Method for the Quantum Metric Tensor Measurement in a Continuous Variable System

Round 1

Reviewer 1 Report

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Comments for author File: Comments.pdf

Author Response

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Author Response File: Author Response.docx

Reviewer 2 Report

All items referred to by initials (e.g. QGT, QMT, KNPO should be spelled out when they first appear.

Author Response

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Author Response File: Author Response.docx

Reviewer 3 Report

The paper by Ling-Shan Lin et al. reports a method to determine the values of components for the quantum geometric tensor and numerical simulations applying these methods to a specific system. The system is a nonlinear parametric oscillator realized as an array of SQUIDs. Significance of the reported results is not evident, and I cannot recommend the paper for publication.

First of all, the title and abstract of the manuscript are misleading, they make an impression that the paper will include some experimental results, while this is a purely theoretical work. That should be definitely changed.

Secondly, the Authors claim that their work tell us something about the geometry of the system with continuous variables. That is claimed to be the main contribution of the work. However, in fact the state space is reduced to a subspace of two degenerate ground states, i.e. to an ordinary qubit. There is nothing specifically “continuous” in the way the system is treated, the simulations are performed for an effective two-level system. If this is not the case, then it should be explicitly clarified and the results of full Hamiltonian simulation should be presented, illustrating population leakage to excited states, non-adiabatic effects and so on. Otherwise, there is nothing to verify by numerics, since the two-level case is well-studied and may be treated analytically (as the Authors perfectly demonstrate).

Some minor related comments:

- The scale at Fig.3(B) should be chosen in such a way that the deviations of fidelity from unity is clearly visible. Also the reasons for these deviations should be discussed.

- The Authors say that “numerical results are consistent with theory, when the evolution time is large enough”. What happens, when it is not large enough? Can we see the fidelity dependence on evolution time T for some points at Fig. 3(B)?

- There are numerous typos, the manuscript should be carefully proofread.

Author Response

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Author Response File: Author Response.docx