{"id":"386dc444-d2ee-4309-9ce0-c3497e9e4ae4","arxiv_id":"2607.19782","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A sample-to-centroid fidelity kernel enables linear-scaling multiclass quantum classification; in simulation it beats pure quantum baselines, and untrained 124-qubit hardware results match an RBF kernel.","lead":"This paper introduces McQuack, a trainable quantum kernel for multiclass classification that compares each data point to trainable class centers, with cost that grows linearly with the number of training samples. The authors test it on 124-qubit IBM hardware and over 150 datasets, finding it outperforms other 'pure' quantum models in simulation but still trails classical neural networks.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Benchmark claim 'strongest pure quantum model' rests on unverified protocol comparability with Bowles et al. baselines; rerun required.","rationale":"The reader's weakest assumption identifies the same load-bearing concern: the central claim that McQuack outperforms existing pure quantum models rests on comparing McQuack's results with baseline rankings taken from [4] under potentially different protocols. I agree that this is the most important weakness because the paper's headline contribution beyond the method itself is this empirical superiority claim. The method's linear scaling and internal consistency are not the issue; the comparison is. The concrete test of re-running all models in a single controlled protocol would settle whether the claim survives. Since the reader already assigned CONDITIONAL for precisely this reason, my analysis does not move the verdict. I therefore recommend UNCHANGED.","tokens_in":26974,"tokens_out":6738,"duration_ms":69034,"concrete_test":"Re-run the full QML Benchmark suite (all 133 datasets in the five reported tasks) using the Bowles et al. codebase, executing McQuack and the seven QNN baselines under one identical protocol: same train/validation/test splits, same five seeds, same evaluation metric and rank normalization, and comparable hyperparameter optimization budgets (ideally the same grid-search procedure). Then compute mean normalized ranks and paired dataset-by-dataset comparisons (e.g., Wilcoxon signed-rank on accuracy). If McQuack no longer ranks ahead of every pure-quantum baseline, or if the advantage is not significant, the 'strongest pure quantum model' claim should be downgraded.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central empirical claim—McQuack is the strongest 'pure' quantum model in the QML Benchmark (Section 4.2.1, Fig. 2a)—is supported only by a cross-paper ranking comparison. Baselines are taken 'as reported in [4]'; McQuack results come from a separate pipeline with its own hyperparameter grid (Table 7), five-seed averaging, and a downsampled MNIST protocol (Appendix B.2.2). If Bowles et al. used different data splits, seeds, preprocessing, or optimization budgets, the normalized rankings are not comparable and the ranking advantage could vanish. This is not merely hypothetical: the paper itself reports that some baselines were evaluated on only a subset of datasets (e.g., QuantumBoltzmannMachine on roughly a third of linearly separable; DressedQuantumCircuitClassifier not on all 133). Average normalized rank computed over heterogeneous evaluation sets can be systematically biased in McQuack's favor. Because code is not released (Section 7), the comparison cannot be audited. The method itself and the linear-scaling analysis are plausible; the unverified benchmark protocol is the load-bearing weakness.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces McQuack, a multiclass quantum kernel method that replaces the full n_train×n_train Gram matrix with an n_train×M fidelity matrix between data samples and trainable class-centroid parameters. The shared embedding parameters (w,b) and the centroid parameters (c_m) are optimized alternately via kernel-target alignment (KTA) losses (Eqs. 22–23), and the method is claimed to have O(n_train·M) training cost (Eq. 10). The authors evaluate an untrained version on 124-qubit IBM hardware, benchmark the trained model in simulation on the QML Benchmark Suite of Bowles et al. and on 19 real-world datasets, and present a trainability study for up to 13 qubits. The central claims are the linear-scaling formulation, the empirical claim that McQuack is the strongest \"pure\" quantum model in the QML Benchmark, and the absence of observed barren plateaus in the tested range.","tokens_in":27295,"tokens_out":7854,"duration_ms":79642,"significance":"If the empirical claims are supported, this is a useful contribution to quantum kernel methods: it directly addresses the quadratic scaling of full-Gram kernels, provides a native multiclass formulation, and includes a rare hardware demonstration on 100+ qubits. The O(n_train·M) derivation in Eq. (10) is explicit and appears sound. The hardware experiment is honestly reported as a feasibility demonstration, and the trainability study, though limited, is practically relevant. However, the headline benchmark comparison rests on a cross-paper ranking against baselines \"as reported in [4]\" without a matched protocol, and this is not yet auditable. I do not see a circularity problem: KTA training on labeled data and test evaluation are standard supervised learning.","major_comments":[{"comment":"The central empirical claim that McQuack is \"the strongest pure quantum model in this benchmark\" is based on normalized ranks in which the seven QNN baselines are taken \"as reported in [4]\" rather than re-run under the protocol used for McQuack. McQuack's hyperparameters were chosen by its own grid search (Table 7), accuracies are averaged over 5 seeds, and for downscaled MNIST the training set was reduced to 500 samples (B.2.2), while the baselines come from a separate pipeline with their own splits, seeds, and search budgets. Moreover, Fig. 2a and Fig. 10 show that some baselines (DressedQuantumCircuitClassifier, QuantumBoltzmannMachine) were evaluated on only a subset of the 133 datasets. Averaging normalized ranks over heterogeneous evaluation sets can bias the comparison. To support the claim, the authors should either rerun all baselines under the identical data pipeline and search","section":"§4.2.1, Fig. 2a, App. B.2.2"},{"comment":"The hardware experiment consists of three runs per model and is explicitly non-significant (Sec. 4.1). The abstract and Contribution 2 nevertheless state that McQuack \"demonstrate[s] performance comparable to an RBF kernel\" on 124 qubits. Table 1 shows 0.83±0.02 (Pittsburgh) and 0.79±0.02 (Aachen) vs. 0.80 for SimpleKernel; with n=3 these differences are within noise. This is a legitimate feasibility demonstration, but the word \"demonstrate\" overstates the evidence. Please align the abstract/conclusion wording with the statistical caveat stated in Sec. 4.1.","section":"§4.1, Table 1, §1.2 Contribution 2"},{"comment":"The trainability claim \"no evidence of barren plateaus up to 13 qubits\" is based on gradient statistics and loss curves for a few system sizes, with no quantitative scaling analysis of gradient variance vs. qubit number. The paper itself notes the result may not generalize (Sec. 6). I do not block on this, but if the claim is kept as a contribution, report the variance of gradients as a function of n (e.g., a table or fit) so readers can judge whether the data actually constrain barren-plateau behavior. At minimum, the abstract should say \"no evidence in the tested range,\" matching the Limitations section.","section":"§4.3, Figs. 4–5"}],"minor_comments":[{"comment":"Typo: \"formulticlass\" should be \"for multiclass\".","section":"Abstract"},{"comment":"The stated upper bound 1/sqrt(M) assumes nonnegative kernel entries; please state this assumption explicitly in the main text and clarify the affine shift in LKAO introduced in footnote 5.","section":"§2.3, Eq. (6)"},{"comment":"The O(ntrain·M) statement suppresses D and d, which are fixed for a chosen architecture and data dimension; this is fine, but please say so explicitly so readers do not misread the complexity as independent of feature dimension or qubit count.","section":"§3.2, Eq. (10)"},{"comment":"The fANOVA method is not defined or referenced. Add a citation or a sentence describing how the relative importance values are computed.","section":"§4.3, Fig. 3"},{"comment":"Several entries contain formatting artifacts such as \"0 .75\" (e.g., Census, McQuack F1). Please fix the spacing throughout the table.","section":"Table 6"},{"comment":"Code availability is pending export control clearance; this is understandable, but in the meantime the QML benchmark comparison cannot be reproduced. Consider releasing at least the benchmark-evaluation scripts and seeds, or provide a detailed protocol document.","section":"§7"}],"recommendation":"major_revision","confidential_remarks":"To the editor: The paper is a plausible incremental contribution, but the headline benchmark claim must be made auditable before publication. If the authors cannot rerun the Bowles et al. baselines under a matched protocol, they should downgrade the claim from \"strongest pure quantum model\" to something like \"competitive with reported baselines under our protocol.\" The reliance on the same group's prior work [7] is not improper, but the novelty relative to Quack should be stated more crisply."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know two things about this paper. First, the method is a neat and clearly specified extension of the authors' own binary Quack: replace the full Gram matrix with an n_train x M sample-to-centroid fidelity matrix, train via KTA by alternating feature-map and centroid updates, and classify by argmax fidelity. The O(n_train M) complexity is derived cleanly (Eq. 10). Second, the headline empirical claim—'strongest pure quantum model in the benchmark'—rests on comparing McQuack's numbers to baselines 'as reported in [4]', not on re-running those baselines under the same protocol. That is a real weakness, and the paper does not fully acknowledge how much the ranking could shift if splits, seeds, or optimization budgets differed.\n\nWhat is new and genuinely useful: the native multiclass formulation avoids one-vs-all overhead, the hardware demo on 124 qubits is a legitimate feasibility study, and the trainability analysis up to 13 qubits is honest—they do not overclaim a barren-plateau guarantee. The paper is refreshingly clear about its own limitations: hardware results are non-significant, noiseless simulation may overestimate performance, and classical NNs still win. The writing is straightforward and the theory is not circular.\n\nThe main soft spot is the benchmark protocol. McQuack's results come from a separate pipeline with its own hyperparameter grid, five-seed averaging, and a downsampled MNIST protocol. The paper even notes that some baselines were evaluated on only a subset of datasets, so average normalized ranks over heterogeneous evaluation sets can be biased in McQuack's favor. Code is not released (pending export control), so the comparison cannot be audited. That does not invalidate the method, but it means the central comparative claim is unsupported as written. A matched-protocol rerun—or at least a clear statement of the comparability assumptions—is needed. The bit-flip tolerance calibration (b=45 on 124 qubits) is another point worth scrutiny, though it is disclosed and the hardware results are appropriately hedged.\n\nOverall: the core method and complexity analysis are sound, the empirical claims are the load-bearing weakness rather than a fatal flaw. This is the kind of paper that should go to peer review with a request for code release and matched baselines. It is a useful reference for anyone working on trainable quantum kernels or multiclass QML, and a good cautionary example of benchmark pitfalls in this area.","headline":"A clean, honest multiclass extension of Quack with a sound linear-scaling argument, undercut by a benchmark comparison to Bowles et al. baselines that are taken as reported rather than re-run under matched conditions.","tokens_in":27754,"tokens_out":2380,"would_cite":true,"duration_ms":24481,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that replacing a quantum kernel's full Gram matrix with a trainable sample-to-class-centroid fidelity matrix yields an intrinsically multiclass quantum kernel method with linear runtime O(n_train·M), and that the model is t","keywords":["quantum kernel methods","multiclass classification","kernel-target alignment","trainable embeddings","sample-to-centroid fidelity","linear runtime","variational classifiers","barren plateaus"],"falsifier":"Re-run the 133-dataset benchmark with identical train/test splits, seeds, and hyperparameter optimization budgets for McQuack and all baseline quantum models; if McQuack's average normalized rank is not lower than the other pure quantum models, the paper's headline comparative claim fails.","tokens_in":26866,"feed_emoji":"⚛️","tokens_out":5761,"duration_ms":53720,"temperature":0.7,"pith_summary":"The paper sets out to show that three standard limitations of kernel methods—quadratic scaling with training-set size, fixed non-trainable kernels, and the absence of a native multiclass formulation—can be removed simultaneously in a quantum setting. Its vehicle is McQuack, a quantum kernel built from a trainable sample-to-class-centroid fidelity matrix instead of a full Gram matrix. The authors claim that training and inference run in time O(n_train·M), that the trained model is the strongest 'pure' quantum baseline across a 133-dataset benchmark, and that even an untrained hardware version on 124 qubits performs comparably to an RBF kernel. If the linear-scaling claim holds, quantum kernel methods could be applied to substantially larger training sets than Gram-matrix approaches allow.","feed_headline":"Linear-time trainable quantum kernel beats pure quantum baselines","feed_subtitle":"Swapping the full Gram matrix for sample-to-centroid fidelities makes multiclass quantum kernels scale linearly with data and classes.","key_machinery":"The central object is the sample-to-centroid fidelity matrix K ∈ R^{n_train×M} with K_{i,m} = |⟨0^{⊗n}|U†(c_m,w,b)U(x_i;w,b)|0^{⊗n}⟩|². It defines a kernel between each sample and each class centroid, rather than between pairs of samples. Training alternates kernel-target alignment on the shared embedding parameters and on the centroid parameters, giving an intrinsically multiclass model whose cost per epoch is O(n_train M) shots via the parameter-shift rule. A secondary object is the mapping of this kernel to a variational-classifier form, which shows that the shared embedding parameters are the key structural difference from an ensemble of independently trained variational classifiers.","core_discovery":"McQuack replaces the n_train×n_train Gram matrix with an n_train×M matrix whose entry K_{i,m} is the fidelity between the encoded data point x_i and a trainable class centroid c_m. The embedding parameters (w,b) and the centroids are optimized alternately, both against the same kernel-target alignment objective, so the model learns both a data embedding and a set of class prototypes in Hilbert space. The paper reports that in simulation on 133 synthetic and 19 real-world datasets, the model outperforms existing pure quantum baselines; on hardware, an untrained instance on a 124-qubit subgraph of two 156-qubit devices reaches accuracy in the range of an RBF kernel. The authors also report no","pith_inferences":["If the centroid representation is the real source of the gain, a purely classical analogue—optimizing RBF centers directly against kernel-target alignment—should reproduce much of McQuack's behavior; this is testable and would help isolate whether a quantum advantage is present.","The O(n_train M) scaling shifts the practical bottleneck toward the shot count and the number of classes, so for very large M the method may still be expensive; gradient-free or hybrid optimizers could change that trade-off.","The 'no barren plateaus' result is confined to 13 qubits; extending the trainability study to larger system sizes with hardware noise would tell whether the observed stability survives scale-up.","If linear-time trainable quantum kernels prove robust, a natural next step is to apply them in online or streaming settings where Gram matrices cannot be maintained."],"forward_implications":["Training and inference costs scale linearly with the number of training samples and the number of classes, removing the O(n_train²) Gram-matrix bottleneck of standard kernel methods.","Because the kernel is trainable through kernel-target alignment, the embedding adapts to the dataset instead of being fixed in advance.","The multiclass formulation is intrinsic: a single model handles M classes through M trainable centroids, without one-vs-rest or one-vs-one decomposition.","Untrained inference on more than 100 qubits is feasible with error mitigation, suggesting that large fidelity-based quantum kernels are not out of reach on current hardware.","Parameter initialization—not regularization—dominates trainability in the tested regime, giving concrete guidance for practitioners."],"fun_headline_variants":["McQuack: quantum kernel that scales linearly and learns centroids","Linear-scaling trainable quantum kernel for multiclass tasks","Quantum kernel with trainable centroids scales linearly with data","Sample-to-centroid quantum kernel: linear scaling, trainable features","McQuack: quantum kernel with sample-centroid fidelities, linear time"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The claim that McQuack is the strongest pure quantum model depends on comparing its benchmark rankings to baseline rankings produced in a separate study with possibly different splits, seeds, and hyperparameter choices; if those protocols are not interchangeable, the comparison is not apples-to-apples.","fun_headline_variants_meta":{"raw":{"variants":["McQuack: quantum kernel that scales linearly and learns centroids","Linear-scaling trainable quantum kernel for multiclass tasks","Quantum kernel with trainable centroids scales linearly with data","Sample-to-centroid quantum kernel: linear scaling, trainable features","McQuack: quantum kernel with sample-centroid fidelities, linear time"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000745,"raw_usage":{"total_tokens":3145,"prompt_tokens":720,"completion_tokens":2425,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":464,"completion_tokens_details":{"reasoning_tokens":2335}},"tokens_in":464,"tokens_out":2425,"duration_ms":14647,"temperature":1.0,"reasoning_tokens":2335,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T11:43:36.552380+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-run the 133-dataset benchmark with identical train/test splits, seeds, and hyperparameter optimization budgets for McQuack and all baseline quantum models; if McQuack's average normalized rank is not lower than the other pure quantum models, the paper's headline comparative claim fails.","supporting_citations":[],"review_version":1}