{"id":"281597e2-c72e-48d0-b2a8-89e444c1a09c","arxiv_id":"2509.10190","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"On a reduced SDSS dataset, quantum-kernel QSVM outperforms HHL LS-SVM, classical SVMs are slightly ahead, and the HHL method's constant scaling stems from using only two class-average representatives.","lead":"This paper benchmarks two quantum support vector machine implementations on a three-class astronomy dataset: a quantum kernel method (QSVM) and an HHL-based least-squares SVM. It finds QSVM more accurate, classical SVMs comparable, and the HHL method's flat scaling comes from representing each class by a single average point.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Central 'QSVM outperforms HHL LS-SVM' claim is not yet established: the HHL implementation uses only two class-average representatives, so the comparison may be an artifact of this capacity limit.","rationale":"The reader's verdict is CONDITIONAL and identifies the same two-centroid weakness. My stress-test agrees but focuses on the claim's external validity: the HHL implementation is not a representative LS-SVM. The suggested test directly establishes whether expanding the representation closes the gap. Since this is an empirical benchmark with transparent admissions, I do not move the verdict; the conditionality is already warranted and the proposed check would turn it into either acceptance for a properly scoped claim or rejection of the unscoped headline.","tokens_in":14951,"tokens_out":5726,"duration_ms":68074,"concrete_test":"Rerun the HHL LS-SVM pipeline for the one-vs-rest and QSO-vs-All cases with n_rep in {2, 3, 4, 5, 8}, choosing representative elements either as k-means centroids or as random samples per class, keeping gamma, QPE precision, and simulator fixed. Report macro F1 and accuracy. If HHL LS-SVM's macro F1 rises monotonically and approaches or exceeds QSVM's 0.963/0.933 values, the central claim is an artifact of the n_rep=2 constraint; if metrics stay at approximately the current levels, the concern is mitigated. This is feasible because HHL circuit width grows only as O(log n_rep).","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 3.3 fixes the number of representative elements to two and builds the HHL kernel from 'the average values of the selected features for each class.' Consequently Eq. (12) is a 2x2 linear system whose solution defines a linear decision rule based on two class centroids, not an LS-SVM trained on the data. The tables therefore compare a full QSVM (300 samples, class weights, explicit feature encoding) against a deliberately capacity-limited baseline. The paper's own conclusion states the design 'was to bias the comparison in favour of the well-established QSVM.' Thus the abstract's unconditional claim that 'QSVM outperforms HHL LS-SVM in most cases' is not a robust statement about HHL LS-SVM; it is an artifact of n_rep=2 and of representing each class by its average. If more representative elements or non-centroid representatives change HHL performance materially, the headline comparison and the 'essentially constant scaling' conclusion would need to be scoped to this two-centroid implementation.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper compares two quantum SVM pipelines for three-class SDSS classification (stars, galaxies, QSOs): a quantum-kernel QSVM with angle encoding and a classical SVM backend, and an HHL-based least-squares SVM in which the kernel matrix is built from two representative elements defined as the per-class average feature vectors. Both one-vs-rest and two-step hierarchical decompositions are evaluated, with accuracy, macro precision/recall/F1, and a scaling analysis reported. The authors state that QSVM outperforms the HHL implementation in most settings, that classical SVMs are competitive or slightly better, and that the HHL implementation has essentially constant resource scaling. All reported results are simulations; real-device HHL runs were abandoned because of noise.","tokens_in":15143,"tokens_out":7013,"duration_ms":79639,"significance":"If the claims were taken at face value, the paper would provide a useful benchmark of two quantum classification pipelines on a realistic astronomical dataset. Its most reliable contribution is the direct QSVM-vs-CSVM comparison, which again shows no quantum advantage, and the transparent account of HHL's noise sensitivity. However, the headline comparison is weakened by the fact that the HHL \"LS-SVM\" is not a sample-based LS-SVM but a two-centroid classifier, so the performance and scaling results are largely consequences of the chosen n_rep=2 rather than empirical discoveries about HHL LS-SVM. The paper does not ship code, and several hyperparameters needed for reproduction are omitted. The manuscript is potentially useful as a scoped benchmark, but the title and abstract overstate the generality of the QSVM-vs-HHL comparison.","major_comments":[{"comment":"The HHL implementation uses exactly two representative elements, defined as the per-class averages of the selected features. Equation (12) is therefore a 2x2 linear system, and the decision rule in Eq. (10) is a linear function of similarities to two class centroids. This is not an LS-SVM trained on the data, nor is it an HHL solution of the general LS-SVM formulation in Eq. (9) with a kernel matrix over training samples. The abstract's statement that 'QSVM outperforms HHL LS-SVM in most cases' is therefore not established for HHL LS-SVM as such; it is established only for this capacity-limited, two-centroid variant. The conclusion's sentence 'The point was to bias the comparison in favour of the well-established QSVM' confirms this. The authors should either (a) run HHL with more representative elements and report how performance changes, or (b) consistently and prominently scope all cl","section":"3.3 and Eq. (12)"},{"comment":"The 'essentially constant scaling' of HHL LS-SVM is a consequence of the construction, not an empirical finding: the circuit width and depth depend on n_rep=2 and log kappa, not on the number of dataset samples. Counting gate operations for a fixed 2x2 linear system cannot reveal any sample-size scaling. This statement should be presented as an identity of the chosen reduction, and the resource analysis should also account for the classical O(N d) cost of constructing the class-average representatives and for how resources grow with n_rep.","section":"4 and Fig. 3"},{"comment":"Reproducibility is hampered by missing hyperparameters. The value of the regularization parameter gamma in Eq. (12) is never stated, despite directly defining the linear system solved by HHL. Similarly, Section 3.2 says the QSVM was repeated 'a number of times' without giving the number of repetitions or the exact standard-error formula. These omissions prevent an independent check of the reported accuracies and uncertainties.","section":"3.3 and 4"}],"minor_comments":[{"comment":"The HHL LS-QSVM Star row reports recall as '0.67.12', which is not a valid number. Table 2 uses a decimal comma ('0,704') in the Star-vs-All precision. These formatting errors should be corrected.","section":"Table 1"},{"comment":"The index structure in Eq. (10) is unclear: the summand is written as a_i k(x_i, x_j) while the sum runs over j. It should likely be a_j k(x_j, x_i) (or similar) with the test sample index kept separate.","section":"Eq. (10)"},{"comment":"The text refers to the HHL circuit as 'illustrated in 3' (Section 2.2), but the figure is numbered 2. Please fix the cross-reference.","section":"Figures"},{"comment":"The notation 'HHL LS-QSVM' and 'HHL LS-CSVM' is used without explicit definition. Since 'LS-QSVM' could be read as a quantum SVM, and 'LS-CSVM' as a classical SVM, the authors should define these terms clearly (e.g., quantum HHL vs. classical HHL solution of the same reduced system).","section":"Tables 1 and 2"},{"comment":"The preprocessing of the ten SDSS features to [0, pi] is mentioned only in passing; the exact scaling or normalization procedure should be specified for reproducibility.","section":"3.2"}],"recommendation":"major_revision","confidential_remarks":"Reference [27] is a preprint by the same group describing the optimized HHL circuit. The manuscript should make this relationship explicit at first citation so that the comparison is not mistaken for an independent baseline. The paper would be substantially strengthened by including n_rep=3 or 4 for at least a subset of the tasks; as it stands, the title and abstract promise a general HHL LS-SVM comparison that the experiments do not deliver, and the scaling conclusion is an artifact of the fixed two-representative setup."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know two things up front. First, the central claim that QSVM outperforms HHL LS-SVM is not established as a statement about HHL LS-SVM. Section 3.3 fixes the number of representative elements to two and builds the kernel from per-class average features. So the HHL system is a 2x2 linear system over two centroids, not an LS-SVM trained on the data. The paper's own conclusion admits this: \"The point was to bias the comparison in favour of the well-established QSVM.\" The abstract still says \"QSVM outperforms HHL LS-SVM in most cases,\" which is only true for this deliberately capacity-limited implementation. Second, the results tables have internal problems: Table 1 lists F1 values for QSO and Star that do not match the accompanying precision/recall, and one entry reads \"0.67.12\". No uncertainties for HHL because the results are deterministic, but that means the comparison mixes noise in one method with none in the other.\n\nWhat's actually new and good: this is, as far as I can tell, the first application of HHL LS-SVM to a three-class SDSS classification task with both one-vs-rest and two-step hierarchical decompositions. The scaling analysis (constant gate count for HHL versus quadratic kernel executions for QSVM) is a useful reminder of why people care about the method. The comparison against classical SVMs is honest and gives practitioners another negative data point: no quantum advantage on this dataset. The paper is transparent about its choices and limitations, which is more than many QML papers do.\n\nThe soft spots are real but fixable. The n_rep=2 class-average choice is the load-bearing simplification. If the authors added more representatives, the HHL results would change, and the \"essentially constant scaling\" claim would need a caveat about circuit size growing with n and possibly worse conditioning. The gamma regularization parameter is not reported, so the HHL results are not reproducible as specified. The table errors suggest the manuscript needs a careful pass. The abstract overreach is the main issue; the design itself is transparent.\n\nWho is this for? Practitioners who want a reference for implementing these two QML methods on real survey data, especially the circuit-level details. Not for someone needing a reliable head-to-head performance comparison.\n\nI would send this to peer review, because there is a real question being asked and the artifacts, if corrected, could make a useful benchmark paper. But the referee should require the abstract to be scoped, the tables fixed, gamma and representative counts reported, and ideally code released. If that happens, this becomes a citeable negative result.","headline":"The HHL baseline is reduced to two class-average centroids, so the headline QSVM-vs-HHL comparison is not about the method itself; the paper still has useful scaling and multi-class decomposition data, but the claims need rescoping.","tokens_in":15724,"tokens_out":2644,"would_cite":false,"duration_ms":30480,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"On a reduced SDSS dataset, the quantum kernel SVM outperforms the HHL-based least-squares SVM in most accuracy, precision, recall, and F1 comparisons, while classical SVMs stay slightly ahead.","keywords":["quantum kernel","HHL algorithm","least-squares SVM","multi-class classification","SDSS dataset","quantum machine learning","class imbalance","scaling analysis"],"falsifier":"Train the HHL LS-SVM with substantially more representative elements, say ten or fifty per-class centroids derived from clustering rather than a single mean, on the same SDSS data and check whether the QSO macro-F1 rises above about 0.7. If it does, the reported performance gap is an artifact of the two-element compression, not an inherent limitation of the HHL algorithm. Conversely, running the same comparison on a dataset with more than three classes or where class means are nearly identical would test whether the representation is the true bottleneck.","tokens_in":1374,"feed_emoji":"🔭","tokens_out":2414,"duration_ms":53796,"temperature":0.7,"pith_summary":"This paper compares two quantum SVM approaches for three-class classification of astronomical objects—stars, galaxies, and quasars—from a reduced Sloan Digital Sky Survey dataset. It implements a quantum kernel SVM (QSVM) using angle encoding and a projection measurement, and an HHL-based least-squares SVM (HHL LS-SVM) that solves a small linear system built from per-class feature averages. Across one-vs-rest and two-step hierarchical schemes, the QSVM achieves higher accuracy, precision, recall, and macro-F1 than the HHL LS-SVM in most cases, while classical SVMs perform comparably or slightly better. The paper also reports a scaling trade-off: QSVM cost grows quadratically with the number of samples, whereas HHL LS-SVM circuit cost stays essentially constant, making the latter potentially attractive for very large datasets if its representation and noise limitations can be overcome.","feed_headline":"Quantum kernel SVM beats HHL LS-SVM on SDSS data","feed_subtitle":"On a three-class astronomy benchmark, the kernel method wins most metrics; classical SVMs stay slightly ahead.","key_machinery":"The QSVM's quantum kernel is a fidelity between angle-encoded states: each sample's ten features are mapped to y-rotations on ten qubits, and the kernel value for a pair of samples is the squared overlap obtained by projecting the composite state onto the all-zero state; this kernel matrix is then fed to a classical SVM. The HHL LS-SVM reformulates training as solving the linear system (K + gamma^-1 I)a = y, with kernel entries computed from the average feature vector of each class (two representative elements), and uses the HHL quantum algorithm to obtain a normalized solution. The contrast between explicit sample encoding and compressed class-average representation is what drives the obser","core_discovery":"The central claim is that on this ten-feature, three-class SDSS subset, the quantum kernel approach yields better classification performance than an HHL-based least-squares SVM. The QSVM typically achieves accuracy around 0.96-0.97 and macro-F1 above 0.93, whereas the HHL LS-SVM's best macro-F1 is about 0.86 for galaxy isolation and much lower for quasars (0.55-0.70). The HHL method's weakness is traced to its reliance on only two representative elements—the class-averaged feature vectors—which cannot adequately capture the minority QSO class, while the QSVM benefits from explicit point-by-point encoding and class-weight balancing. Classical SVMs remain slightly ahead of both, indicating tha","pith_inferences":["The two-centroid representation used for HHL LS-SVM means the comparison effectively tests whether per-class means can separate the SDSS classes; a dataset with heavily overlapping class distributions would likely degrade the HHL results even further than observed here.","A natural extension is to increase the number of representative elements, for instance using several centroids per class from clustering, and check whether HHL LS-SVM approaches QSVM accuracy while preserving its scaling advantage.","The constant-scaling claim applies to circuit size and gate count; the classical preprocessing and kernel computation would still grow with dataset size, so end-to-end computational cost is not constant.","The QSVM's need for pairwise kernel evaluations makes it impractical for very large surveys; randomized or low-rank kernel approximations could close that gap without changing the core methodology."],"forward_implications":["If the paper is correct, quantum kernel SVMs can be applied to moderately sized multi-class datasets and match classical performance while operating in a quantum feature space.","The HHL LS-SVM's essentially constant circuit scaling means it could in principle handle datasets with many more samples without adding qubits or circuit depth, if the number of representative elements is increased beyond two.","The two-step hierarchical scheme reduces the number of quantum classifiers from three to two with only a small accuracy loss, offering a resource-efficient structure for multi-class problems.","The minority-class failures of HHL LS-SVM indicate that class imbalance must be addressed directly, through weights, more representative elements, or a different decomposition, before the method becomes practically useful.","The reported noise sensitivity of HHL suggests that error-corrected quantum hardware is a prerequisite for real-device deployment of this approach."],"fun_headline_variants":["Quantum kernel SVM beats HHL, but classical still slightly ahead","QSVM tops HHL LS-SVM on SDSS; classical SVMs remain best","Kernel quantum SVM wins over HHL; classical edges it out","Quantum kernel edge over HHL, yet classical SVMs lead","QSVM outguns HHL in multi-class, though classical wins"],"cache_read_input_tokens":17024,"weakest_assumption_plain":"The load-bearing premise is that a 2x2 linear system built from the per-class average features adequately represents the SDSS classes for classification; if the class means do not capture the decision boundaries, especially for minority quasars, the HHL LS-SVM comparison and the constant-scaling conclusion apply only to this compressed toy representation.","fun_headline_variants_meta":{"raw":{"variants":["Quantum kernel SVM beats HHL, but classical still slightly ahead","QSVM tops HHL LS-SVM on SDSS; classical SVMs remain best","Kernel quantum SVM wins over HHL; classical edges it out","Quantum kernel edge over HHL, yet classical SVMs lead","QSVM outguns HHL in multi-class, though classical wins"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000843,"raw_usage":{"total_tokens":3562,"prompt_tokens":853,"completion_tokens":2709,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":597,"completion_tokens_details":{"reasoning_tokens":2616}},"tokens_in":597,"tokens_out":2709,"duration_ms":19500,"temperature":1.0,"reasoning_tokens":2616,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T18:05:51.282395+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Train the HHL LS-SVM with substantially more representative elements, say ten or fifty per-class centroids derived from clustering rather than a single mean, on the same SDSS data and check whether the QSO macro-F1 rises above about 0.7. If it does, the reported performance gap is an artifact of the two-element compression, not an inherent limitation of the HHL algorithm. Conversely, running the same comparison on a dataset with more than three classes or where class means are nearly identical would test whether the representation is the true bottleneck.","supporting_citations":[],"review_version":1}