Quantum 3D FFT in Tomography

Round 1

Reviewer 1 Report

My comments are listed as follows.

(1)Figs.2 and 3 can be combined. The variable \varphi should be re-edited, since it is covered by a line.

(2)In the part of results, the author should add some quantitative analysis data.

(3)The author needs to add some comparative results to show the advanced nature of the research work in this paper.

(4)The quality of some figures can be improved.

(5)The equation before Fig.10 can be re-written as a matrix.

(6)The following papers should be cited.

[1]N. E. Protonotarios, A. S. Fokas, A. Vrachliotis, V. Marinakis, N. Dikaios, G. A. Kastis, Reconstruction of preclinical PET images via Chebyshev polynomial approximation of the sinogram, Applied Sciences, 2022, 12(7), 3335.

[2]Y. Geng, J. Tan, C. Guo, C. Shen, W. Ding, S. Liu, Z. Liu, Computational coherent imaging by rotating a cylindrical lens, Optics Express, 2018, 26(17), 22110-22122.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

In this papers authors address and propose a way to use 2D quantum Fourier transform and quantum inverse 3D Fast Fourier transform for the composition of cross-sections of an object from its projections. Athough the work is a first stage of the research process on improving the conventional Radon transform in these applications, the work is sound and the paper well written. Therefore it can be published in current form expecting that the authors will keep researching the subject and provide new insights and improvements in a near future.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

In this manuscript, the authors generalize the 2D radon transform and 3D Fourier transform to the quantum scenario. They apply them to the 3D quantum state tomography and provide the explicit circuit to implement the tomography procedure.

I think this work will be interesting if we can produce a 3D quantum object with a coherent wavefunction on the whole space.  In this case, the quantum tomography method provide here will be useful.  

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

The revision is ok.