Robust Quantum Neural Networks Against Dynamic Noise Landscape in the NISQ Era

• Based on Eqn. (5), Equitable Training can be interpreted as standard QNN training with a modified loss function, where the loss function combines a weighted sum of the noiseless loss and the worst-case noisy loss (fatal loss). Essentially, this strategy seeks a parameter set that mitigates fatal noise while preserving accuracy in the noiseless scenario. In the beginning, the authors present the noise variance in the calibration of real devices, which raises a natural question: why not define the loss function as a weighted sum of loss functions from randomly sampled noise scenarios? Or take the weighted sum between noiseless loss and the average noisy loss instead? (As the evaluation or real environment is unpredictable)

• In the Evaluation section, the authors benchmark the performance of different strategies; however, I noticed that Figure 4 does not clearly support the superior performance of the equitable training strategy. For instance, in some cases, the NI-H approach outperforms equitable training in the N.Acc (H) setting. This raises the question of whether the fatal loss function is perhaps not well-suited for scenarios with random noise.

• In Tables 5 and 6, I noticed a significant gap between the fatal and noisy accuracy (or loss) in the baseline case, even under heavy noise conditions. Is the fatal case truly this severe, or could this discrepancy results from choice of noise parameters? Also, your equitable training strategy shows no obvious advantage over noise injection strategy in the N.Acc senario.

• The authors conclude that their noise-aware training strategy is "aimed at general fatal error mitigation, rather than a specific error rate." However, from another perspective, the fatal error model identified through the low-complexity search is itself a specific error model with a fixed error rate for each gate. In particular, I am curious how the fatal errors are determined in Table 2; specifically, what is the error set used in evaluation? Was it derived from a Gaussian distribution? Additionally, it would be beneficial to include comparisons on real devices or noise data directly from device calibration.

Minor issues:

• In the section 4.3, there are typos “ithrough” and “signle-generation” at the third and fourth row.
• The authors use an error-free strategy as the baseline; however, it’s important to note that this baseline is error-free during training but includes errors during evaluation. Therefore, I suggest a more careful treatment of the term "error-free" to avoid potential confusion. Instead, the author can consider use “error-neglect” or just baseline to replace it.
• Table 5, 6 are labeled with Figure 5, 6.

Overall, while the paper addresses an important challenge of fatal error in quantum machine learning, its contributions feel somewhat limited and may lack broad applicability, particularly in dynamically noisy environments. The proposed equitable training approach has potential, but there are aspects of the methodology and evaluation that remain unclear. It would be better if the authors can address the questions and concerns raised, particularly around the choice of error models and the empirical validation on real devices.

• The experiments in the paper are all classically simulated with noise based on calibration data from known quantum computers. I think the biggest flaw of the paper is that when the authors tested their method on a real quantum device, it did not give any significant improvement, in fact, it was worse than the baseline error-free strategy almost half the time. I think this result should be in the main text with a strong justification and explanation of why the proposed method is still important, but the authors put it in Appendix H.1.1. This gives the impression that the authors are trying to sweep this result under the rug.
• Furthermore, the authors mention in the same appendix that "Since our evaluations are performed on a SOTA IBM quantum computer, which has relatively low error rates during execution, the observed improvements are not significant", which shows the weakness of the proposed method. As quantum hardware gets better and better and error rates get lower and lower, the fatal error may become less and less likely and the proposed method will become irrelevant. It is also undeniable that at some point, the NISQ era will come to an end and possibly the early fault-tolerance era will come.
• As shown in Table 2, the effectiveness of the proposed method deteriorates as the number of layers in the QNN increases. Meanwhile, from Figure 4, it seems that the noisy accuracy still increases as the number of layers increases. I believe that solving complex tasks with QNN could also extend to 10 or more layers, making the proposed method less effective.
• In Table 2, the results for some tasks are also not shown (e.g., M4 in 5, 7, and 10Layer, F4 in 7Layer), which might raise some suspicion about the result. If the reason is scalability, why is there a result of F4 in 10Layer? Please justify or provide the full experiments in the appendix.

Conclusion: Based on the comment above, the weaknesses outweigh the strengths. Therefore, I believe that this paper is not good enough to be accepted at the ICLR.

Minor issues:

• Please use the same x-axis range in Figure 4.
• In Figure 5, to be fair, the 0.94 +- 0.01 of the NI-M in the N.Acc(L) should also be bold.
• Typo “minimium” in Figure 2 caption line 175.

The authors focus only over a certain subset or errors without discussing how the method can be applied alongside error correction methods during execution (combining this NAT strategy with error mitigation is discussed in the appendix). The efficiency of the combined strategies and identifying the highest contributors of fatal errors would be of interest for the community.

I am not completely sure whether bolding of certain phrases as well as some other choices to emphasise complies with the style guide.

• Scalability: The article only presents 4-qubit QNN experiments, which is insufficient to effectively demonstrate the scalability of the proposed method. Current classical quantum simulators can provide simulations with at least 20+ qubits, the authors should consider conducting experiments on a larger scale.

• Typo: Line 352 'ithrough' and Line 354 'signle'.

For more weakness, please refer to the questions.