{"id":"a62c15d7-a7e7-4bfd-9e81-df5d315219c5","arxiv_id":"2501.05350","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"oQMLA extends the Quantum Model Learning Agent framework to open quantum systems, learning Hamiltonian and Lindblad jump operators simultaneously via Bayesian inference and a genetic algorithm.","lead":"This paper introduces oQMLA, an algorithm that learns both the coherent interactions and the incoherent noise of an open quantum system from measurement data. It matters because identifying noise sources on quantum hardware is a key step toward error mitigation and better calibration.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Section III.D shows jump-operator rates are non-identifiable when the true jump operator is a superposition in S; hardware evidence cannot support the 'independently captures' claim.","rationale":"The reader's weakest assumption highlights Markovianity and representability in the primitive library S. My concern is a sharper, internal consequence: even when the component primitives of a true jump operator are in S, the diagonal Lindblad model class does not allow the exact representation of a superposition of jump operators, and the resulting cross-term ambiguity makes the learned rates non-identifiable. Section III.D demonstrates this empirically: the learned rates on D[YX] and D[ZI] differ from the true decomposition, and the paper explains this as compensation for missing cross-terms. This is not merely an approximation error; it is a structural ambiguity in the mapping from data to operator decomposition. The RMSE fitness (Eqs. 7, 8) rewards predictive accuracy, not structural correctness, so two models with identical predictive power can assign very different rates to the same primitives. The hardware experiment, where the true noise model is unknown and certainly not certified to lie in S, inherits this problem: the output cannot be interpreted as an independent estimate of coherent and incoherent dynamics. This supports the CONDITIONAL verdict, but for a more specific reason than code/data availability: the authors should either provide identifiability conditions (e.g., restrictions on S or a uniqueness guarantee for the (H, rate) decomposition) or weaken the abstract claim to predictive modeling rather than independent physical capture. The proposed test directly checks whether the non-identifiability is realized in the paper's own simulation setting.","tokens_in":15801,"tokens_out":6963,"duration_ms":71116,"concrete_test":"For the Section III.D setup, generate data from H[IZ] + 0.6 D[0.3YX + 0.7ZI] and run oQMLA 20 times with the same S. Record the best model's rates on D[YX], D[ZI], and its fitness. Then generate a second dataset from the best learned model and run oQMLA again. If the two runs converge to different rate vectors with statistically indistinguishable fitness (within Monte Carlo noise), the operator split is non-identifiable. Additionally, compute the fitness of the true model on the same test set; if it falls within the run-to-run fitness spread, the algorithm cannot certify the learned structure over the true one.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim (abstract, Sec. I) asserts oQMLA independently captures coherent and incoherent dynamics. The model class, Eq. (2), represents each dissipative channel by D[L] for L drawn from a fixed set S (Sec. II A). This class is not closed under linear combinations of jump operators: D[aX+bZ] contains cross terms that a sum of D[X] and D[Z] with adjusted rates cannot reproduce. Section III D is precisely this case: the true jump operator O=0.3YX+0.7ZI is not in S, and oQMLA returns D[YX] and D[ZI] with rates differing from the ground-truth components (Fig. 6b). The text attributes this to the Bayesian routine 'compensating for the missing cross-terms.' But this means the reported rates are not estimates of any physical quantity; they are gauge degrees of freedom chosen to minimize RMSE. Since the RMSE fitness (Eqs. 7, 8) only measures predictive equivalence, structurally different (H, rate) vectors can score identically. The hardware experiment (Sec. IV B) is in the same regime—the true noise is unknown and likely not confined to S—so the 'qualitative' model in Fig. 9b is not evidence that the identified Hamiltonian and jump operators correspond to the device's actual coherent and incoherent dynamics. The paper does not provide identifiability conditions or an error bound for the learned operators, only a bound on prediction RMSE. Thus the load-bearing step from 'model predicts the data' to 'the operator decomposition is independently captured' is unsupported.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper extends the Quantum Model Learning Agent (QMLA) framework to open quantum systems by modeling dynamics with the diagonal Lindblad master equation, Eq. (2). Candidate models are built as weighted sums of Hamiltonian and dissipator primitives drawn from a fixed operator set S (Section II.A), with rates learned by sequential Monte Carlo Bayesian inference, models ranked by an RMSE-based fitness function, and new models proposed by a genetic algorithm. The method is validated on simulated two-qubit systems, including restricted local operations, readout errors, and a case where the true jump operator is not in S, and it is then interfaced with IBM's ibm_lagos processor to study CNOT noise. The central claim is that oQMLA simultaneously learns the Hamiltonian and jump operators and thereby 'independently captures both the coherent and incoherent dynamics of a system.'","tokens_in":16071,"tokens_out":4747,"duration_ms":44861,"significance":"If fully substantiated, oQMLA would be a useful tool for interpretable, operator-level characterization of Markovian open quantum systems, potentially requiring fewer resources than full process tomography while returning physically meaningful rates and channels. The simulated validations against ground truth not used in fitting are a genuine strength, as is the demonstrated robustness to readout errors and local-only operations, and the hardware interfacing is a useful practical contribution. However, the paper presents a heuristic fitting procedure inside a restricted model class, and it does not establish uniqueness or error bounds for the learned operator decomposition outside the exactly representable cases. The hardness result of the stress-test concern is real: in the approximate-only and hardware regimes, good predictive fitness does not by itself imply that the returned Hamiltonian and jump operators describe the actual coherent and incoherent dynamics. The contribution is therefore promising but currently overstated.","major_comments":[{"comment":"The model class is restricted to sums of dissipators D[L_k] for L_k in a fixed primitive set S, and this class is not closed under linear combinations of jump operators: for example, D[aX+bZ] contains cross-terms that cannot be represented by any sum of D[X] and D[Z] with adjusted rates. Since the RMSE fitness in Eq. (7) is invariant under re-parameterizations that yield the same predictive distribution, the mapping from data to a unique operator decomposition is underdetermined in general. The paper does not provide identifiability conditions or an error bound relating the RMSE-optimal model to the true operators. The claim that oQMLA 'independently captures' both coherent and incoherent dynamics therefore needs to be either restricted to cases where the true jump operators lie in S or qualified with a quantitative identifiability analysis.","section":"Section II.A, Eq. (2)"},{"comment":"The approximate-only test case is exactly the non-closed-class problem: the true jump operator O=0.3YX+0.7ZI is not in S, and Fig. 6b shows that oQMLA returns D[YX] and D[ZI] with rates that differ from the ground-truth components. The text attributes this to the Bayesian routine 'compensating for the missing cross-terms,' which means the resulting rates are not estimates of any physical quantity but gauge degrees of freedom chosen to minimize prediction error. Since the paper gives no error bound linking predictive RMSE to operator-space error, this simulation does not support the central claim that oQMLA independently captures the coherent and incoherent dynamics; it only supports predictive equivalence within the model class. This limitation should be stated prominently rather than as a parenthetical remark.","section":"Section III.D, Fig. 6b"},{"comment":"The hardware demonstration is only qualitative and lacks ground truth. The best fitness is about 30, corresponding to a mean prediction error of roughly 3% (footnote [52]), and the authors attribute the degraded performance to measurement noise and poor parameter estimation rather than to model misidentification. Given the acknowledged model-class restriction of Section II.A and the likely presence of non-Markovian and non-Pauli noise on real hardware, the operator list in Fig. 9b cannot be claimed to describe the device's actual coherent and incoherent dynamics. The paper should either provide a quantitative approximation-error analysis against an independent characterization method (e.g., gate-set tomography or randomized benchmarking of the same gate) or explicitly reframe the hardware section as a demonstration of the interface and workflow rather than as a validation of the operator-level characterization.","section":"Section IV.B, Fig. 9"}],"minor_comments":[{"comment":"The text states that the highest fitness value is 'around 30,' while footnote [52] reports lowering the convergence threshold to 33; these numbers appear inconsistent and should be clarified.","section":"Section IV.B, footnote [52]"},{"comment":"The notation ⌊·⌉_1 is nonstandard and is not defined in the text; a short definition of this rounding operation would improve readability.","section":"Equation (10)"},{"comment":"The learned rates are reported without error bars or credible intervals, even though each experiment is repeated over five independent executions; reporting the spread of the learned parameters would materially strengthen the claim of robustness.","section":"Figures 3-6"},{"comment":"The data availability statement only offers data 'upon reasonable request' and no code is released; given the large number of algorithmic hyperparameters (target number of primitives T, particle counts, mutation probabilities), a public release of the oQMLA implementation would substantially improve reproducibility.","section":"Data Availability"},{"comment":"The paper does not benchmark oQMLA against existing process-characterization methods, such as process tomography, Lindblad tomography, or other model-learning agents (e.g., Refs. [12, 21, 28]); a quantitative comparison on the same simulated test cases would help calibrate the claimed advantages in interpretability and measurement efficiency.","section":"Overall validation"}],"recommendation":"major_revision","confidential_remarks":"This is a solid, clearly written contribution with convincing simulated validation when the true jump operators are in the primitive set S. The main issue is that the abstract's 'independently captures both the coherent and incoherent dynamics' claim goes beyond what is demonstrated: the approximate-only and hardware sections show predictive fitting within a restricted model class, not unique operator identification. If the authors add an identifiability analysis or clearly delimit the claim to the exactly representable regime, and if they provide a code release and ideally a comparison with existing methods, the paper would be suitable for publication. The current overstatement is fixable within the manuscript's scope."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Bottom line: this is a solid, useful extension of QMLA to open systems, and the simulator sections mostly back it up. The abstract's \"independently captures both the coherent and incoherent dynamics\" is too strong for cases the paper itself studies, and the hardware evidence is only qualitative. The paper should go to referees, but with revisions.\n\nWhat's new: the authors take the existing QMLA Hamiltonian-learning framework, replace the closed-system evolution with a diagonal Lindblad master equation, add jump operators as primitives, add a target-size regularization to the mutation step, and switch the fitness metric to RMSE. That combination is new relative to the cited closed-system QMLA and to Ref. [21]. The simulations in Sec. III.A-C are the strongest part: with known ground truth, the algorithm finds the correct primitives and rates for two-qubit Hamiltonians plus dissipators, including under local operations and 2% readout errors. This is concrete evidence for the method's predictive capability.\n\nThe soft spots are in the interpretive claims. The stress-test concern is on target. In Sec. III.D the true jump operator is a superposition, 0.3 YX + 0.7 ZI, not in the primitive set S. The learned rates for D[YX] and D[ZI] do not match the ground-truth components, and the text attributes this to compensation for missing cross-terms. That is an admission that the rates are gauge degrees of freedom chosen to minimize RMSE, not estimates of physical rates. The RMSE fitness measures predictive equivalence, so structurally different models can score the same. The abstract's \"independently captures\" claim therefore only holds when the true model is representable in S. The paper acknowledges this limitation in III.D and the discussion, but it doesn't soften the abstract, and it offers no identifiability conditions or error bounds on the operator decomposition. The same caveat applies to the hardware experiment: the true CNOT noise is unknown and likely not exactly in S, so the learned operator structure in Fig. 9b is best read as one possible predictive model, not as the device's actual coherent and incoherent dynamics.\n\nOther issues are practical: no code or data are shipped, hyperparameters are not fully specified, and there is no quantitative comparison against Ref. [21] or other open-system learning methods. These are fixable. The hardware section is honest about the low fitness and variability, and the qualitative agreement in Fig. 9c is real, but it doesn't support the strong operator-level claim.\n\nWho should read this: anyone doing Hamiltonian learning, noise characterization, or calibration of small quantum devices. It deserves a serious referee. I would accept it for review, with the expectation that the claims get tightened, the code and data are released, and a comparison is added.","headline":"Useful and honest extension of QMLA to open systems; the simulations support the predictive claims, but the abstract's 'independently captures' operator claim overreaches when the true jump operator lies outside the primitive set.","tokens_in":16643,"tokens_out":2730,"would_cite":true,"duration_ms":27156,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["03.65.Yz"],"model":"deepseek-v4-flash","headline":"The paper's oQMLA framework learns both the Hamiltonian and the jump operators of a Markovian open quantum system from experimental data, returning an interpretable operator-level model rather than a dense process matrix.","keywords":["open quantum systems","quantum model learning agent","Lindblad master equation","quantum process characterization","genetic algorithm","Bayesian inference","noise characterization","superconducting qubits"],"falsifier":"Run oQMLA on a system with known non-Markovian noise, or with a true jump operator deliberately omitted from the primitive library, hold out some experiments, and check whether the output model's predicted probabilities match the held-out data within the RMSE the algorithm reported; a persistent or schedule-dependent mismatch would show that the recovered Hamiltonian and jump operators do not independently capture the true dynamics.","tokens_in":15560,"feed_emoji":"⚛️","tokens_out":12720,"duration_ms":117014,"temperature":0.7,"pith_summary":"The paper introduces oQMLA, an extension of the Quantum Model Learning Agent that targets open quantum systems. Its claim is that a single adaptive procedure can learn both the Hamiltonian and the jump operators of a Markovian system from experimental data, so that the coherent and incoherent parts of the dynamics are recovered independently. Candidate models are defined through the diagonal Lindblad master equation, searched with a genetic algorithm over a library of coherent and dissipative operator primitives, and parameterized by Bayesian inference. The payoff is an interpretable, operator-level description of a device's dynamics rather than a dense process matrix, which is exactly the information needed to design error mitigation and calibration. Simulations on two-qubit systems recover the true primitives and rates even with local operations and readout errors, and a test on a superconducting processor yields a qualitative characterization of the noise in repeated CNOT gates.","feed_headline":"Quantum agent extracts Hamiltonian and noise operators from data","feed_subtitle":"Simulations and a superconducting-qubit test show the same routine recovers coherent and incoherent dynamics.","key_machinery":"The central object is the open Quantum Model Learning Agent (oQMLA), whose model class is the diagonal Lindblad master equation $\\partial_t \\rho = \\sum_i \\alpha_i \\mathcal{H}[h_i](\\rho) + \\sum_k \\Gamma_k \\mathcal{D}[L_k](\\rho)$, with Hamiltonian superoperators $\\mathcal{H}[h] = -i[h,\\rho]$ and dissipators $\\mathcal{D}[L] = L\\rho L^\\dagger - \\frac{1}{2}\\{L^\\dagger L,\\rho\\}$ built from a fixed primitive library $S$. A genetic algorithm encodes each candidate model as a bit-string chromosome and applies elitism, roulette-wheel selection, uniform crossover, and regularized mutations to explore the model space. A sequential Monte Carlo Bayesian inference routine updates a particle distribution over the rates, and the particle-guess heuristic sets the evolution time to the inverse of the current parameter uncertainty. The RMSE-based fitness function, defined as the inverse of the root mean squared error between predicted and observed outcome probabilities, ranks models independently of their shape and tolerates small spurious terms.","core_discovery":"The paper's central claim is that an agent can simultaneously identify the coherent and incoherent parts of a quantum evolution governed by the diagonal Lindblad master equation, treating Hamiltonian terms and jump operators as weighted primitives in one shared model space. The genetic search over that space, combined with sequential Monte Carlo Bayesian inference for the rates and an RMSE-based fitness for ranking, converges to the correct primitives and accurate rates in simulated two-qubit systems. The method keeps working when operations are restricted to local measurements and when readout errors of a few percent corrupt the data, and it returns an approximate decomposition when the true jump operator is absent from the primitive library. On real hardware, the same routine produces a qualitative prediction of the dynamics of repeated CNOT gates on a superconducting processor, with the main practical limits being measurement noise and the difficulty of estimating many correlated rates.","pith_inferences":["A natural extension the paper leaves implicit is to let the genetic search grow its own operators: when two jump operators with comparable rates appear, add their linear combination to the primitive library, allowing oQMLA to discover arbitrary jump operators rather than only their components.","A testable way to probe the Markov assumption is to re-run the learned generator at different circuit depths or time scales; if the inferred rates drift, memory effects are present that the diagonal Lindblad model class cannot represent.","The RMSE fitness gives a hardware-independent scale for comparing model quality in probability space, which could be reused to rank alternative noise models across different devices without redefining the score."],"forward_implications":["When the primitive library contains the true operators, oQMLA identifies the correct Hamiltonian and jump-operator primitives and estimates their rates accurately in about twelve generations, after searching only a few hundred of the $2^{50}$ possible models.","The method remains functional when restricted to separable initial states and local measurements, at the cost of slower and more variable convergence than with full-state access.","Simulated readout errors averaging around 2% leave the recovered model essentially unchanged and mainly set a lower bound on achievable prediction error.","When the true jump operator is a combination of library operators, oQMLA returns a decomposition into those components with adjusted rates, and its fitness function tolerates small spurious terms.","On a superconducting processor, oQMLA predicts the measured evolution of repeated CNOT gates qualitatively, with the hardware model achieving a mean prediction error around three percent."],"supporting_citations":[{"why":"Defines the original QMLA framework that oQMLA extends from closed to open systems.","marker":"[19]"},{"why":"Supplies the QMLA genetic-algorithm exploration, chromosome encoding, and benchmarking that oQMLA adapts.","marker":"[20]"},{"why":"Provides the Lindblad master equation and the Born-Markov conditions underlying the system's model class.","marker":"[26]"},{"why":"Introduces the diagonal Lindblad form and the definitions of the dissipator superoperators used in Eq. (2).","marker":"[27]"},{"why":"Gives the Bayesian inference and particle-guess heuristic used to choose experiment times during training.","marker":"[35]"},{"why":"Supplies the sequential Monte Carlo particle-filter update used to estimate model parameters.","marker":"[36]"},{"why":"Provides the genetic-algorithm machinery (selection, crossover, mutation) used to search the model space.","marker":"[39]"},{"why":"Supplies the noisy superconducting processor and reported error rates used for the hardware demonstration and its simulation.","marker":"[45]"},{"why":"Provides the quantum-circuit interface used to prepare and execute the CNOT experiments on the processor and its noisy simulator.","marker":"[47]"}],"fun_headline_variants":["Agent learns Hamiltonian and noise operators in one model","Open quantum systems: agent captures coherent and incoherent dynamics","Quantum agent: local ops and real hardware yield full characterization","Simultaneous fit of Hamiltonian and jump operators from data","Agent sees both sides: coherent and incoherent dynamics from experiments"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the device being characterized forgets its past quickly and that its dominant errors can be expressed, exactly or almost exactly, by the fixed library of Hamiltonian and jump operators the algorithm is given; outside that regime the output is only a best approximation within a restricted model class.","fun_headline_variants_meta":{"raw":{"variants":["Agent learns Hamiltonian and noise operators in one model","Open quantum systems: agent captures coherent and incoherent dynamics","Quantum agent: local ops and real hardware yield full characterization","Simultaneous fit of Hamiltonian and jump operators from data","Agent sees both sides: coherent and incoherent dynamics from experiments"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000271,"raw_usage":{"total_tokens":1630,"prompt_tokens":948,"completion_tokens":682,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":564,"completion_tokens_details":{"reasoning_tokens":602}},"tokens_in":564,"tokens_out":682,"duration_ms":7613,"temperature":1.0,"reasoning_tokens":602,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T21:12:43.846780+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run oQMLA on a system with known non-Markovian noise, or with a true jump operator deliberately omitted from the primitive library, hold out some experiments, and check whether the output model's predicted probabilities match the held-out data within the RMSE the algorithm reported; a persistent or schedule-dependent mismatch would show that the recovered Hamiltonian and jump operators do not independently capture the true dynamics.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the noisy superconducting processor and reported error rates used for the hardware demonstration and its simulation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines the original QMLA framework that oQMLA extends from closed to open systems."},{"cited_title":"Flynn, A","cited_arxiv_id":null,"evidence_quote":"Supplies the QMLA genetic-algorithm exploration, chromosome encoding, and benchmarking that oQMLA adapts."},{"cited_title":"Wiebe, C","cited_arxiv_id":null,"evidence_quote":"Gives the Bayesian inference and particle-guess heuristic used to choose experiment times during training."},{"cited_title":"Doucet, N","cited_arxiv_id":null,"evidence_quote":"Supplies the sequential Monte Carlo particle-filter update used to estimate model parameters."}],"review_version":1}