-->PONE-D-25-63743-->-->FPGA-Based Emulation Framework for Two-Qubit Quantum Computation: Design, Implementation, and Validation-->-->PLOS One

Dear Dr. Khalid,

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Academic Editor

PLOS One

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Reviewers' comments:

Reviewer's Responses to Questions

-->Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. -->

Reviewer #1: Partly

Reviewer #2: Yes

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-->2. Has the statistical analysis been performed appropriately and rigorously? -->

Reviewer #1: N/A

Reviewer #2: Yes

**********

-->3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.-->

Reviewer #1: No

Reviewer #2: Yes

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Reviewer #1: Yes

Reviewer #2: Yes

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-->5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)-->

Reviewer #1: In the paper, the authors present an FPGA-based solution for simulating a quantum register with two qubits.

The subject matter of the work is topical, as it is easy to give the application of this type of solution, e.g. the use of FPGA and, for example, the NISQ solution would allow for continuous monitoring of the real system with its equivalent in the form of an FPGA-simulated equivalent of a quantum register.

Unfortunately, various shortcomings can be pointed out in the reviewed work, from technical comments to substantive ones, e.g.:

+ Fig. 10 contains very small descriptions, unfortunately due to the fact that it is a bitmap, enlarging the image does not help, we still have blurry text,

+ The authors did not describe the details of the implementation of qubit emulation (how many LUTs, BRAM and etc.), nor did they present the hardware platform on which the emulation is carried out, only in the summary it was written that the Zynq-7000 was used,

+ how the probability amplitudes were represented, with what accuracy, how the calculations were performed, how quantum noise was simulated,

+ how measurements were conducted, the expectation value, another types of measurements, quantum channels have been simulated,

+ the architecture from Fig. 6, 8 is only a record of the operation of a unitary operation, unfortunately Fig. 6 is misrepresented, because the notation suggests that these are gates controlled by a zero qubit in state one, unless the Authors introduce gates separately for individual qubits, but the graphic form is not unambiguously presented in this case, it is enough to write it directly using Dirac notation and the product of the tensor,

+ the automata shown in Fig. 10, 12, 14 are not properly defined automata, they are a graphical record of the use of individual quantum gates,

+ Fig. 11 is not a representation of architecture, but quantum circuits forming a Bell pair,

+ The authors state that their solution is universal, unfortunately it is not, because in order for it to be simulated, any unitary single gate should be simulated, and such a computational procedure is not presented in the article,

It is possible to point out many other shortcomings, e.g. the lack of analysis of the latency in FPGA calculations, so despite the interesting topic, although there are other descriptions of the use of FPGAs for simulation already known in the literature, I cannot recommend this article, it requires, in my opinion, a complete rewrite.

Reviewer #2: Thanks for sharing your research work. Overall, the paper is well written.

The paper presents a FPGA-based quantum emulation framework.

However, there are some aspects that the authors need to take care of before this paper can be published.

1. Please add Scalability Discussion: As your approach is very limited to small number of qubit, please clearly state its limitation and discuss how it could be scaled in the long term.

2. Add experiments to benchmark with other FPGA based emulator, eg, FPGA (ISE) Khalid et al. [10], 2021, listed in table; also consider other benchmarks to add to justify its advantages.

3. Consider gate-depth sensitivity experiments -- The goal is to evaluate how numerical errors accumulate as the depth of the quantum circuit increases. So that the readers could know quantitively the limitation of this approach and when it outforms.

**********

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Reviewer #1: No

Reviewer #2: No

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-->PONE-D-25-63743R1-->-->FPGA-Based Emulation Framework for Two-Qubit Quantum Computation: Design, Implementation, and Validation-->-->PLOS One

Dear Dr. Khalid,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

Please submit your revised manuscript by May 07 2026 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:-->

• A letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.
• A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.
• An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols.

We look forward to receiving your revised manuscript.

Kind regards,

Zeheng Wang

Academic Editor

PLOS One

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If the reviewer comments include a recommendation to cite specific previously published works, please review and evaluate these publications to determine whether they are relevant and should be cited. There is no requirement to cite these works unless the editor has indicated otherwise.

Additional Editor Comments:

According to the reviewers, please only claim with strong evidence on the e.g. novelty and advancement. Just letting you know that Plos ONE does not require novelty for publishing. If you really want to demo a certain level of novelty, please provide the justification in detail. Otherwise, the MS might be rejected according to the journal's policy.

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Reviewers' comments:

Reviewer's Responses to Questions

-->Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.-->

Reviewer #1: All comments have been addressed

Reviewer #2: (No Response)

**********

-->2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. -->

Reviewer #1: Yes

Reviewer #2: Partly

**********

-->3. Has the statistical analysis been performed appropriately and rigorously? -->

Reviewer #1: N/A

Reviewer #2: Yes

**********

-->4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.-->

Reviewer #1: Yes

Reviewer #2: No

**********

-->5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.-->

Reviewer #1: Yes

Reviewer #2: Yes

**********

-->6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)-->

Reviewer #1: The authors made a number of corrections and answered the questions and comments posed. The current version can be rated better than the original version of the article. The current figure contains useful information for people who would like to try to implement quantum computing simulation using FPGAs.

Reviewer #2: The manuscript claims to implement a “complete universal quantum gate set” on FPGA , but prior works have already implemented similar gate-level or algorithm-level FPGA quantum emulators. The paper mainly extends an existing framework by adding Phase and CNOT gates, which appears to be an incremental improvement rather than a fundamentally novel contribution.

The evaluation only includes Bell states and the Deutsch algorithm , which are basic two-qubit demonstrations. There is no validation on more complex quantum algorithms or larger qubit systems, making it unclear whether the framework can scale beyond small test cases.

The emulator is compared with IBM Aer simulator and IBM quantum hardware , but:

The comparison is limited to error rates without runtime, latency, or energy efficiency metrics

The paper itself acknowledges that hardware noise differences make direct comparison difficult

No comparison with other FPGA-based emulators is provided

Thus, the claimed advantages are not rigorously demonstrated.

**********

-->7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

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Reviewer #1: No

Reviewer #2: No

**********

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To ensure your figures meet our technical requirements, please review our figure guidelines: https://journals.plos.org/plosone/s/figures

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-->PONE-D-25-63743R2-->-->FPGA-Based Emulation Framework for Two-Qubit Quantum Computation: Design, Implementation, and Validation-->-->PLOS One

Dear Dr. Khalid,

Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

Please submit your revised manuscript by Aug 13 2026 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:-->

• A letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.
• A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.
• An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

-->

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: https://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols. Additionally, PLOS ONE offers an option for publishing peer-reviewed Lab Protocol articles, which describe protocols hosted on protocols.io. Read more information on sharing protocols at https://plos.org/protocols?utm_medium=editorial-email&utm_source=authorletters&utm_campaign=protocols.

As the corresponding author, your ORCID iD is verified in the submission system and will appear in the published article. PLOS supports the use of ORCID, and we encourage all coauthors to register for an ORCID iD and use it as well. Please encourage your coauthors to verify their ORCID iD within the submission system before final acceptance, as unverified ORCID iDs will not appear in the published article. Only  the individual author can complete the verification step; PLOS staff cannot  verify ORCID iDs on behalf of authors.

We look forward to receiving your revised manuscript.

Kind regards,

Zeheng Wang

Academic Editor

PLOS One

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If the reviewer comments include a recommendation to cite specific previously published works, please review and evaluate these publications to determine whether they are relevant and should be cited. There is no requirement to cite these works unless the editor has indicated otherwise.

Please review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice.

Additional Editor Comments:

The reviewer still has some concerns regarding the expression. please accordingly revise your MS.

Kindly be noted that this will be last chance to revise all the issues.

Some pioneering works in small-scale qubit applications below may be of interest of the authors:

https://doi.org/10.1002/advs.202506213 (DOI)

https://doi.org/10.1002/advs.202411573 (DOI)

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Reviewers' comments:

Reviewer's Responses to Questions

-->Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.-->

Reviewer #3: (No Response)

**********

-->2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. -->

Reviewer #3: Partly

**********

-->3. Has the statistical analysis been performed appropriately and rigorously? -->

Reviewer #3: N/A

**********

-->4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.-->

Reviewer #3: (No Response)

**********

-->5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.-->

Reviewer #3: (No Response)

**********

-->6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)-->

Reviewer #3: The revised manuscript has been substantially improved compared with the earlier version. The authors have clarified that the work is an extension of a previous FPGA-based quantum emulation framework rather than a wholly new architecture. They have also expanded the gate set by including parameterized Phase gates and the CNOT gate, and they now validate the emulator using Bell states, the Deutsch algorithm, Superdense coding, Grover’s search, and BB84 QKD. The addition of resource utilization, runtime comparison, fixed-point error discussion, and comparison with other FPGA emulators strengthens the technical presentation. However, several claims still require refinement before publication, particularly regarding scalability, energy efficiency, and reproducibility. Hence, I recommend minor revision for the following reasons.

1. The manuscript still contains an inconsistency between the claimed two-qubit emulator and the reported 16-qubit Superdense coding experiment. The title, architecture description, and memory model emphasize a two-qubit framework, while later sections describe a 16-qubit Superdense coding circuit and use it as evidence of scalability.

2. The energy-efficiency claim remains insufficiently supported. The revised manuscript discusses runtime and FPGA resource utilization, but the comparison with IBM Aer and IBM hardware does not provide normalized energy, power, or energy-per-operation measurements.

3. The comparison with IBM quantum hardware is useful but still risks misleading interpretation because physical QPU noise and deterministic FPGA emulation are fundamentally different execution environments.

4. The fixed-point precision analysis has improved, but the accuracy loss in deeper circuits remains a limitation. The reported Deutsch and Grover error rates show that finite precision and sampling effects can become non-negligible.

5. Reproducibility remains underdeveloped. For an FPGA-based emulation framework, readers need sufficient access to design artifacts, test benches, circuit descriptions, and simulation settings.

6. Some technical and language issues remain, including typographical errors such as “Atrix 7” instead of “Artix 7,” inconsistent spacing in terms such as “P hase,” and uneven notation for CNOT, QFT, and fixed-point formats. Please conduct a final technical proofreading pass to ensure consistent terminology, notation, figure captions, table labels, and grammar throughout the manuscript.

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-->7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review?  For information about this choice, including consent withdrawal, please see our Privacy Policy.-->

Reviewer #3: No

**********

[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

To ensure your figures meet our technical requirements, please review our figure guidelines: https://journals.plos.org/plosone/s/figures

You may also use PLOS’s free figure tool, NAAS, to help you prepare publication quality figures: https://journals.plos.org/plosone/s/figures#loc-tools-for-figure-preparation.

NAAS will assess whether your figures meet our technical requirements by comparing each figure against our figure specifications.

-->

FPGA-Based Emulation Framework for Two-Qubit Quantum Computation: Design, Implementation, and Validation

PONE-D-25-63743R3

Dear Dr. Khalid,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

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Kind regards,

Zeheng Wang

Academic Editor

PLOS One

Additional Editor Comments (optional):

Reviewers' comments: