Paper: Towards LLM4QPE: Unsupervised Pretraining of Quantum Property Estimation and A Benchmark (ICLR-2024)

Reviewer comment (Novelty):
While the authors emphasize the unsupervised pre-training as a key novelty of their proposed method, I just feel that the approach they employ in the pre-training phase, involving the regeneration of measurement results, follows a similar logic to that found in [1]. In [1], the model generates measurement results from incomplete measurement results. Although the proposed model here incorporates additional input information, such as physical conditions, I still believe the authors should cite this previous work.

Author response:
**A1:** Thank you for the insightful comments. We have cited the suggested paper [1].

In addition, we would like to highlight some differences in the pre-training methodology between our work and that presented in paper [1]. 

In [1], the pre-training process involves gathering diverse measurement strings ($\mathbf{m}$) and the corresponding reliable frequencies/distributions ($p_{true}$) obtained through post-processing. The loss function is primarily designed to reconstruct the distribution $p_{true}$ for new measurement strings. 

In contrast, our approach does not rely on such assumptions. The loss function we designed directly corresponds to the reconstruction of the joint probability distribution of the wave function (Eq.3). Therefore, we only require the measurement string (along with some other easily obtainable physical condition features). This design facilitates real-time adjustments to the pre-trained model without the need for calculating $p_{true}$, contributing to a more responsive adaptation process.

Reviewer comment (Novelty):
Furthermore, the fine-tuning phase of the model shares similarities to the framework described in [2]. Despite the results demonstrating the superiority of the proposed method in Table 1, it would be valuable for the authors to engage in a more in-depth discussion regarding the distinctions between their model and this prior work. Given that Q-TAPE without pretraining also outperforms NN-Classical Shadow, it would be appreciated if the authors could provide further analysis or intuitive explanations for the results to highlight the novelty of the proposed model.

Author response:
**A2:** Thanks for your valuable question. We would like to clarify the distinctions between our approach and the method outlined in reference [2], and we have supplemented this clarification in the new version of the paper.

While both Q-TAPE and NN-Classical Shadow employ a similar transformer structure in their pipelines, the purpose of the transformer differs. 

In Q-TAPE, it functions as an encoder, whereas in NN-Classical Shadow, it resembles more of a decoder. The fact that Q-TAPE, even without pre-training, can to some extent surpass NN-Classical Shadow can be subjectively attributed to its **end-to-end** model nature. The parameters in Q-TAPE are specifically optimized for corresponding objectives (such as quantum phase of matters and correlation function), which often leads to superior performance. 

On the other hand, NN-Classical Shadow is essentially a **two-step** model, lacking a conventional fine-tuning phase. The transformer in NN-Classical Shadow primarily serves as a generative model used to reconstruct the quantum state and generate measurements records conditioned on specific physical variables. The transformer is followed by the use of classical shadow to predict specific quantum properties. Thus, it is highly possible that the parameters in the model may not be optimal for the specific task.

Reviewer comment (Evaluation):
In the section concerning the prediction of correlation functions for the anisotropic Heisenberg model, it would be beneficial if the authors could include an analysis of the prediction MSE for correlation functions associated with two quantum sites at **different** distances.

Author response:
**A3:** Thank you for your question. For the task of predicting the correlation function, our model outputs a symmetric matrix ($H$) of size $L × L$ for a given training sample. Here, $H_{ij}$ represents the predicted correlation function between the ith and jth qubits. Assuming the true correlation function is denoted as $H'$, the MSE is $1/L^{2} \sum_{ij}(H_{ij}-H^{'}_{ij})^2$. And the loss is the root squared value averaged over the batch samples. This incorporates the correlation functions associated with two quantum sites at different distances. 

The explanation above has been metioned in Section 4.2, and we will provide a more explicit explanation in the new revised version.

Reviewer comment (Novelty):
Even though the work somehow makes the generated quantum data suitable for the classical LLM architecture, the new hybrid quantum-classical architecture is not interesting. For classical-to-quantum data conversion, a simple quantum tensor encoding, amplitude encoding, or a more advanced method of the quantum kernel can efficiently deal with quantum data generation. If you could collect quantum datasets, the use of quantum machine learning models is more important and that is the most advantage of quantum neural networks.

Author response:
Thank you for the reviewer's response. We apologize for any lack of clarity. We will try our best to provide a detailed explanation below (and also in our paper).

Our model, Q-TAPE, is an **entirely classical machine learing model** and is designed to address quantum many-body problems (including classifying quantum phase of matters and predicting the correlation matrix of quantum systems). 

In our paper, **we define the "quantum data" required for training the Q-TAPE to handle quantum many-body related problems**. This data is obtained through **multiple measurements on identical copies of a "quantum" system**. The collected data is "classical", capable of being stored on disk and in memory for training and testing Q-TAPE. **This process involves only quantum-to-classical transformations, such as measurements through POVM, and does not involve classical-to-quantum data conversion.**

As mentioned in response to Question 1, quantum models (including quantum neural networks and quantum kernel methods mentioned by the reviewer) inherently possess advantages in handling quantum problems and quantum data. At least, there is no need for us to convert quantum data into classical data, which often incurs significant computational and experimental costs. 

**However, considering the current limitations of quantum computers—small-scale (a few hundred qubits), high noise, and short coherence times—it is often impractical to use such quantum computers to solve real-world problems. Even when these quantum algorithms run in classical simulation environments, the scale of simulation is generally limited to toy models.** Therefore, employing purely classical machine learning methods to address quantum problems remains a viable consideration. We hope that our proposed Q-TAPE provides a new perspective on pre-training methods for solving quantum many-body problems.

Reviewer comment (Novelty):
Similar techniques of pre-training strategy have been shown in many quantum machine learning works. For example, Yang's quantum NLP work has demonstrated the effectiveness of pre-training hybrid LLM for dealing with quantum data. Moreover, Qi's recent work has provided a solid theoretical understanding of pre-training LLM for quantum machine learning. Unfortunately, those important and very related works are not cited in this work.

Author response:
Thank you for your consideration. We carefully reviewed these valuable works mentioned by the reviewer (Yang et al. and Qi et al.) and we also have appropriately cited them in our revised paper.

Although both our paper and the papers mentioned by the reviewer include the term "quantum", it is crucial to emphasize that, to a large extent, our motivations and methodology are not directly relevant to the papers mentioned by the reviewer. The reasons include:

1. Firstly, we note that both two papers focus on using hybrid models to address classical problems, with Yang et al. concentrating on text classification and Qi et al. on image classification. **In contrast, our model is entirely classical and developed to tackle quantum problems.**
2. Secondly, in our paper, the term "**quantum data**" refers to **measurement data obtained from quantum systems through random Pauli measurements**, preserving the characteristics of the quantum system. It is essential to note that in the mentioned papers, "quantum data" specifically refers to **quantum embedding**, which involves encoding classical data through quantum circuits, essentially creating a **quantum representation of classical data**.
3. While Yang et al. and our model both incorporate components of large language models (LLMs), Yang et al.'s motivation lies in **utilizing a hybrid model to address classical problems, specifically text classification. In their approach, a quantum neural network serves as an additional layer to enhance the expressive power of the traditional BERT model.** On the other hand, **our proposed Q-TAPE is designed to characterize and predict features of quantum systems without the involvement of any quantum models.** Q-TAPE achieves this by unsupervised pre-training, learning hidden patterns of quantum systems, and utilizing these patterns during fine-tuning to achieve better results with fewer measurements.