In this study, the authors propose using the Quantum Annealers to solve the data assimilation in the Earth science field. This is the first study to employ quantum annealing for data assimilation problems. The quantum annealing machine can significantly reduce the execution time, which will be very useful for the development of the data assimilation. However, there are several problems that need to be clarified in the current version of the manuscript.

1. In the data assimilation field, many readers may be not familiar with the quantum optimization. So could you give more detailed statements about the quantum optimization algorithm? Maybe, you can add an appendix for the quantum optimization algorithm and how to use it.
2. In this manuscript, the quantum data assimilation was only tested using the 40-variable Lorenz-96 model. This is a relatively simple model. In the realistic atmosphere and ocean data assimilation, the model is complicate. In this situation, how to carry out the quantum data assimilation? Especially, how to select the values of parameters in Eq. (19)? Can you also discuss the possible advantages and disadvantages of the quantum data assimilation in the realistic application?
3. Figure 3 shows that the NL-BFGS is closer to the truth than the Sim-QA. This seems to be inconsistent with Fig. 2a. Why?
4. To conduct the quantum data assimilation, the linearization needs to be done. For a strong nonlinear case, whether quantum data assimilation cannot be used?
5. Some details need to be clarified. For example, in the Lorenz-96 model, how to generate the observation data? How to perform the control run?
6. Line 114, Inoue and Yoshida (2021) should be Inoue et al. (2021)?

Review of “Quantum Data Assimilation: A New Approach to Solve Data Assimilation on Quantum Annealers” by S. Kotsuki, F. Kawasaki, and M. Ohashi.

General comments: 

This manuscript proposes a novel approach named quantum data assimilation and claims that execution time is reduced significantly with the D-Wave System’s physical quantum annealing machine. In my opinion, this work is valuable, combining data assimilation and quantum computation. However, several problems prevent me from recommending the manuscript for publication in its present form.

Specific comments: 

• In this manuscript, the introduction to data assimilation methods and quantum computation, especially the quantum annealers, is a little brief. Some essential references should be also included.
• In line 54 of the manuscript, the authors explain briefly how to solve the 4D-VAR using the quantum annealers. The authors should elucidate the algorithmin the method section.
• To my knowledge, in quantum computation, quantum states are operated, like , ,, nor binary variables (0 or 1). So, actually, the algorithm proposed in this work may be not relevant to the quantum computation. The authors need to explain this query clearly.
• Can the proposed method be used for real numerical models (for example the WRF model) and what are the operational difficulties?
• How does the methodaffect the accuracy of numerical forecasts in the design of numerical experiments? Please provide additional