Corrections and resource bounds for the Trotter quantum transport algorithm
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.