Quantum Compressive Sensing: Mathematical Machinery, Quantum Algorithms, and Quantum Circuitry

Round 1

Reviewer 1 Report

It is presented a proposal of a protocol for performing "quantum" compressive sensing, and suggested several ways each step of the protocol may be implemented on a quantum computer, which is of scientific interest, I have only two observations:

1.- Indicate a minimum development for the expressions that are proposed by the authors, for example: (3), (6). (7). (7)....

2.- Attach a workflow diagram where each of the calculation steps proposed by the authors can be visualized in a quick way, which will facilitate a better understanding of Fig. 3 and 4.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

In this paper the Authors give an interesting overview on quantum compressive sensing, especially mathematical machinery, quantum algorithms, and quantum circuitry.

The results show that as a sensing protocol that facilitates reconstruction of large signals from relatively few measurements, the compressive sensing can exploit known structures of signals of interest. However in order to further improve the paper, I would only recommend to remove some minor English bugs and to improve more references on the background, such as

1. Recently appeared data-driven approach trained tensor networks to learn the structure of signals of interest. How does this trained tensor network to “project” its state onto one consistent with the measurements taken, and  then be sampled site by site to “guess” the original signal？What are the similarities and differences between it and other methods?

2. As  the paper says, we take advantage of this computing protocol by formulating an alternative “quantum” protocol but the point is, what is the advantage and how to reflect it?

3. Whether the  results only indicate that a quantum, data-driven approach to compressive sensing, may have significant promise as quantum technology continues to make new leaps or not? As a complete paper, it needs to be supported by corresponding data and conclusions.

Author Response

Please see the attachment

Author Response File: Author Response.pdf