Quantum reservoir probing: an inverse paradigm of quantum reservoir computing for exploring quantum many-body physics

1. The authors introduced a new concept, quantum reservoir probing, which I think is interesting and worth exploring to deepen understandings of properties of quantum systems.
2. Numerical simulations successfully demonstrate how well the authors’ proposal works.

1. This study lacks discussions on possible downsides of this framework.
2. There is no theoretical guarantee on performance and efficiency.

This paper introduces a new research question on the connection between properties of quantum systems and their information processing capabilities. To answer this question, the authors propose a new paradigm called quantum reservoir probing, which uses the framework of quantum reservoir computing to diagnose the property of quantum systems. The proof of concept is shown using numerical simulations for quantum Ising chain with transverse and longitudinal magnetic fields. The manuscript is well-written, but some concerns prevent me from recommending the manuscript for publication in the journal.

- In line 133, the authors mentioned that “Successful (unsuccessful) estimation indicates that the input information does (does not) influence the read-out operator”. However, does unsuccessful estimation always mean input information does not influence operator? The error could arise in the weight optimization. Does the error have an effect on the judge of the information propagation? Also, does a finite number of measurement shots affects the judge?
- Why do the authors consider 2-local observables at most? I agree that the increase of the number of operators does not necessarily mean the improvement of performance for quantum reservoir computing. On the other hand, I assume global observables could provide some valuable information for certain tasks. For instance, although it is a task with static quantum data, the phase recognition task could require information of global information. For quantum dynamical systems, is there no situation where the global information is needed? If it is not true, I think it is important to see if the QRP framework can efficiently capture the global information as well. It would be great if the authors could elaborate on it.
- Due to the definition of QRC, the result does not depend on the initial state of the quantum reservoir system. On the other hand, the result seems dependent on the initial state of the ancilla qubits used for input injection. How can we interpret this? Could it be possible to eliminate the effect of the dependence on the input-initial state?
- Why do the authors start with the ground state, despite the fact that the QRC is not influenced by the initial state. Is the washout time not enough to guarantee the independence on the initial state?
- As shown in the literature of reservoir computing, the range of input have an impact on the information capability. E.g., see a work by Kubota et al on the information processing capacity: https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.3.043135. Does it affect the performance of the QRP as well? If these factors including ones mentioned above matter, is it fair to say the QRP always tell the property of quantum systems? Could it be possible to provide certain theoretical guarantee?
- The short-term memory is used to see the information propagation in this work. Actually, there is a metric called the information processing capacity (IPC) in the context of reservoir computing that is used to see the profile of the reservoir’s ability to process the time-series data. Can it be used to see the nonlinear processing of the information through the quantum channels?
- The authors mentioned that an advantage of the framework is efficient operation compared to OTOC and TMI. I feel it boils down to the 2-localness of the observables considered for QRP, in contrast to these methods requiring the global information. In case the target property of the system is global, does the statement that the QRP is efficient still hold? In addition, does the result for QRP mean that observing local operator is enough to perform the task in the manuscript? Also, do the additional washout time or longer training and testing period lead to less efficiency of the proposal compared to other method?
- As for the applicability, how likely do we have the information of the input in practical situations? To perform QRP, we always need to have a supervised-learning-like setting. Thus, I wonder if it is likely to happen in practical settings. Moreover, in QRP, the dynamics should be expressed as Eq.(1). Can we extend this assumption to the case of unitary evolution, which could also be a common target property in quantum physics.
- Why do the authors consider the STM task as a function of the virtual time \tau, not k. In the original QRC, the STM objective function is a function of k. Thus, if we follow the concept of QRC straightforwardly, I think it makes sense to regard the objective function in the same way. It would be great if the authors could elaborate on the reason why the virtual time is introduced and it is the main parameter of the STM task. The way the virtual time is used is also different from the QRC perspective; QRC uses the virtual node to improve the expressivity. Therefore, I would recommend to note the difference in the manuscript.

1. There is an inconsistency in reference; e.g., Initials are used for the first and family names in [5], while others use the initials for first names only.
2. Some sentences are confusing; e.g., what does “general” mean in “Hereafter, we denote 〈O(ktin +τ)〉 for general k by 〈O(τ)” in line 162?

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