarity on the experimental methods, function, and connection to the presented results.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Spin-based quantum dot arrays are promising candidates for universal quantum computation. Material or fabrication imprecisions of these spin qubits affect their manipulation, the understanding of which requires measurement of the shape of specific convex polytopes. In this paper, the authors present an algorithm, based on machine learning, that discovers automatically certain details of the facets of a convex polytope. The algorithm is implemented on simulating polytopes and devices, and a real quantum dot array. It has been found that the algorithm can reliably find facets of the convex polytopes at about the measurement precision.

 

Overall the paper is nicely written with sufficient details. The results are valid and sound. The proposed algorithm is certainly useful to the research community on quantum-dot spin qubits. Therefore I recommend publication of this article. There are some presentational issues that I would like to bring to the attention of the authors: (1) In Figs 3, 5 a portion of the (a) and (b) labels are covered by lower panels. (2) Some typos are found while I read through the article, e.g. "itnroduce" on line 166.

Author Response

Thanks for the review of our work.

We added additional spacing to the captions of Figures 3 and 5 and added another round of proofreading.

Reviewer 3 Report

1) Perform a grammar check of the paper. There are minor inaccuracies in the text, such as in the abstract the word "evalaute" instead of evaluate (line 5).
2) The expression "we do something" often appears in the paper, which is totally inelegant, and must be replaced by the third person singular, "it does something", or "one does something".
3) Please develop the idea from lines 62-66, with more explanations, being extremely interesting.
4) All equations, even explanatory ones, must be numbered successively.
5) Explain separately all the parameters used in the equations presented in the paper.
6) In the text, refer to absolutely all equations.
7) If you marked the algorithm presented with 1, there must be other algorithms introduced and presented in the paper, marked with 2, 3 ...
8) Explain in more detail the results designated by the diagrams in figures 2-5.
9) Develop section 5 "Discussion", with a review of all the new methodologies introduced by the paper, compared to those already known in the literature, with the highlighting of the advantages of the new methodology but also with the presentation of possible limitations.
10) Also here, in section 5, or in a new section, enter a few words about possible future applications and developments based on the new methodology presented in the paper.
11) Insert a final section, "Conclusions".

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

I am satisfied with the edits and response. I recommend this paper for publication.

Author Response

Thank you very much for your review!

Reviewer 3 Report

In general, the authors redid the work and added the missing elements. It would be good if a Conclusions section was introduced at the end.

Author Response

Thank you very much for your review.

 

We have followed your suggestion and added a conclusion section to our manuscript.