{"id":"0badb1a5-9b4e-42b5-a249-aa4d4240a0c2","arxiv_id":"2607.25795","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"low","formal_verification":"none","parameter_count":5,"one_line_summary":"Local Pauli responses, inverted through a known generator dictionary, separate coherent from dissipative Lindbladian coefficients and recover all of them to accuracy epsilon from O~(M/epsilon^2) short-time measurements.","lead":"Researchers show how to learn both the interactions and the noise rates of an open quantum system from short-time local measurements, by inverting a response matrix that separates coherent from dissipative effects. This gives a near-optimal sample-efficient recipe for calibrating and diagnosing noisy quantum devices.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"No significant objection identified; the central claim holds under its stated assumptions. Minor issue: Lemma 3 states equality where conjugation is required.","rationale":"I read the full text and checked the load-bearing mathematics: the construction of the square response family, the support-ordered block-triangular invertibility (Prop. 1), the inverse-norm and sparsity bounds (Thm. 7), the Taylor growth bounds (Thms. 5-6, 10), and the two finite-time reconstruction schemes (Thms. 8, 9, Cor. 8). The derivations are internally consistent and the claimed O~(M/ε^2) sample complexity plus the stated classical scalings follow from the stated assumptions. The reader's weakest assumption — a known, complete, nonredundant dictionary — is indeed the most load-bearing premise, but the paper explicitly scopes Problem 1 and Appendix A to that setting, so it is a limitation of scope rather than a flaw in the proof. I found one genuine technical error: Lemma 3 states F_{S,R}=F_{R,S} for Hermiticity-preserving maps, but the correct identity is F_{S,R}=\\overline{F_{R,S}}. The proof as written confuses (RPS)^† with RPS. However, the response combinations used in the main construction are constructed so that they are real under the corrected relation (e.g., F^H_C=(F_{C,I}-F_{I,C})/(2i) = Im F_{C,I}), so the central argument is unaffected. This minor issue does not change the verdict.","tokens_in":28563,"tokens_out":43686,"duration_ms":410971,"concrete_test":"Check the reality relation on a one-qubit example: for Φ(O)=i[X,O], compute F_{X,I}=i and F_{I,X}=-i, which confirms F_{S,R}=overline{F_{R,S}} and that F^H_X=(F_{X,I}-F_{I,X})/(2i)=1 is real. Then re-derive Theorem 7 with the corrected conjugate relation to confirm that G and H are real and the response rows remain valid.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The core mathematical claim is sound within Problem 1's scope: given a known, complete, nonredundant Pauli–GKSL dictionary and the uniform bounded-overlap regime (S_D, Λ = O(1)), the support-ordered block-triangular response matrix G is invertible, H=G^{-1} has O(1) row norm/sparsity, and the normalized response identity g_α(t,θ)=tθ_α+O(t^2) is correctly derived. The Chebyshev and contraction error analyses are internally consistent and support the stated eO(M/ε^2) sample and classical complexities. The only genuine caveat is the one the paper itself declares out of scope (App. A): a true generator containing an unmodeled Pauli term, time dependence, or non-Markovianity would make G misspecified and silently bias the estimates. This is a scoping limitation rather than a defect in the argument. Separately, Lemma 3's statement F_{S,R}=F_{R,S} is incorrect for Hermiticity-preserving maps; the correct identity is F_{S,R} = \\overline{F_{R,S}}. Under this correction, all subsequent reality claims and the real-valued response matrix construction remain valid, so the central argument survives.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies learning the generator of a time-independent Lindbladian evolution on N qubits, assuming a known, complete, nonredundant Pauli–GKSL dictionary with bounded overlap. It defines raw Pauli response functionals whose linear-in-time part is a known response matrix G mapping generator coefficients to response slopes, and proves that support ordering makes the dissipative block triangular, so G is invertible. Under bounded-overlap assumptions, H=G^{-1} has O(1) row norm and row sparsity. The normalized responses g_alpha(t,theta)=sum_j H_alpha j F_j(e^{tL^dagger_theta}-I) then satisfy g_alpha(t,theta)=t theta_alpha+O(t^2). Two estimators are proposed: Chebyshev–Lobatto interpolation at r=O(log(1/epsilon)) short times, and a single-time projected contraction at t_*=Theta(Lambda^{-2}) with geometric convergence. Both estimate all M coefficients to entrywise accuracy epsilon using O~(M/epsilon^2) experimental shots and O~(M/epsilon^2) total classical post-processing.","tokens_in":28728,"tokens_out":12169,"duration_ms":126649,"significance":"If it holds, this is a significant advance: it extends the local-response paradigm from Hamiltonian learning to Markovian open systems by explicitly resolving the coherent-dissipative and common-extension ambiguities, and it does so with concrete algorithms and explicit complexity bounds. The paper's central chain is sound: Lemma 2's response formula, Proposition 1's block-triangular invertibility, Theorem 7's uniform inverse bounds, and the finite-time error analyses of Theorems 8 and 10 are internally consistent. The main caveat is the Problem 1 assumption of a known complete dictionary; a true generator with an unmodeled term, time dependence, or non-Markovianity would make G misspecified and silently bias the estimates. The paper explicitly declares structure learning out of scope in Appendix A, so this is a scoping limitation rather than an internal inconsistency.","major_comments":[],"minor_comments":[{"comment":"The stated identity F^W_{S,R}(Phi)=F^W_{R,S}(Phi) is not correct for a general Hermiticity-preserving map; the proof applies trace cyclicity incorrectly. The correct relation is F^W_{S,R}(Phi)=overline{F^W_{R,S}(Phi)}. Fortunately, every use in Section C survives under this correction: the combinations F^H_C, F^diag_A, F^Re_AB, F^Im_AB remain real on Hermiticity-preserving maps. Please fix the lemma and its proof.","section":"Appendix C, Lemma 3 (Eq. C4)"},{"comment":"The framework assumes a known, complete, nonredundant dictionary. If the true generator contains a term outside the dictionary, the estimator is biased and no diagnostic is provided. Since the paper explicitly excludes structure discovery, this is not a blocking issue, but a one-sentence warning near Eq. (1) would help readers avoid overgeneralizing the claims to structure-learning settings.","section":"Problem 1 and Appendix A"},{"comment":"The paper uses O~ informally in several places without a single definition. Given that the stated sample and post-processing bounds mix polylogarithmic factors from r, n_it, and the union bound, a brief formal definition of O~ in Section IV or the appendices would improve precision.","section":"General notation"}],"recommendation":"minor_revision","confidential_remarks":"The core technical contribution is sound and the paper is within the journal's scope. The Lemma 3 issue is a local, easily repairable error that does not affect the main results once the conjugation is inserted. I recommend minor revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague, what you should know most: this paper is the first to show how to undo the coherent–dissipative mixing in local Pauli responses for Lindbladian learning. The key idea is to treat the responses as a simultaneous linear system, notice the mixing is support-ordered triangular, invert the response matrix G, and then construct normalized responses whose linear term is exactly t*theta_alpha. That is new algorithmic content, not a repackaging of Hamiltonian learning. The authors also give two finite-time reconstruction methods – Chebyshev–Lobatto interpolation and a single-time projected contraction – and both hit near the information-theoretic sample lower bound, O~(M/epsilon^2), with classical post-processing that is close to linear in M under their locality assumptions.\n\nI checked the load-bearing math by hand and it holds up. Lemma 2 gives the common-extension response formula, Proposition 1's block-triangular invertibility with unit diagonal blocks is sound, and Theorem 7's uniform inverse bounds follow from the nilpotence of U. Corollary 1's g_alpha = t*theta_alpha + O(t^2) is a coordinate construction, not a fit, so the circularity concern some might raise does not land. The Taylor bounds and both error analyses in the appendices are internally consistent.\n\nThe soft spots are real but not fatal. First, the entire framework assumes a known, complete, nonredundant local Pauli–GKSL dictionary. If the true generator has a term outside that dictionary – a long-range coupling, time dependence, non-Markovianity – G is misspecified and the estimates silently bias; there is no robustness or structure-discovery guarantee. The paper declares this out of scope, but a reader should know the result is conditional on the dictionary. Second, the classical post-processing costs use a unit-cost symbolic-Pauli model and explicitly defer bit complexity. That is an honest limitation, but it means the O~(M/epsilon^2) total classical cost is not yet a fully bit-level guarantee. Third, there are no numerical experiments. The constants in the inverse bounds depend on S_D and Lambda; the theory says they are O(1), but actual conditioning is untested. That is a gap, not a flaw in the proofs.\n\nOne minor technical issue: Lemma 3 states F_{S,R}=F_{R,S} for Hermiticity-preserving maps, but the correct identity requires conjugation, F_{S,R} = \\overline{F_{R,S}}. The authors' subsequent real-response construction implicitly uses the correct form, so the argument survives, but the statement should be fixed.\n\nOverall: this is a genuinely useful paper for people doing quantum device calibration or noise characterization, and it should be peer reviewed. I would cite it. The referee should push on the misspecification behavior and ask for at least small-scale numerics, but the central result is solid.","headline":"A technically sound and genuinely new framework for learning Lindbladians from short-time Pauli responses, provided the generator lies exactly in the known candidate dictionary; the paper deserves a serious referee, with attention to the misspecification caveat and the lack of numerics.","tokens_in":29416,"tokens_out":1025,"would_cite":true,"duration_ms":12485,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["81S22","81P18","81P45"],"pacs":["03.65.Yz","03.67.-a"],"model":"deepseek-v4-flash","headline":"Local Pauli responses, analyzed jointly as a linear system, identify both coherent and dissipative Lindbladian coefficients in open quantum systems.","keywords":["Lindbladian learning","open quantum systems","Pauli response functions","GKSL generator","coherent-dissipative ambiguity","local response inversion","quantum process tomography","Hamiltonian learning"],"falsifier":"On a system whose generator includes a known dissipative term supported on more than S_D sites, or a Hamiltonian term not in the dictionary, run the single-time protocol at t = t*. If the claim is false, the projected iteration will converge to a parameter whose response residual stays above the statistical error even as the number of shots grows, and the normalized response g_alpha(t)/t will show a systematic drift larger than O(t) between two different short times.","tokens_in":28242,"feed_emoji":"⚛️","tokens_out":5504,"duration_ms":59983,"temperature":0.7,"pith_summary":"Learning the generator of an open quantum system is harder than Hamiltonian learning because a local response mixes coherent coupling with dissipative noise, and even different dissipative terms can masquerade as each other. This paper shows that if the possible generator terms are known as a Pauli–GKSL dictionary, the mixing is not an obstruction: ordering the candidate terms by support makes the response matrix block-triangular and invertible. Multiplying raw responses by the inverse produces normalized responses whose linear-in-time term is exactly one coefficient each. The paper gives two protocols—Chebyshev–Lobatto endpoint differentiation and single-time projected contraction—that estimate all M coefficients to entrywise accuracy epsilon using O~(M/epsilon^2) experimental shots and comparable classical post-processing. If correct, the result turns local response inversion into a scalable calibration and diagnostic tool for noisy many-body quantum devices.","feed_headline":"Response inversion separates coherent and dissipative generator terms","feed_subtitle":"Two short-time protocols estimate all Lindbladian coefficients to accuracy epsilon with near-linear sample and classical cost.","key_machinery":"The load-bearing object is the real response matrix G_{j beta} = F_j(L^dagger_beta), built from raw Pauli response functionals F_j over a known local Pauli–GKSL dictionary. Its key structural property is support-ordered block triangularity: after ordering dissipative candidates by decreasing support, a response row only sees candidates whose support is a common extension of its own, making the dissipative block triangular and the Hamiltonian block an identity; hence G is invertible. The inverse H = G^{-1} defines normalized response functionals C_alpha, and the paper proves the normalized-response identity g_alpha(t,theta) = t theta_alpha + O(t^2). The uniform bounded-overlap regime ensures","core_discovery":"The central claim is that the coherent–dissipative ambiguity in Lindbladian learning is algebraically resolvable from local Pauli response data. For a known nonredundant Pauli–GKSL dictionary, the paper constructs an M by M response matrix G whose entries are the linear-in-time contributions of each candidate generator term to each measured response. Because a term supported inside a region can only contaminate responses whose outside Pauli labels are extended by a common string, ordering dissipative terms by decreasing support makes the dissipative block triangular with nonzero diagonal; Hamiltonian terms form an identity block, so G is invertible. With H = G^{-1}, the normalized responses","pith_inferences":["The fixed-point residual of the single-time protocol could be turned into a model-misspecification test: after fitting, one can check whether the residual shrinks with increasing shot count; if it does not, an unmodeled generator term is likely present.","The support-ordered triangularization relies only on the notion of a common operator extension, so a similar response-inversion construction may transfer to other algebraically closed operator bases, such as fermionic or qudit Pauli-like bases, whenever such an ordering exists.","The near-linear cost suggests a practical calibration primitive: on a noisy device with a known local noise model, one could periodically re-estimate all generator coefficients using only constant-depth state preparation and local measurements."],"forward_implications":["Both coherent coupling strengths and Markovian noise rates can be estimated simultaneously from the same short-time Pauli response data, instead of fitting one effective Hamiltonian.","The protocols work at evolution times t = O(1), avoiding the need for long-time dynamics or full process tomography.","The total experimental and classical cost scales as O~(M/epsilon^2) for M candidate coefficients, making the approach viable for many-body systems whose generator has a local, known dictionary.","Computing G and H is a one-time preprocessing step for a fixed dictionary, and the inverse can be reused across different systems sharing that dictionary.","An optional projection onto the physical set of GKSL parameters yields a valid Lindbladian estimate at the cost of a factor 2 in accuracy."],"fun_headline_variants":["Short-time Pauli responses reveal open-system generators","Inverting local responses disentangles quantum dissipation","Constant-time responses learn Lindbladians efficiently","One-shot response contraction maps dissipative terms","Chebyshev-Lobatto trick cuts Lindbladian learning cost"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The true dynamics is exactly e^{t L_theta} for a time-independent Markovian generator drawn from a known, complete, nonredundant Pauli–GKSL dictionary with coefficients in [-1,1] and bounded overlap; if the real generator contains a term outside this dictionary, such as an unmodeled long-range coupling, time dependence, or non-Markovian memory, the response matrix is misspecified and the estimators fail silently.","fun_headline_variants_meta":{"raw":{"variants":["Short-time Pauli responses reveal open-system generators","Inverting local responses disentangles quantum dissipation","Constant-time responses learn Lindbladians efficiently","One-shot response contraction maps dissipative terms","Chebyshev-Lobatto trick cuts Lindbladian learning cost"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000563,"raw_usage":{"total_tokens":2522,"prompt_tokens":769,"completion_tokens":1753,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":513,"completion_tokens_details":{"reasoning_tokens":1681}},"tokens_in":513,"tokens_out":1753,"duration_ms":12003,"temperature":1.0,"reasoning_tokens":1681,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T01:28:22.175497+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"On a system whose generator includes a known dissipative term supported on more than S_D sites, or a Hamiltonian term not in the dictionary, run the single-time protocol at t = t*. If the claim is false, the projected iteration will converge to a parameter whose response residual stays above the statistical error even as the number of shots grows, and the normalized response g_alpha(t)/t will show a systematic drift larger than O(t) between two different short times.","supporting_citations":[],"review_version":1}