Machine Learning with Quantum Matter: An Example Using Lead Zirconate Titanate

Round 1

Reviewer 1 Report

The authors perform a reservoir computing experiment with a piece of piezoelectric material. 

I found the paper to be a fairly fun read, although to be frank I expect many readers with my expertise would not react so positively, particularly once quantum correlations and boson sampling is introduced. The paper throws around analogies that almost surely wrong, or at least are worded in a way that one may get the wrong idea. Throughout the paper the authors make statements that imply they believe that the physics involved in the PZT, at room temperature, are useful for quantum computation, and they draw numerous comparisons or "hints" to how classical computations may be (equivalent to? analogous to?) quantum computations such as boson sampling. In short, I found the paper a confusing read. Personally, I like that the authors are clearly thinking about things a little differently than the mainstream of quantum computing (which I feel has gotten quite boring and uncreative), and I don't wish to rush to a harsh judgement despite some of the more outlandish-seeming comparisons or comments. 

To make the paper a bit more technically sound, or perhaps safe, a few suggestions:
- First, the authors need to cite (and perhaps be aware) of the vast volume of similar work on the topic of "in materio" computing, physical reservoir computing, and more recently, quantum physical reservoir computing. In particular, groups like Tim Liew's group or Keisuke Fujii have considered reservoir computing using realistic models for quantum materials. References to physical reservoir computing literature were surprisingly sparse. 

- Second, the description of PZT as a quantum correlated material needs to be much more heavily qualified. In what sense is PZT a quantum-correlated material? (I agree there is a sense perhaps, but this must be explained in the text) What implications does this sort of quantumness have for its computational capacity, realistically? I recognize that the authors understand this, but of course the PZT, at room temperature, almost certainly does not support the kinds of internal quantum dynamics that are hard to simulate classically, i.e. by a conventional classical computer. 

Personally, I found the last paragraph a reasonable summary of what has been done - adopting that tone in the rest of the paper would help the reader, since one doesn't get to this until the very end. (Other than the last line - the CNOT is both not shown, and is classical). 

- Third, what is the performance on the MNIST task if, instead of putting the data into the PZT, they simply send it to the output layer that is executed on the digital computer? I believe this would be around 90% accuracy, but I could be mistaken. The authors should include this as a reference, since what we should really consider is how much the PZT's computation improves over simply replacing the PZT's computation with an identity operation. I expect that, unfortunately, the PZT actually decreases the the computational power.

- Fourth, I (and surely many other readers) really found some of the excursions in the text hard to see as part of a coherent story. First, the authors relate piezoelectric materials and memristors. I do not understand why this is relevant to subsequent parts. At the end of the paper, the authors make comparisons to boson sampling, and make very unsubstantiated comments on the presence of entanglement in their experiment. Again, I am not sure what this is intended to do in this paper. 

Overall, I do feel like perhaps there are some intriguing and original ideas within this paper, even if they are currently arranged in a way that lacks a clear narrative coherence and conclusions. Currently, parts of the paper are written in a way that will surely offend many quantum computing readers. Assuming other referees are not in that category, I encourage the authors to revise. With apologies to the editor, I am not quite aware of the standards for this journal (I admit, I have never submitted nor even read a paper from this journal, despite working intensively on quantum computing, physical computing etc. ), but I feel this work is within a revision of being publishable in it. 

Author Response

Report to Reviewer #1

 

First, I thank you for your candor. I am also glad you gave such positive criticisms so that I could improve the manuscript. And lastly, I hope you would agree that the edited manuscript is acceptable. Now to address your specific suggestions.

 

1. Yes, I am aware of in-materio One of my coauthors suggested we remove that term. Anyway, it’s now back in the expanded introduction that includes a brief review of novel computing methods, reservoir architectures, and quantum reservoirs. Yes, I am familiar with Liew’s work and also Fujii’s work on quantum reservoirs and I have now included a brief review in the expanded introduction.
2. With respect to the term “correlated quantum matter,” I have not only changed the title, but also downplayed to the more acceptable term quantum matter, with no implications of correlated. Though the term is in the title of reference 33. The term quantum matter is used in a website https://oqmd.org/ and is now cited in the manuscript, reference 34. I have also included an Appendix with detailed descriptions of experiments and results.

The comment about CNOT gate has been removed, per not only your suggestion, but also the other reviewer’s suggestion. Also, much of the Discussion section has been rewritten to remove any hint about quantum processing taking place inside the PZT cube.

3. Yes, we realize that a simple one hidden layer perceptron would do better, as we now point out explicitly. But that of course, was not the point of the work reported. One could also criticize the work being done now to demonstrate quantum reservoirs. For example, demonstrating the ability of a quantum reservoir in simulation or “hardware” to learn a chaotic attractor. We already know a simple one hidden layer perceptron can successfully predict some number of time steps into the future of a chaotic attractor.
4. Sorry about the confusion of memristors. I hope that is now clarified in the last paragraph of the introduction.

 

 

 

 

 

Reviewer 2 Report

Review result of the manuscript by Edward Rietman, Leslie Schuum, Ayush Salik, Manor Askenazi and Hava Siegelmann, "Machine Learning with Correlated Quantum Matter: An Example Using Lead Zirconate Titanate", 

 

The authors of this paper presented experimental results of machine learning using unpoled Lead zirconate titanate (PZT) crystal as a programmable matter. By bonding nine electrodes for every nice faces of the PZT cube, the authors sent certain input data from MNIST data and control data and recorded output data, and adjust the control data (learning). Then after these learning processes, the average accuracy is about 80% after 100 reads.

I state that the paper is written clearly and properly citing recent references. The obtained results are interesting as the first demonstration of this matter for machine learning. However, I am not sure if "quantum"-ness is important in this results and constructive/destructive interferences are the decisive role of this phenomena. I would like to point-out several points to be improved:

(1) The term "MNIST" seems standard in the machine learning business, the definition of this abbreviation should be stated.

(2) In Sec. 2.2, line 54 and 60, the word "resistance" is used for the variable \rho. Rigorously speaking, this should be "resistivity" instead of "resistance".

(3) In Figure 1(b), the term "hyperparameters" is used but I could not find any explanation of this. 

(4) In Sec. 5 line 216 and also in the caption to Fig. 8, the stoichiometry is Pb[ZrxTi_{x-1}]O3. However, I think Pb[ZrxTi_{1-x}]O3 is more reasonable.

(5) In Sec. 6, lien 260, the normalization condition of the probability amplitudes, r, s, t, u, is expressed as r^2+s^2+t^2+u^2=1. However, the probability amplitudes are complex in general, the condition should be |r|^2+|s|^2+|t|^2+|u|^2=1 instead.

 

Author Response

Report to Reviewer # 2

 

Thank you for taking the time to review the manuscript and to make suggestions for improving it. The Introduction and Discussion sections have been completely rewritten, Also an Appendix has been added.

 

1. I have explicitly defined MNIST.
2. Resistance and resistivity correction noted and fixed.
3. Hyperparamaters has now been defined.
4. Noted and fixed, thank you.
5. Removed in the rewrite of the discussion section.

Round 2

Reviewer 1 Report

I am satisfied with the revisions and recommend publication.