Shallow-Depth Quantum Circuit for Unstructured Database Search
Round 1
Reviewer 1 Report
Comments and Suggestions for Authors
I am responding to MDPI request for me to provide you with a report in connection with the submitted manuscript “Shallow-depth Quantum Circuit for Unstructured Database Search” by Junpeng Zhan. I am pleased to do so.
In this article, the author has studied two quantum circuits called HX and Ry layers for the searching problem. Remarkably, both circuits maintain a fixed circuit depth of 2 and 1, respectively, irrespective of the number of qubits used. He introduces two algorithms to construct the depth-2 HX layer and the depth-1 𝑅𝑦 layer. He proves that either layer, along with the 𝐶𝑛(𝑋) gate, can efficiently amplify the probability of the sole good element in any large unstructured databases from 1/2n to nearly 1, exhibiting an exponential advantage in circuit depth compared to the GSA. Both algorithms assume prior knowledge of the good element’s position index.
His research topic is very interesting, the presentation is very good and his results appear to be correct. It would be better if the author could consider the following comments:
1) Could the author specify the following states |0, 𝜓0>, |𝜓1⟩, and |𝜓2>?
2) Although the paper is in the applied mathematics area, in the introduction section, it would more complete if the author makes some references in theoretical physics aspects related to construct qubits (charge qubits, spin qubits, light qubits, quantum dots etc). Please mention papers for any kind of physical structures for qubit generation e.g. (a) Michael A. Nielsen “Quantum Computation and Quantum Information”, Cambridge, 2010 (b) Solid state communications 191, 10-13 (2014), (c) Phys. Rev. B 104, 115425, (2024).
3) I would appreciate, if the author could make some more comments related to experimental results (Fig 2).
Comments on the Quality of English Language
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Author Response
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Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThe author claimed to have a variational quantum algorithm for unstructured database search with exponential advantage in circuit depth. (A shallow depth algorithm for this search problem when the result (index of good element) is known was also presented, but I will not comment due to the lack of practical applicability of this situation.) Unfortunately, the result is poorly presented with insufficient evidence that I cannot recommend the paper for publication. Significant details are hidden in ref [35] which I think should be made explicit in this paper. Most importantly, when the index of the good element is unknown, how can the objective function f(theta) in equation (12) be known so that a variational method can be deployed? After this issue has been resolved, the correct accounting of resources for the *entire* quantum algorithm must also be presented: this includes all the resources spent in obtaining a value of f(theta) at an intermediate run. I believe that when correct accounting is done, no significant advantage can be found in general. From an abstract point of view, variational quantum algorithms are a family of algorithms with extensive use of classical intermediate computation. In particular, there is no "entanglement" between different runs which modify the variational parameters thete. Consequently, additional quantum resources (specifically time or number of gates) must be used to re-establish a new quantum state for each run. For these reasons, I recommend a significant rewrite in order for the paper to be publishable.
Comments on the Quality of English LanguageGood.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsThis is a paper with significant congtributions to the field. It is well written, with (almost) all intriduced abbeviations (of special terms) defined, well formulated explanations of all steps in the presentation, and an appropriate (and helpful to the non-specialized readersm too) list of references. [Refs 35 snf 36 need a little more specific information.]
The Introduction clarly states the aim and goal of the paper, and its relation to the Grover Algorithm (GSA) of quantum computing theory. Namely, it das not "improve" the effectiveness of GSA in speed, but it provides novel insigths into the "guts of GSA", i.e. into the concrete gates-structure of quantum circuits of GSA. To phrase this differently: It may appear that the "knowledge of target element’s position index" in the database is a "too strong" assumption, which makes the parctical value of the new results irrelevant. But this criticism is incorrect, becuase the paper shows proves a means for minimazing/otimazing the CSA circuit depth --- which certainly DOES have practical value.
Tha author provides mathematicl proofs of his statements and moves some longer partrs of the to the Appendix --- which is appreciated! As a whole the presentation is sgtraigthforward and well fomulated.
The extension of the results with the aid of VQS (variational quntum search) alrorithms is presented, Here is the position of the "good" element in the database not known apriori --- as traditionally requested. The related r esults again underly the important aspect of the present paper: It psovides "new insights into the guts" of the algorithms/circuits.
Some indications concerning connectrions with topics of comcputation-complexitiy, e.g. NP-complet problems, as well cryptograpyh, machime learng etc, are indicated.
The numerical results presented confirm the theoretical derivations,
Author Response
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Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
Comments and Suggestions for AuthorsThe authors made appropriate changes to the manuscript making it easier to comprehend it impact. I therefore suggest a publication.
