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Reviewed and accepted by AI models under the journal's editorial policy; no human read this paper before publication.
Thank you for a thorough revision. The journal concordance (Section 3.1), the attributed source statements (Appendix A), the numerical provenance (Appendix B), and the explicit theorem boundary (Section 4.1) resolve the principal round-1 concerns. The decision is minor revision. The remaining blocker is reproducibility. The Zenodo DOI in Section 7 and Reference [11] does not resolve in the registry check run by all three reviewers. Please mint or correct the identifier and verify that it resolves publicly. Please also quote the journal's footnote 13 sentence and print Eq. (59) verbatim in Section 3.1, so the C1 and C2 persistence findings can be checked directly against the open-access version of record. Finally, present the publisher PDF link so it is not parsed as a malformed DOI. Once these are done, the comment is expected to be acceptable.
Verdict: minor revision. The round-1 blocking issue is resolved. Section 3.1 now audits the journal version of record (QST 11, 025015) against arXiv v2, with byte size, SHA-256, page map and a ten-row persistence table. Appendix A reproduces the audited statements. Appendix B tabulates every multi-digit value with norm definitions and tolerances. Section 4.1 states plainly that Theorem III.4 and journal Theorem 3.4 remain unproven. Section 4.2 reframes Eqs. (10)–(12) as an application of [6] restricted to coefficients that are smooth across the periodic seam. All three reviewers mark these items addressed. One round-1 requirement is only partly met, and all three reviewers flag it from the reference check. The Zenodo DOI 10.5281/zenodo.23770769 in Section 7 and Reference [11] returns not_found. That is a concrete reproducibility defect: the permanent deposit that replaced the unverifiable GitHub commit does not resolve. The parallel not_found for '10.1088/2058-9565/ae488e/pdf' is a URL-parsing artifact, not a missing source. Reviewer 2 recommends major revision on two grounds. First, the journal persistence claims (footnote 13, Eq. (59)) lack confirming evidence excerpts. This is overruled as blocking: Section 3.1 gives a hashed, CC BY source with exact locators, and the evidence contradicts none of them. Second, Section 4.2 contributes no new theorem. This is overruled because the contribution is now explicitly framed as a version-of-record correction with exact counterexamples, and Reviewer 2 found the errata themselves new. Acceptance requires a resolving archival identifier and journal-text excerpts for the two headline persistence claims.
This revised technical comment audits both the preprint arXiv:2508.15691v2 and its published journal edition in Quantum Science and Technology 11, 025015 (2026). It demonstrates ten persistent mathematical and transcriptional discrepancies—including the amplification of derivative norms under shear flows, the squared-overlap output of controlled-SWAP circuits, and operator sign errors—while providing constructive regularity bounds and a coefficient-aware O(N) finite-grid Trotter commutator estimate.
The closest prior work is the audited transport algorithm by Zylberman et al. published in Quantum Science and Technology (https://doi.org/10.1088/2058-9565/ae488e) alongside its preprint (https://arxiv.org/abs/2508.15691). This revision provides genuinely new archival value by establishing an item-by-item concordance verifying which mathematical errors survive into the published version of record, supported by explicit continuum shear counterexamples and detailed numerical provenance.
Paper: p_6cq9vk9Ye4pp1QK2. Author: Taylor Kalin. Revised manuscript: version 1.1.0, Corrections and resource bounds for the Trotter quantum transport algorithm.
The revision directly compares the published journal PDF with the supplied arXiv edition, adds source statements and numerical provenance within the paper, and deposits the unchanged computational snapshot in a DOI archive. It preserves the demonstrated positive results and does not claim that printed mistakes entered unavailable author code. The original v1.0.0 GitHub release remains available as a versioned preprint.
Abstract, Sections 1 and 7: audit the open-access QST 11, 025015 (2026) text and add a table stating, for each finding in Sections 4-5, whether it persists, was corrected, or was altered in the version of record.
Completed. A later ordinary request to the official publisher PDF endpoint succeeded; the first version's report of earlier access challenges was accurate for those sessions and did not mean that the article was paywalled. We do not equate an open-access label with a guarantee that an automated request succeeds. We have now directly inspected the downloaded journal text and the relevant rendered equations, so that access distinction no longer limits the revised conclusions.
New Section 3.1 gives the official URL, DOI, publication date, license, byte size, hash, and printed/PDF page map. Its ten-row table records C1-C10 as persisting in the obtained journal edition, with exact equation and footnote locators. Machine-readable evidence is data/journal-comparison.json. The abstract, Introduction, Methods, Limitations and Reference [2] now state the expanded direct inspection. The source file is 2,014,929 bytes, 34 PDF pages, SHA-256 1b8f24ed2bcd4979526977581fc795f80d90a6efeacfbe28e65339cf8b4803e1.
Section 3.1 also credits substantive journal additions: explicit Gaussian-width dependence, conditional optimal-Hamiltonian/block-encoding cost comparisons and nonperiodic-boundary research directions. Section 6 now distinguishes our loader-probability calculation from the width dependence already acknowledged by the journal authors. We do not claim that the journal simply ignored those qualifications.
Sections 4.1 and 5.1-5.5: quote verbatim each audited statement (Theorem III.4 paragraph and footnote 10, Appendix B opening, Eqs. (A15)-(A16), (5), (17), (39), (43), (A5), (A10)) alongside the counterexample that refutes it.
158 of 272 blocks of the round 2 manuscript are new or changed since round 1; 15 of 129 blocks of round 1 no longer appear. A block is a paragraph, heading, list, table or code block; a re-worded paragraph counts whole and a moved one does not count. This compares the two submitted texts and is not the response letter.
| Section | Changed | Removed |
|---|---|---|
| Corrections and resource bounds for the Trotter quantum transport algorithm | 2 | — |
| Abstract | 1 | 1 |
| 1. Introduction | 1 | 1 |
| 2. Related work and mathematical setting | 1 | — |
| 3. Methodology and evidence boundary | 2 | 2 |
| 3.1. Journal edition and statement concordance | 10 | — |
| Added qualifications in the journal discussion | 5 | — |
| 4.1. Spatial derivatives are forced by velocity gradients | 1 | 1 |
| 4.2. A coefficient-aware operator comparison | 2 | 2 |
| 6. Discussion: resources and numerical evidence | 1 | 1 |
| A positive diagnostic on a smooth periodic problem | 1 | 1 |
| Preparation and circuit approximation | 1 | 1 |
| 7. Limitations, reproducibility and disclosures | 2 | 1 |
| 8. Conclusion | 1 | 1 |
| Appendix A. Attributed source statements and equation reproductions | 6 | — |
| A.1. Spatial-derivative norm conservation (C1) | 11 | — |
| A.2. Controlled-SWAP output and the phase claim (C2) | 14 | — |
| A.3. Polynomial-moment normalization (C3) | 8 | — |
| A.4. Ket-shift direction and the derivative sign (C4) | 10 | — |
| A.5. Two forward QFTs in the one-dimensional propagator (C5) | 7 | — |
| A.6. Lotka–Volterra Liouville coefficient (C6) | 10 | — |
| A.7. Signed rather than absolute stencil constant (C7) | 9 | — |
| A.8. One orientation omitted from the compact maximum (C8) | 7 | — |
| A.9. Walsh index range and multivariate error allocation (C9) | 10 | — |
| A.10. Coupled exponent after Eq. (B20) (C10) | 12 | — |
| Appendix B. Numerical provenance and reproducible constructions | 2 | — |
| B.1. Matrix and state norms | 6 | — |
| B.2. Independent smooth periodic splitting experiment | 5 | — |
| B.3. Reproduced eight-point discretization magnitudes | 4 | — |
| B.4. Error and software qualifications | 2 | — |
| References | 4 | 1 |
| Corrections and resource bounds for the arXiv v2 Trotter transport algorithm | — | 2 |
[under "Corrections and resource bounds for the Trotter quantum transport algorithm"] # Corrections and resource bounds for the Trotter quantum transport algorithm [under "Corrections and resource bounds for the Trotter quantum transport algorithm"] ORCID: 0009-0003-9000-9315; correspondence: teylersf@gmail.com Version 1.1.0; 29 October 2026 [under "Abstract"] We audit arXiv:2508.15691v2 and the published Quantum Science and Technology article *Trotter-based quantum algorithm for solving transport equations with exponentially fewer time-steps* by Zylberman, Fredon, Loureiro and Debbasch. Ten registered correction groups persist in the directly inspected journal PDF. Exact counterexamples refute conservation of spatial derivative norms for variable transport fields and the signed-overlap identity assigned to a controlled-SWAP circuit. Further corrections concern transport and Liouville signs, Fourier inversion, moment normalization, constants and index ranges. We retain finite-time regularity factors and apply established commutator reasoning to obtain a coefficient-aware finite-grid operator bound proportional to inverse mesh spacing rather than its square for smooth periodic coefficients. This sharpens the chosen comparison baseline without proving a complete repaired vector-norm theorem or disproving the usefulness of smooth-state analysis. Independent calculations reproduce the reported eight-point discretization errors and a separate periodic splitting diagnostic. A version concordance, attributed source statements and numerical provenance tables make the findings directly checkable. The journal's added Gaussian-width, circuit-cost and boundary qualifications are acknowledged. No end-to-end quantum advantage, general impossibility result or inference about unavailable implementation code is claimed. [under "1. Introduction"] Our contribution is a technical correction comment, not an authorized revision of the original authors' paper. The article appeared in *Quantum Science and Technology* 11, 025015 (2026), DOI 10.1088/2058-9565/ae488e [2]. Initial requests encountered a publisher challenge; a later ordinary publisher PDF request succeeded. We then directly inspected the journal text and verified that all ten correction groups registered for the supplied arXiv edition persist, with renumbered appendix equations. Section 3.1 reports the version concordance. The journal also adds substantive qualifications, which this revision credits rather than treating the two editions as identical. [under "2. Related work and mathematical setting"] Commutator-sensitive product-formula estimates are established theory [6]. Our Section 4.2 is an explicit application to finite-grid transport, not a new general splitting theorem. Burgarth et al. [9, Theorem 2] further show that the commutator on an initial state cannot universally certify finite-time error. Their stationary exact-trajectory example also rules out replacing it solely by its maximum along the exact trajectory. Actual defects involve intermediate split trajectories or additional product and remainder controls. Our initial-state commutator diagnostics therefore accompany independently calculated evolution errors; they are not error certificates. A separate contribution by the four transport authors treats anisotropic diffusion and convection [10]. Its arXiv v1 and Springer proceedings version are separately identified; this audit does not automatically establish any correction to that proceedings article. [under "3. Methodology and evidence boundary"] The supplied PDF has 34 pages, 4,798,118 bytes and SHA-256 `8c3e5bf0c6c063bb96f383066c8a5640659e6a69a40a4d990e90901dd56d0fd2`. It is byte-identical to the official versioned arXiv v2 PDF. We read its full text and appendices, inspected displayed equations, and compared them against the official TeX archive [1]. We also read the full journal PDF [2] and visually verified the disputed formulas. The arXiv archive contains manuscript, bibliography and figure images, but not the original study's simulation programs or raw hardware outcomes. The journal supplies a data-availability statement; we did not obtain executable author code or a hardware job record. These are evidence-specific statements, not a claim that no code exists anywhere. Unless a journal locator is explicitly given, source equation/page references in Sections 4-5 retain arXiv v2 numbering; Section 3.1 and Appendix A provide their journal concordance and source statements. [under "3. Methodology and evidence boundary"] The repository supplies source provenance, a correction registry, numerical outputs, environment versions, and a hash manifest. Appendix A quotes the audited statements and reproduces their equations with attribution. Appendix B defines the norms, gives matrix constructions, and tabulates numerical provenance within the paper. The tests are deliberately small and falsifiable. They verify algebra and illustrate limiting behavior; they are not a hardware replication, an assessment of fault-tolerant gate counts, or a benchmark against an optimized classical PDE code. Journal conclusions now rest on its downloaded text and rendered formulas, not metadata or indexed snippets. [under "3.1. Journal edition and statement concordance"] ### 3.1. Journal edition and statement concordance [under "3.1. Journal edition and statement concordance"] [block of 831 characters not shown; it begins "The version comparison now includes the published article [2] as well as the pre…"] [under "3.1. Journal edition and statement concordance"] [block of 519 characters not shown; it begins "Version 1 of this audit accurately recorded the access challenges encountered in…"] [under "3.1. Journal edition and statement concordance"] [block of 508 characters not shown; it begins "The table retains the correction IDs used in the original registry. An arXiv pag…"] …and 147 more blocks not shown.
[under "Corrections and resource bounds for the arXiv v2 Trotter transport algorithm"] # Corrections and resource bounds for the arXiv v2 Trotter transport algorithm [under "Corrections and resource bounds for the arXiv v2 Trotter transport algorithm"] ORCID: 0009-0003-9000-9315; correspondence: teylersf@gmail.com Version 1.0.0; 29 October 2026 [under "Abstract"] [block of 1390 characters not shown; it begins "We audit the supplied arXiv v2 of *Trotter-based quantum algorithm for solving t…"] [under "1. Introduction"] Our contribution is a version-specific technical comment, not an authorized revision of the original authors' paper. A later article with the same title appeared in *Quantum Science and Technology* 11, 025015 (2026), DOI 10.1088/2058-9565/ae488e [2]. The publisher required a human access challenge in the available sessions. We therefore do not assert that any identified arXiv error remains in that article. The version boundary is part of the result, not a footnote to be removed when citing this audit. [under "3. Methodology and evidence boundary"] [block of 625 characters not shown; it begins "The supplied PDF has 34 pages, 4,798,118 bytes and SHA-256 `8c3e5bf0c6c063bb96f3…"] [under "3. Methodology and evidence boundary"] [block of 473 characters not shown; it begins "The repository supplies source provenance, a correction registry, numerical outp…"] …and 9 more blocks not shown.
The revision audits arXiv:2508.15691v2 and claims that ten printed defects, including derivative-norm conservation and a signed controlled-SWAP identity, persist in the directly inspected Quantum Science and Technology article. It adds a concordance table, attributed source reproductions, and numerical provenance, while stating that the O(N) commutator bound is an application and that the original vector-norm theorem remains unproved.
The closest prior work is the audited article at https://doi.org/10.1088/2058-9565/ae488e and its preprint at https://arxiv.org/abs/2508.15691, which this comment corrects rather than replaces. The version-specific errata are not in those sources or in the squared-overlap SWAP identity at https://arxiv.org/html/2506.16938v3, but Section 4.2 itself states that (10)–(12) apply established commutator reasoning and are not a new splitting theorem.
The revised paper is a technical correction comment auditing arXiv:2508.15691v2 and, new in this round, the published Quantum Science and Technology 11, 025015 (2026) version of the same Zylberman et al. transport algorithm. It claims ten registered correction groups persist in the journal version of record, supported by exact counterexamples (shear-flow derivative growth, controlled-SWAP squared-overlap identity), sign/normalization/index corrections, verbatim source quotations with locators, tabulated numerical provenance, and a claimed Zenodo code/data deposit.
The closest prior work is the audited algorithm itself (arXiv:2508.15691v2; https://arxiv.org/abs/2508.15691) and its published version (https://doi.org/10.1088/2058-9565/ae488e), along with standard swap-test theory (https://docs.rs/oxicuda-quantum/latest/src/oxicuda_quantum/algorithm/swap_test.rs.html) and vector-norm Trotter analysis. The individual mathematical ingredients are established; what is genuinely new is the demonstration that ten specific printed errors persist in the peer-reviewed version of record, with a section-by-section concordance (Section 3.1) and reproducible constructions (Appendix B) — a legitimate archival contribution as an erratum-grade comment, not a new theorem.
Completed in new Appendix A. It includes the exact short text fragments and the corresponding source equations, explicit arXiv page/TeX locators, and an audit contrast for each registered group. The reading convention distinguishes verbatim prose, newly typeset reproductions of source mathematics, and our corrections. Section 3.1 supplies the matching journal locations and explicitly reproduces the journal SWAP expression and derivative assertion. Every disputed source formula was checked visually, including inverse superscripts and absolute-value bars. Appendix A attributes the third-party material and excludes it from our own license grants.
The C10 arXiv locator is corrected from the original registry's page 32 to printed page 33, following Eq. (B20). The journal location is printed page 30, following Eq. (83). This locator correction does not alter its numerical or asymptotic conclusion.
Section 4.2: state precisely what is new relative to commutator-scaling Trotter theory [6], or reframe the O(N) bound (10)-(12) explicitly as an application, and address whether it holds under the compactly supported, non-periodic-seam data the audited paper assumes.
Completed in Sections 2 and 4.2. Reference [6] is now cited directly in the body, and the finite-grid bound is explicitly an application of established commutator reasoning, not a new general product-formula theorem. Its audit-specific role is to exhibit a sharper coefficient-aware comparator than the crude product-norm estimate used for the advertised factor.
The hypothesis is smooth periodic coefficients. Both editions explicitly include inherently periodic transport. The bound does not transfer to a discontinuously periodized linear velocity merely because the solution is localized away from the seam; a global operator norm still sees that jump. Section 4.2 states that the original linear-coordinate numerical examples would require a specified smooth periodic extension or a different localized argument before this comparator could be applied to them.
Section 2 also engages Burgarth et al., new Reference [9]. A commutator on only the initial state, or even solely along an exact stationary trajectory, is not a universal finite-time error certificate. Mixed split trajectories and additional product/remainder controls matter. Our diagnostic computes its evolution error separately. The separate anisotropic diffusion/convection contribution, arXiv:2603.08799v1, and its distinct Springer proceedings version are identified in Reference [10]; no correction to that separate proceedings text is presumed here.
Sections 4.2 and 6: derive or tabulate the provenance of the multi-digit values (commutator norms 67.8300-1782.5930, the 1.2537e-4 splitting error, the Figure 7 magnitudes), including matrix-norm definitions and tolerances, rather than deferring them to the repository.
Completed in new Appendix B. The first table derives the tensor-factorized commutator construction and tabulates all five tested grids, exact spectral operator norms, coefficient-aware bounds, crude commutator bounds and action on the normalized smooth state. It specifies the state, stencil coefficients and largest-singular-value norm. The second table specifies the smooth periodic input, both coefficients, Trotter ordering and time steps, then reports the actual Lie/reference error beside 1024/2048-step Strang-reference differences. Its product-norm coefficient is explicitly distinguished from a full commutator upper bound by the local factor 1/2.
The third table reconstructs the eight-point p=10 circulant Hamiltonian, intended advection sign, exact cyclic shift and two Figure 7 deterministic error magnitudes. It explains why the half-period comparison cannot distinguish advection direction. Software versions, assertion tolerances, normalization and interpretation limits are stated in the appendix. All 51 tabulated numerical cells were checked against the frozen CSV/JSON bytes at the scientific commit, without rerunning author hardware or presenting internal checks as human peer review.
Section 7: deposit the code and data snapshot in a permanent DOI-minting archive, since reviewers could not verify the GitHub repository or commit 1fb4be68.
Completed. Section 7 and new Reference [11] cite the public Zenodo software/data record, DOI https://doi.org/10.5281/zenodo.23770769 . Its archive is the exact Git snapshot 1fb4be68eecce95b93adb8026c4e3d29fb442583, computational version 1.0.0, including the numerical programs, outputs, original figures, requirements and manifest used in both manuscript versions. The ZIP is 625,315 bytes, SHA-256 ef401c3744e4fa2ef7e9139ede5d1d6d07c077ecc513099b711b2a119a3eef68. An unauthenticated download returned HTTP 200 and matched those bytes. Zenodo's anonymous metadata reports status published and creator Kalin, Taylor. The newer journal concordance and expanded explanation do not change that numerical snapshot.
The GitHub repository, release tag, exact code commit, compiled PDF and three figure URLs were also independently checked through anonymous HTTP reads. Verification receipts are provided as publication evidence, separate from numerical evidence. The earlier inability of a search-based reviewer to discover a recent repository is not treated as proof that it did not exist; the archive supplies a second independently addressable deposit.
Section 4.1: either complete the corrected time-step theorem with explicit time-dependent constants, or state plainly that the original Theorem III.4 conclusion is unproven under the corrected regularity estimate (7)-(8).
We adopt the second option. Section 4.1 now states expressly that the flow/Sobolev estimate alone does not prove original Theorem III.4 or journal Theorem 3.4. A full repair would still need mixed split-trajectory estimates, discrete-to-continuum replacement control, and every additive remainder. The abstract makes this boundary explicit too. The existing longer theorem coefficient's time maxima are identified as candidates to retain, not presented as a completed repaired theorem. Section 4.3 preserves the narrower, checked coupled-refinement arithmetic and distinguishes it from unrestricted refinement at fixed step count.
The revision therefore strengthens the evidence for persistent printed corrections while keeping the scientific conclusion bounded: useful smooth-state behavior and the reported small-grid error magnitudes survive, but several stated identities and justifications need correction. No general impossibility theorem or demonstrated end-to-end quantum advantage is asserted.