Paper: Randomized Benchmarking of Local Zeroth-Order Optimizers for Variational Quantum Systems (ICLR-2024)

Reviewer comment (Writing):
Two sentences start with “beyond” in the second paragraph (a minor point on readability)

Author response:
We agree with all of these reviewer’s criticisms. The easily actionable things (readability issues, explaining SPSA in more detail, adding exact solutions to the plots, extra citations, making it more approachable to the ICLR audience) we are happy to add to this paper for future versions.

Reviewer comment (Novelty):
There are a few citations that this would benefit from using [1-3], some of which include randomised hamiltonians as a benchmark.

Author response:
We agree with all of these reviewer’s criticisms. The easily actionable things (readability issues, explaining SPSA in more detail, adding exact solutions to the plots, extra citations, making it more approachable to the ICLR audience) we are happy to add to this paper for future versions.

Reviewer comment (Novelty):
The core of my issue with this paper is that it doesn’t do enough to build on previous work. The results are not new, SPSA as a good non-parameter shift gradient optimizer and the importance of hyperparameter tuning are both mentioned in [2]. Although more verification and more problem evaluation is always good, the results and methods are generally similar to a growing lineage of QML optimization benchmarks.

Author response:
Although it’s not necessarily possible to make larger fundamental changes for this submission, we would especially appreciate extra feedback from this reviewer about how they would suggest we further distinguish this sort of study from prior work for future submissions. We attempted to do this by shifting the focus to using more randomness in problem selection and studying only a narrow type of optimizer, but we agree with the criticism that this isn’t necessarily enough to make it significantly novel. Other reviewers also mentioned looking at the scalability as we shift the number of parameters and number of qubits, so would something along these lines be novel enough of an addition? Though as also briefly touched on in the paper, adding extra dimensions like this would make a fair comparison extra difficult as we’d have to hyperparameter tune significantly many more times. So it would probably necessitate some adaptive strategy for choosing hyperparameters and readers would have to accept that such a strategy is good enough for the purposes of a fair comparison.

Reviewer comment (Theory):
SPSA would benefit from more mathematical background and explanation when first presented.

Author response:
We agree with all of these reviewer’s criticisms. The easily actionable things (readability issues, explaining SPSA in more detail, adding exact solutions to the plots, extra citations, making it more approachable to the ICLR audience) we are happy to add to this paper for future versions.

Reviewer comment (Reproducibility):
Would the code be available if the publication is accepted?

Author response:
And yes, code will be provided if the publication is accepted. We are also happy to provide a ZIP of it for additional review beforehand.

Reviewer comment (Theory):
Considering the barren plateaus issue in many variational quantum algorithms, do the main results in this paper still hold?

Author response:
With respect to barren plateaus, this is a nuanced topic that is a little difficult to connect to empirical results we are currently able to simulate. But the short answer is that once you reach the regime where barren plateaus become a problem, it’s unlikely that any of these optimizers will work at all. This is because the barren plateaus literature basically implies that, in many VQA situations, the loss landscape’s variance is inversely proportional to the dimensionality of the Hilbert space (which is exponential in the number of qubits). So as you increase the number of qubits, you need to sample exponentially more to overcome the noise in your system. So to avoid this scaling you would require either a good initial guess, or a fundamentally different optimization procedure that changes the type of loss landscape. So while it’s certainly possible that scaling up would affect these results in other ways, with respect to specifically barren plateaus I don’t believe it would matter too much. Because once we get into the regime where they become a problem for these type of optimizers, all of them are likely to fail dramatically.

Reviewer comment (Theory):
What is the theory to guarantee that the randomized quantum circuit is random?

Author response:
With respect to the randomness in the quantum circuit, I’m not sure what the reviewer means in this question? As explained in the paper (last paragraph section 3), we use a Gaussian for initial parameter initialization. And all random circuits use uniform distributions for placing and choosing gates. (This is explained in the Pennylane documentation for RandomLayers circuit, which we say we use in section 3.1 and 3.2. Though we never explicitly say uniform in the paper, so we are happy to make that edit for clarity.)

Reviewer comment (Reproducibility):
What are the parameterized circuits used in this paper?

Author response:
For the ansatz we use, as said above please refer to section 3.1 and 3.2. We use the RandomLayers circuit from Pennylane (uniformly randomly placed RX, RY, RZ, and CNOT gates). The only exception is one of the generative modeling experiments where we use the quantum circuit born machine (QCBM). The reference we provide in the paper lays out the construction of this circuit.