Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 8: Strong Accept: Technically strong paper, with novel ideas, excellent impact on at least one area, or high-to-excellent impact on multiple areas, with excellent evaluation, resources, and reproducibility, and no unaddressed ethical considerations.
review_content: summary: This work introduces a general technique to evaluate gradients of time-evolved states, in the analog quantum computing setting. 
strengths_and_weaknesses: This is a very interesting and conceptually (very) important work, because it allows to compute exact gradients on large analog quantum computers. While some of the technical tools have been heavily borrowed from ref 3, I believe that the extension to the analog case is crucial. Also, the numerical experiments seem to consistently indicate a superior performance to existing approaches (say, CRAB, etc). 


questions: The VQE experiments compare only against finite differences, what about SPSA? 
limitations: Yes
review_title: null

final_score: rating: 8: Strong Accept: Technically strong paper, with novel ideas, excellent impact on at least one area, or high-to-excellent impact on multiple areas, with excellent evaluation, resources, and reproducibility, and no unaddressed ethical considerations.
review_content: summary: The paper proposes a differentiable programming framework for analog quantum computing with a specialized froward scheme based on Monte-Carlo sampling to get estimates of gradients. The rationale of the gradient estimation is justified theoretically. Moreover a sensitivity analysis to modeling errors of the quantum system is provided to handle real applications. Finally, the framework is illustrated on several examples, ranging from quantum optimization and quantum control. In all examples, the proposed framework appears not only efficient but  also outperforms previous methods by some orders of magnitudes. 
strengths_and_weaknesses: Strengths: 
- The subject of the paper itself, namely proposing a differentiable programming framework for quantum computing is an exciting avenue for research to broaden the applicability of quantum computing. 
- The approach taken by the authors, namely, considering analog quantum computing systems appears clearly driven by a good understanding of the underlying system and is original to me, though I'm not an expert in quantum computing. The authors could explain better the previous approaches. However, their experimental evaluation clearly demonstrates empirically the benefits of their approach. 
- I personally come from a differentiable programming viewpoint, for which the framework posed by the authors exhibits exciting challenges, namely, computing gradient information without access to the intermediate states of the computations. The authors present a simple Monte-Carlo estimator that is easily implemented and already efficient. The framework proposed by the authors can serve as a strong baseline to build upon and provide alternative gradient estimators for analog quantum computing.
- The authors link their approach to well-known frameworks in differentiable programming such as differentiable physics which help understand the differences and challenges in this setting. 
- Last but not least, the experimental evaluations are well selected and the comparisons show clearly the strength of the proposed approach compared to previous work.  

Weaknesses: 
- While this paper appears to be a strong contribution and an interesting bridge between differentiable programming and quantum computing, it somehow quickly passes over some technical details that could be better explained as asked int he questions section
questions: - One simple, yet powerful addition to the experiments would be to write down exactly the optimization problem (such as min_x f(x) with some constraints) to help the reader understand how quantum computing is used for classical problems and what are the challenges compared to classical optimization. This would greatly help other communities understand how the framework proposed by the authors differ from traditional algorithms. 
- I cannot find any readme file to run the code. I appreciate that the code is commented and a simple readme/tutorial to navigate the code would also be a simple yet great improvement for the paper. 

- In the definition of the AQAM: what does evolving under H_j at time t means? 
- For non-experts, it could be good to either provide a quick introduction to the parameter shift rule though reference [50] is good. 
- I do not understand what the authors mean by "weak" in "multi-qubit interactions are not tunable and weak compared to tunable single-qubit Halmitonians" or in "may be imprecise due to weak non-tunable terms in H_c".
- A reference for the claim "Almost on every architecture of quantum devices, the number of control signals m is at most quadratic in the number of qubits n" would be appreciated. 
- For non-experts, it may be good to explain why equation (7) is presented up to Hermitian conjugate terms. 
- A formal statement for equation (7) with assumptions and proof would be appreciated. Generally, a pass on the Appendix from lines 624 to 631 with detailed reasoning would greatly help clarify the theoretical contributions of the paper. 
- Maybe, recall that the dagger symbol is the hermitian operator for non-experts. 
limitations: The authors have properly described the limitations of their work, namely the fact that the current experiments are not very large scale although the framework had been designed to be scaled. As the authors say, the current experiments already demonstrate the potential of the framework and the "limitations" of the paper can clearly be seen as future work and not dead-ends.
review_title: null

final_score: rating: 5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.
review_content: summary: The paper studies the problem of variational quantum algorithms and proposes to tune the parameters on the pulse level to achieve better efficiency than optimizations on the gate level. Results on both quantum optimization (QAOA) and quantum control show large advantages. 

strengths_and_weaknesses: Strengths:
1. Good motivation of optimizations the algorithms on the pulse level to better leverage the current quantum machines. 
2. Good explanations on the parameter shift method to obtain the gradients.

Weekness:
1. The proposed work is similar to the existing works on pulse-level variational quantum algorithms and quantum optimal control. [1,2,3]
2. The idea of using parameter shift to obtain gradient is not new. 
3. For parameter shift, the number of circuit runs on real quantum machine is linear to the number of parameters in the circuit so when the size of the circuit is large, the number of gates will growing rapidly. For instance, the pulse length is O(2^(2n)) for quantum optimal control, so the proposed method is not very scalable either.

[1] Meitei, Oinam Romesh, et al. "Gate-free state preparation for fast variational quantum eigensolver simulations: ctrl-vqe." arXiv preprint arXiv:2008.04302 (2020).
[2] Liang, Zhiding, et al. "Variational quantum pulse learning." arXiv preprint arXiv:2203.17267 (2022).
[3] de Keijzer, Robert, Oliver Tse, and Servaas Kokkelmans. "Pulse based Variational Quantum Optimal Control for hybrid quantum computing." arXiv preprint arXiv:2202.08908 (2022).
questions: 1. What are the core differences to the previous pulse-based variational learning methods besides the parameter shift method to obtaining gradients?

2. Figure 1 caption 'an' initial
limitations: No significant negative societal impact.
review_title: null

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: This papers introduces the first differentiable analog quantum computing framework with a quantum SGD algorithm which optimizes the analog pulse control singla on quantum computers.
strengths_and_weaknesses: Strengths:
- The paper looks serious and does what it claims to achieve.
- The benchmarks are convincing.
- I liked the fact that there was a robustness analysis.
- The paper is well written and structured.

Weaknesses:
- I am not knowledgeable enough in the field to spot weaknesses.
questions: Sorry, I don't know enough in the field to ask relevant questions and initiate fruitful discussions.
limitations: No negative societal impact
review_title: null

Meta-review: metareview: The paper proposes a differentiable programming framework for analog quantum computing with a specialized forward scheme based on Monte-Carlo sampling to get estimates of gradients. This idea is an exciting avenue for research to broaden the applicability of quantum computing to practical machine learning and computation. There is a clear consensus among referees that this submission constitutes an interesting and important work.  In all examples, the proposed framework appears not only efficient but also outperforms previous methods by some orders of magnitudes.
confidence: Certain
Decision: Accept