{"id":"4ace68b5-4de0-411b-9015-6c7a4c98d552","arxiv_id":"2411.10254","paper_version":3,"verdict":"CONDITIONAL","confidence":"LOW","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Quantum feature transformation changes the uncertainty estimates and outlier counts of classical regression models on synthetic supply chain data as qubit count increases from 4 to 16.","lead":"This paper applies standard uncertainty quantification methods to machine learning models fed by quantum circuit outputs, comparing them with purely classical versions on synthetic supply chain data. It finds that increasing the number of qubits from 4 to 16 changes uncertainty estimates and outlier detection counts, although the data and code are not released and some claims contradict the reported results.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Qubit scaling is confounded with input dimensionality: hybrid models receive 3x features (X/Y/Z per qubit), and qubit count increases together with RFE feature count, so observed UQ changes may reflect dimensionality, not quantum effects.","rationale":"I chose this concern because it attacks the identification strategy behind the central claim. The reader's weakest assumption concerns the expressivity/convergence of the chosen parameterized circuit; that is a secondary issue. Even if the ansatz were optimal and perfectly trained, the experiment still cannot distinguish quantum effects from a trivial dimensionality effect, because the hybrid branch always receives more features than the classical branch, and the qubit sweep is confounded with the feature-count sweep. This is not a matter of 'outside current consensus' or an internal inconsistency in equations; it is a missing control condition in an otherwise straightforward empirical comparison. The paper contains internal contradictions (target variable defined as cost efficiency in Section III.1 but disruption_impact in the supplementary; RMSE/MAE values larger than the 0-1 target range), but those are reporting errors that could be corrected. The confounding is structural: Table II, Figure 7, and Figure 9 all compare conditions that differ in both quantum processing and input dimensionality. Releasing code/data would help, but even with code, the existing comparison cannot support the causal statement. Therefore the appropriate verdict remains conditional: the authors should add a classical dimensionality-matched control and a classical nonlinear feature map control, or substantially weaken the claim to 'adding features via quantum circuits changes UQ' rather than 'qubit scaling changes UQ.'","tokens_in":11363,"tokens_out":4605,"duration_ms":44092,"concrete_test":"Obtain or regenerate the synthetic dataset using the supplementary generation steps. Run the exact same pipeline (BRR, QR, RF, NN; same hyperparameters, 5-fold CV, uncertainty estimators, OD methods, Wilcoxon/Kruskal-Wallis tests) with classical models trained directly on the RFE-selected 4, 6, 8, ..., 16 original features, bypassing the quantum circuit. If the classical-only sweeps produce Kruskal-Wallis p<0.05 and OD-count trends similar to Figures 7-9, then the reported qubit effects are explained by input dimensionality rather than quantum transformation. To further separate 'quantum' from 'nonlinear feature map,' repeat with classical random Fourier features or polynomial features matched to 3n dimensions; if these also reproduce the UQ shifts, the quantum-specific contribution is not established.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central empirical claim is that quantum feature transformation and qubit scaling change predictive uncertainty (Section IV, Figures 4, 7, 9). The experiment does not isolate this effect. In Section III.1, RFE selects 4, 6, ..., 16 input features, and each configuration feeds that many features into a quantum circuit of the same qubit count. Section III.2 then measures Pauli X, Y, and Z per qubit, so an n-feature input produces 3n quantum features. Classical models are trained on the original n features (Section IV.1: 'classical models directly used these features'), while hybrid models receive 3n features. The 4-qubit comparison is therefore a 4-feature classical model versus a 12-feature hybrid model. The 4-to-16 qubit sweep simultaneously sweeps input dimensionality from 12 to 48 features (and from 4 to 16 raw features before encoding). Uncertainty estimators such as BRR's aleatoric/epistemic variance depend directly on feature dimension and conditioning, so changes in UQ across configurations are expected even with no quantum circuit. The Kruskal-Wallis tests across qubit configurations (Section IV.2) test the joint null hypothesis of no effect of feature count and circuit size; they cannot attribute the differences to qubits. A classical model given progressively more RFE-selected features would very likely reproduce the qualitative trends. Thus the conclusion that 'higher qubit configurations enhance model sensitivity to data variability' is a causal claim the current design cannot support, independent of whether the parameterized ansatz is expressive or the training converges.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a quantum-classical hybrid framework for uncertainty quantification (UQ) in supply chain digital twin predictions. It applies Bayesian ridge regression (BRR), quantile regression (QR), random forest (RF), and a neural network (NN) to both classical features and quantum-transformed features (generated by parameterized circuits with 4 to 16 qubits), and compares UQ metrics such as uncertainty-error correlation, prediction interval coverage (PICP), outlier detection (OD) counts, and a proposed risk-adjusted cost efficiency (RACE) score. The central claim is that quantum feature transformations and increasing qubit counts alter predictive uncertainty and outlier detection outcomes without degrading predictive accuracy.","tokens_in":11689,"tokens_out":5015,"duration_ms":45585,"significance":"If the claims were established, the work would provide a practical demonstration that quantum feature transformations and qubit scaling can change UQ outputs in hybrid ML models, which could be relevant for supply chain risk management. The paper uses established UQ techniques, reports model-specific results including cases where quantum and classical models behave similarly, and includes a reproducibility-oriented supplement with code and synthetic data generation steps. However, the current experimental design does not isolate the qubit-count effect from input dimensionality, and an internal contradiction about the target variable undermines the quantitative results. As presented, the central claim is not convincingly supported.","major_comments":[{"comment":"The target variable is defined inconsistently. Section III.1 states 'The target variable for this study is cost efficiency, which is a score between 0 and 1,' while the supplementary data-generation instructions (steps 5 and 6) create a feature called cost_efficiency and then define 'Target variable: disruption_impact,' using all columns except cost_efficiency and disruption_impact as features. This contradiction is load-bearing because Section IV.1 reports R2 ≈ 0.79, RMSE ≈ 0.78, and MAE ≈ 0.75 for models trained on the target. For a target bounded in [0,1], RMSE cannot be 0.78 with R2 = 0.79: R2 = 0.79 implies a target variance of about 2.90, which is impossible for a bounded 0–1 variable. The entire quantitative evaluation and the RACE analysis (Section IV.3) depend on which variable was actually predicted, so the manuscript must clarify the target, correct the metrics, or rerun the analysis accordingly.","section":"III.1 and Supplementary 'Synthetic data generation'"},{"comment":"Qubit count is confounded with input dimensionality. Section III.1 states that RFE outputs 4, 6, ..., 16 features for different configurations, and Section III.2 uses the same number of qubits, measuring Pauli-X, -Y, and -Z expectation values per qubit. Therefore the hybrid models receive 3n features (e.g., 12 features for 4 qubits, 48 features for 16 qubits), while the classical models receive only the n original features (as confirmed in Section IV.1: 'Classical models directly used these features'). The Kruskal-Wallis tests in Section IV.2 across qubit configurations consequently test the joint effect of circuit width and feature dimensionality; they cannot attribute observed UQ differences to qubit count. The conclusion in Section V that 'higher qubit configurations enhance model sensitivity to data variability' is therefore unsupported. The experiment needs a control that keeps the number of input features fixed while varying qubits, or a classical baseline trained on the same 3n-dimensional feature set, to separate quantum effects from dimensionality effects.","section":"III.1, III.2, IV.2"},{"comment":"The interpretation of the qubit-scaling results is internally contradictory. Section IV.2 reports that 'Figure 7 shows a decline in OD samples with more qubits' and concludes that 'higher qubit counts affect uncertainty modelling through feature representation and reduce OD detection,' yet Section V lists as a contribution 'the introduction of qubit scaling as a method to improve outlier detection, showing that higher qubit configurations enhance model sensitivity to data variability.' If the number of detected outliers decreases with qubit count, that is more naturally read as reduced sensitivity, not enhanced sensitivity. The authors need to reconcile these statements and specify the operational meaning of 'sensitivity' in the outlier-detection context, ideally with a precise definition and supporting statistics.","section":"IV.2 and V"},{"comment":"The statistical evidence for 'distinct' or 'enhanced' uncertainty behavior relies on p-values without effect sizes or qualitative comparisons of magnitude. The Wilcoxon tests for BRR (p = 6.08E-51) and QR (p = 9.33E-06) in Section IV.1, and the Kruskal-Wallis tests in Section IV.2, can reach extremely small p-values even for negligible distributional shifts when the sample size is 300. The paper should report effect sizes (e.g., standardized mean differences, rank-biserial correlation) and show that the observed UQ differences are practically meaningful, especially because Table II shows modest differences in PICP and OD counts for several models. Without this, the claim that quantum features 'offer unique predictions' in terms of uncertainty is overstated.","section":"IV.1 and IV.2"}],"minor_comments":[{"comment":"The phrase 'unique predictions' is used in the abstract and conclusions, but the paper reports comparable predictive accuracy (R2 ≈ 0.79 across models) and differences in uncertainty, not unique predictions. Consider replacing with 'unique uncertainty estimates' or 'distinct uncertainty behavior'.","section":"Abstract and V"},{"comment":"There is a missing closing parenthesis in 'quantum models exhibited narrower uncertainty bounds compared to classical models (see Figure 4.' Should be 'see Figure 4).'","section":"IV.1, third paragraph"},{"comment":"The sentence 'HQBRR drops from 27 samples to 22, 18 for qubits 4th, 6th, 8th, 10th and 12th' lists five qubit counts but only three values; it should be rewritten to list the OD count at each qubit configuration explicitly.","section":"IV.2"},{"comment":"The RACE formula in Eq. (7) is described as 'derived using [41]', but reference [41] is a CAPM/WACC financial modeling document and does not derive this linear penalty. Either provide an appropriate derivation or rephrase to say the formula is introduced as a risk-adjustment heuristic.","section":"IV.3, Eq. (7)"},{"comment":"The supplement says the data 'can be generated' but Section IV.1 says the dataset is 'provided as supplementary files.' Clarify whether the actual data files or only the generation code are provided.","section":"Supplementary 'Synthetic data generation'"}],"recommendation":"major_revision","confidential_remarks":"The target-variable inconsistency and the qubit-count/feature-dimensionality confound are serious enough that the current experiments do not support the paper's central claims. However, the issues are fixable within the manuscript's scope: the authors can rerun the analysis with a clearly defined target, control for feature dimensionality, and add effect-size reporting. The topic is of moderate interest to the quantum-ML and UQ communities, but the current version would not withstand scrutiny."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: the paper is a parameter sweep over an already published pipeline, and the sweep's main result is not trustworthy because qubit count is tangled up with input dimensionality. On top of that, the paper's own conclusion contradicts its Figure 7.\n\nWhat is genuinely useful: the authors lay out a clear pipeline for applying classical UQ methods (BRR, QR, RF, MC dropout) to quantum-transformed features, and they use nonparametric tests rather than just eyeballing plots. The supplementary circuit diagrams and the synthetic data generation steps are a nice touch, even if code and data are not released.\n\nThe soft spots are serious. First and most load-bearing: hybrid models get three features per qubit (Pauli X, Y, Z expectation values) while classical models get the raw features only. So the 4-qubit comparison is 4 features versus 12. And as qubits rise from 4 to 16, RFE also selects more raw features, so the experiment sweeps qubit count and input dimensionality together. The Kruskal-Wallis test can only say something changed; it cannot attribute the change to qubits. A classical model given 12, 18, ..., 48 features would likely show the same UQ shifts. The stress-test note is correct; the paper does not address this confound.\n\nSecond, there is an internal contradiction in the target variable. Section III.1 calls it cost_efficiency, a score between 0 and 1; the supplement's data generation steps define disruption_impact as the target. The reported RMSE (around 0.78) and MAE (around 0.75) are implausibly large for a 0-1 target, suggesting something is off.\n\nThird, the conclusion that 'higher qubit configurations enhance model sensitivity to data variability' conflicts with Figure 7, which shows outlier count declining as qubits increase. That is a direct contradiction with their own data.\n\nThese are not minor copy edits. The central empirical conclusion is unsupported by the design, and the internal inconsistencies undermine trust in the numbers. The paper could be rehabilitated with a redesigned experiment that fixes the feature-count confound and releases code and data, but as it stands the results should not be used as evidence for a quantum effect on UQ.\n\nWho is this for? Someone working on quantum feature encoding and UQ might find the pipeline a useful starting point, but not the conclusions. I would not cite it. A serious referee would likely send it back for major revision, and I think the paper deserves that scrutiny if only to document the pitfalls. My recommendation: don't desk reject it, but a good referee will need to enforce the confound fix and the consistency corrections.","headline":"The qubit effect on UQ is confounded by feature dimensionality, and the paper's own outlier data contradict its headline claim; the pipeline is a known assembly, and the internal inconsistencies (target variable naming, RMSE scale) undermine the numbers.","tokens_in":12255,"tokens_out":4953,"would_cite":false,"duration_ms":43321,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper claims that quantum feature transformation shifts uncertainty estimates and outlier flags in supply-chain hybrid models, with qubit count as the tuning lever and accuracy unchanged.","keywords":["uncertainty quantification","quantum-classical hybrid models","supply chain digital twins","quantum feature engineering","qubit scaling","outlier detection","prediction intervals","risk-adjusted cost efficiency"],"falsifier":"Re-run the same pipeline with classical nonlinear feature maps of identical output dimension (for example random Fourier features or a fixed random rotation of the inputs) and the same mutual-information selection; if the 4-to-16 dimension scaling reproduces the same uncertainty shifts, outlier counts, and RACE curves, the quantum-specific part of the claim is not supported. A permutation test with shuffled targets should also be done: if qubit-count effects persist under label shuffling, the differences are not signal-driven.","tokens_in":11116,"feed_emoji":"⚛️","tokens_out":6799,"duration_ms":58355,"temperature":0.7,"pith_summary":"This paper asks whether adding a quantum feature-transformation step to ordinary regression models changes what the models report about their own uncertainty, in the setting of supply-chain digital twins. It argues that it does: with the same predictive accuracy, quantum-classical hybrids produce narrower uncertainty distributions, different outlier detections, and different risk-adjusted cost-efficiency scores than classical models alone. The paper also claims that scaling the circuit from 4 to 16 qubits measurably shifts the uncertainties, but not the errors, of Bayesian ridge regression and quantile regression. A sympathetic reader would care because trustworthy uncertainty estimates, not just point predictions, are what let a planner decide when to trust a digital twin and when to investigate an outlier.","feed_headline":"Qubit scaling changes model uncertainty while accuracy holds","feed_subtitle":"Quantum-transformed features shift uncertainty and outlier flags compared with classical-only inputs.","key_machinery":"The mechanism is a hand-designed parameterized quantum feature map: input features are rotated onto qubits with RX/RY/RZ gates, Hadamard gates create superposition, parameterized RY/RZ rotations and CY/CRZ/CNOT/CZ entangling gates build expressivity, and the circuit is read out by Pauli-X/Y/Z expectation values that become the new feature vector. Its parameters are optimized to maximize mutual information with the target while penalizing feature correlation. Feeding these quantum-computed features into Bayesian ridge regression, quantile regression, random forest, and a Monte-Carlo-dropout neural network creates the hybrid UQ models, so qubit count effectively controls the dimension and structure of the feature space whose uncertainty behaviour the paper measures.","core_discovery":"The central claim is that quantum feature transformation is a lever on uncertainty quantification, not just on accuracy: substituting quantum-transformed features for raw features keeps point predictions comparable (R² ≈ 0.79, RMSE ≈ 0.78, MAE ≈ 0.75) while systematically changing the uncertainty estimates. The paper shows the hybrid Bayesian ridge and quantile models have significantly different predictive uncertainty than their classical counterparts (Wilcoxon p = 6.08E-51 and 9.33E-06), that hybrid models flag more uncertainty-based outliers, and that increasing the qubit count from 4 to 16 produces significant differences in uncertainty across configurations (Kruskal-Wallis p < 0.05) with no significant change in errors. The authors present this as evidence that larger quantum feature spaces alter how uncertainty propagates through classical UQ machinery, and they translate the effect into financial terms through a risk-adjusted cost-efficiency penalty.","pith_inferences":["A natural extension the paper leaves implicit is a direct comparison against classical kernel feature maps of the same dimension, which would separate quantum expressivity from sheer input-space expansion.","The paper's own results show RF and NN barely react to qubit scaling, so a follow-up could test whether the sensitivity difference tracks the UQ mechanism (tree variance vs. MC dropout) rather than the quantum features per se.","If the qubit effect is real, it should reproduce on real supply-chain datasets and should change the calibration of prediction intervals (PICP) in a way that can be tested against classical baselines."],"forward_implications":["Qubit count can be used in practice as a tunable sensitivity knob for uncertainty reporting, since accuracy does not degrade while uncertainty changes.","Supply-chain digital twins built this way will produce different outlier flags and confidence intervals than classical twins, which changes which transactions get flagged for human review.","The risk-adjusted cost-efficiency formula gives managers a direct way to price the uncertainty difference, converting a statistical change into a financial consequence.","Because HQBRR and HQQR are the models most sensitive to qubit count, deployment should involve choosing the qubit configuration per model rather than assuming one setting works for all."],"supporting_citations":[{"why":"provides the variational-quantum-algorithm foundation that justifies parameterized circuits as expressive maps in hybrid models.","marker":"[12]"},{"why":"supports the premise that larger quantum feature spaces improve data representation and generalization, motivating qubit scaling.","marker":"[23]"},{"why":"supplies the classical regression models, feature-selection routine, and evaluation tools used throughout the pipeline.","marker":"[25]"},{"why":"gives the Bayesian linear-regression framework whose aleatoric-plus-epistemic variance decomposition defines BRR uncertainty.","marker":"[34]"},{"why":"provides the Monte Carlo dropout method used to quantify neural-network uncertainty via repeated forward passes.","marker":"[36]"},{"why":"is the Wilcoxon signed-rank test that confirms significant uncertainty differences between quantum and classical BRR and QR models.","marker":"[39]"},{"why":"is the Kruskal-Wallis test used to establish that qubit-count changes produce significant differences in uncertainty.","marker":"[40]"}],"fun_headline_variants":["Qubit scaling shifts uncertainty, not accuracy","Quantum features alter uncertainty in digital twins","Hybrid quantum ML changes uncertainty without error change","Uncertainty shifts with qubit count, accuracy steady"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing assumption is that this particular quantum circuit is a genuinely expressive feature map for the data; if the circuit's optimization just adds noise or extra dimensions, the observed qubit-dependent uncertainty differences could be artifacts of dimensionality rather than quantum-enhanced representation.","fun_headline_variants_meta":{"raw":{"variants":["Qubit scaling shifts uncertainty, not accuracy","Quantum features alter uncertainty in digital twins","Hybrid quantum ML changes uncertainty without error change","Uncertainty shifts with qubit count, accuracy steady"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000222,"raw_usage":{"total_tokens":1408,"prompt_tokens":857,"completion_tokens":551,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":473,"completion_tokens_details":{"reasoning_tokens":492}},"tokens_in":473,"tokens_out":551,"duration_ms":5763,"temperature":1.0,"reasoning_tokens":492,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T19:48:12.774182+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-run the same pipeline with classical nonlinear feature maps of identical output dimension (for example random Fourier features or a fixed random rotation of the inputs) and the same mutual-information selection; if the 4-to-16 dimension scaling reproduces the same uncertainty shifts, outlier counts, and RACE curves, the quantum-specific part of the claim is not supported. A permutation test with shuffled targets should also be done: if qubit-count effects persist under label shuffling, the differences are not signal-driven.","supporting_citations":[{"cited_title":"Methodology and application of the kruskal-wallis test,","cited_arxiv_id":null,"evidence_quote":"is the Kruskal-Wallis test used to establish that qubit-count changes produce significant differences in uncertainty."}],"review_version":1}