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REVIEW 6 major objections 5 minor 38 references

A continuous-variable quantum model matches classical medical-image classifiers

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2026-08-04 00:14 UTC pith:YVH5766N

load-bearing objection A plausible feasibility result undercut by misreported tables: the comparable-performance claim cannot be trusted until Table 3 is reconciled with the text. the 6 major comments →

arxiv 2511.02051 v1 pith:YVH5766N submitted 2025-11-03 quant-ph cs.ETphysics.med-ph

Towards Continuous-variable Quantum Neural Networks for Biomedical Imaging

Daniel Alejandro Lopez , Oscar Montiel , Oscar Castillo , Miguel Lopez-Montiel This is my paper
classification quant-ph cs.ETphysics.med-ph PACS 03.67.Lx
keywords continuous-variable quantum computingquantum neural networksbiomedical image classificationGaussian gatesvariational quantum circuitsPCA dimensionality reductionnoise robustnessmulticlass classification
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper tries to establish that a small continuous-variable quantum neural network, built from Gaussian gates and trained on heavily compressed medical images, can classify three diagnostic tasks as accurately as a classical network of the same size and a discrete-variable quantum counterpart. If true, this would make photonic, continuous-variable hardware a plausible candidate for computer-aided diagnosis without requiring a large number of qubits. The authors report no statistically significant difference among the three models on accuracy, recall, precision, or F1 score, with the CV model showing slightly better multiclass performance on the organ task and better focus on the minority class in breast ultrasound. The study is a feasibility demonstration, not an advantage claim: the Gaussian circuit is small enough that what is being tested is its expressiveness, not quantum speedup.

Core claim

On its own terms, the paper's discovery is that a 4-qumode Gaussian circuit—displacement gates encoding four PCA components, alternating rotation and squeezing gates, beamsplitter entangling layers, and position-quadrature measurements feeding a linear head—produces test-set F1 scores of about 85% on pneumonia chest X-rays, 75% on breast ultrasound, and 45% on an 11-class organ CT task. These numbers sit within a few points of a same-parameter classical network and a same-parameter discrete-variable quantum circuit, and the CV model is the most robust of the three when Gaussian noise is added to the images. The authors interpret this as evidence that continuous-variable encoding offers compa

What carries the argument

The central object is a continuous-variable variational circuit whose modes are quantum harmonic oscillators (qumodes). Data enters through displacement gates; trainable rotation and squeezing gates reshape the phase-space state; beamsplitter gates entangle adjacent modes; and the model output is the vector of position-quadrature expectation values. All gates are Gaussian, so the circuit functions as a learned linear-optical feature map, and the trainable parameters number 42 including the classical output layer.

Load-bearing premise

The experiments stand or fall on the assumption that four PCA components keep enough diagnostic information: the paper itself reports retaining only about 60% of variance for the two binary datasets and 48% for the organ dataset.

What would settle it

Train the same classical linear head on the original 784-pixel images, or on PCA with 8–16 components, and compare accuracy on the organ dataset; if accuracy climbs well above 47%, the reported parity among CV, DV, and classical models is an artifact of the compression bottleneck rather than a property of the quantum circuits.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • CV and DV quantum models perform within statistical noise of a classical network on all three imaging tasks at the same 42-parameter scale.
  • The CV model holds up better than the DV model when Gaussian noise is added, staying closer to the classical model's stability across the full noise range.
  • On the 11-class organ task, the CV model beats the DV model by roughly six to seven points in F1, suggesting continuous encoding helps as class count grows.
  • On the small imbalanced breast dataset, the CV model correctly identifies substantially more true negatives than the DV or classical models, pointing to a minority-class focus.
  • Decision heatmaps differ across paradigms, with the CV model attending to more localized regions, which the authors link to better interpretability for clinical use.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Because the circuit uses only Gaussian gates, it is efficiently simulable classically; the value shown here is representational, not computational speedup. A non-Gaussian gate, such as a cubic-phase gate, would be needed to test whether an actual quantum advantage appears.
  • The PCA bottleneck at 48–60% retained variance likely bounds every result; a natural test is to rerun the same models with 8 or 16 components, or on raw images, to see whether the classical baseline pulls ahead once more signal is available.
  • If the CV model's minority-class advantage holds under less aggressive compression, it could matter for screening tasks where false negatives are costly, since averaged accuracy hides that asymmetry.
  • The Gaussian layer is essentially a learned linear-optical transformation; the right control is a classical linear model on the same PCA features, and a useful extension would be a nonlinear classical model to clarify what the quantum feature map adds.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

6 major / 5 minor

Summary. This paper reports a feasibility study of a continuous-variable (CV) quantum neural network for biomedical image classification. The model is a 4-qumode photonic circuit composed of Gaussian gates (displacement, rotation, squeezing, beamsplitter) with position-quadrature expectation measurements feeding a 10-parameter classical linear head (42 parameters total). Inputs are 4-dimensional PCA projections of 28x28 grayscale images from three MedMNIST subsets: PneumoniaMNIST (binary), BreastMNIST (small, imbalanced binary), and OrganAMNIST (11-class multiclass). The CV model is compared with a nominally matched 4-qubit DV quantum circuit and a classical 'same-scale' network under identical hyperparameters, using accuracy/precision/recall/F1, AUROC/AUPRC, Gaussian noise robustness, Grad-CAM heatmaps, and Friedman/Wilcoxon hypothesis tests. The central claim (Section 6) is that the CV QNN attains performance comparable to the classical and DV counterparts while showing higher noise robustness, minority-class focus, and multiclass classification advantages; the paper explicitly disclaims quantum advantage.

Significance. Strengths: the comparison is controlled at a fixed parameter scale with identical hyperparameters, fixed seeds, and the same PCA-compressed inputs across three datasets of different task structure; the paper honestly states that no quantum advantage is demonstrated; and the topic — CV quantum models on medical imaging — is genuinely underexplored, so a careful feasibility benchmark would be useful if the numbers are reliable. The significance is currently bounded by four structural limitations: the Gaussian circuit is affine in its inputs and classically simulable (so the model is effectively linear); the 4-component PCA retains only 48-60% of the variance; test metrics come from a single chosen fold; and most importantly the reported numbers are internally inconsistent — Table 3 disagrees with the text and Table 2 contains impossible p-values. The stress-test concern about Table 3 is confirmed on reading the manuscript. Until these points are resolved, the quantitative content of the central claim is not established.

major comments (6)
  1. [Section 4, Experiments 1-3; Table 3] Table 3 cannot be reconciled with the prose of Experiments 1-3, and both conflict with Table 2 in places. (i) Breast CV: text gives ACC=R=F1=75.64%, P=73.17%; Table 3 lists P=0.7564, R=0.7317 (P/R swapped). (ii) Pneumonia CV: text gives ACC=R=F1=84.29%, P=84.37%; Table 3 lists P=0.8429, R=0.8437 (again swapped). (iii) Organ CV: text gives ACC=R=F1=45.63%; Table 3 lists R=0.4257. (iv) Breast DV: text reports P=80.67%; 0.8067 appears nowhere in Table 3. (v) Experiment 1 reports CV Pneumonia validation accuracy 89.67%, while Table 2 lists 0.864±0.059. Since Section 6's quantitative claims ('comparable performance,' 'minority class focus,' '+7% F1') are built on these tables, the metrics must be recomputed from the confusion matrices and reconciled with the text before the central claim is evaluable. The 'PENDING' code repository prevents independent verification.
  2. [Section 4, Experiments 1-3; Table 3] All test-set metrics are reported for the single best fold of the threefold cross-validation, with no variance or confidence intervals. The Section 6 claims rest on small between-model differences (e.g., 84.29% vs 85.40% on Pneumonia; 75.64% vs 76.28% on Breast) that are comparable to the fold-to-fold standard deviations in Table 2 (e.g., CV Pneumonia ACC 0.864±0.059). Selecting the best fold post hoc inflates expected performance and makes the claimed parity/advantages unquantified. Report test metrics per fold or as mean±std across folds, as is already done for the validation metrics in Table 2.
  3. [Section 4, Experiment 6; Table 2] The statistical analysis has three problems. First, the p column of Table 2 repeats the chi-square statistic in the Pneumonia and Organ rows (e.g., χ²=0.441, p=0.441; the true p for χ²(2)=0.441 is ≈0.80). Second, with only three folds the exact two-sided Wilcoxon signed-rank p can take only the values 0.25, 0.5, 0.75, 1.0; the table reports 0.111, 0.180, 0.273, 0.778, which are impossible for n=3. Third, the Bonferroni-corrected threshold 0.0167 is below the minimum achievable Wilcoxon p at n=3, so non-rejection is guaranteed by construction. 'No statistically significant difference' is therefore vacuous and cannot serve as evidence for the 'comparable performance' conclusion in Section 6.
  4. [Section 3 vs Section 4, Experiment 1] The classical baseline on which the central parity claim rests is never defined. Section 3 specifies the CV and DV circuits (42 parameters each) but contains no classical architecture; Section 4 states only that 'a classical counterpart with an identical architecture and number of parameters is trained.' A 42-parameter 'identical' classical network is not described (a 4x2 linear head has only 10 parameters), so the reader cannot determine what function class the classical model represents, how it compares structurally with the affine Gaussian circuit, or whether the comparison is fair. The classical architecture (layers, nonlinearities, parameter count) must be specified.
  5. [Section 3.1, Table 1; Section 6; Abstract] The 4-component PCA projection retains only ~60% (Breast, Pneumonia) and ~48% (Organ) of the variance, and Section 3.1 itself notes that OrganAMNIST 'cannot be represented with only 4 components per sample.' Because all three models consume the same 4-dimensional projection, the reported accuracies largely measure the PCA bottleneck, and the near-parity across models is partly forced by the shared input. This does not invalidate the comparative claim 'under this configuration,' but it does not support the abstract's 'viability for future computer-aided diagnosis systems' or Section 6's 'promise in clinical practice' at test accuracies of 45-85%, far below common MedMNIST baselines. Re-scope the conclusions or add experiments at higher k.
  6. [Section 3.2; Section 4, Experiment 6; Abstract] The CV circuit uses only Gaussian gates (D, R, S, BS) and position-quadrature measurements, so as a function of the 4 PCA inputs it implements an affine map (followed by the affine classical head) and is efficiently classically simulable. The paper acknowledges at the end of Experiment 6 that 'the results fail to demonstrate quantum advantage,' yet the same paragraph asserts that 'the CV quantum model offers higher representational capacity for structured and imbalanced biomedical data,' and the abstract lists 'model expressiveness' as an evaluated property. No expressivity measure is reported, and a Gaussian circuit has the same function class as a linear model; the 'feature extraction'/'feature amplification' language of Section 3.2 is correspondingly overstated. Recommend stating the affine/simulable nature explicitly and tempering these claims, or adding non-Gaussian gates.
minor comments (5)
  1. [Section 3.2, Figure 2] The qumode diagram appears garbled in the text: the gate sequences shown for different modes are inconsistent with each other and with the stated two-layer repeated structure. Please redraw and align with the parameter count.
  2. [Sections 3.2 and 3.3, parameter tables] The displacement gate (CV) and first RY gate (DV) are described as data encoding, yet the per-layer gate count (2×4×4) counts them as trainable parameters; the beamsplitter is two-mode but is counted per-mode. Clarify the split between data-encoding and trainable parameters in both quantum models.
  3. [Section 4, Experiment 5; Section 6] Applying Grad-CAM to 4-dimensional PCA inputs produces heatmaps that are at most linear combinations of the four retained eigenimages; the Section 6 claims of a 'more comprehensible heatmap' and 'better output interpretability' should be tempered or the method validated on the PCA bottleneck.
  4. [Declarations, Code availability] The code repository is listed as 'PENDING' although the introduction promises release of 'all code, trained weights, and logs to ensure transparency and replication.' This must be resolved for the reproducibility claim to hold.
  5. [Throughout] Typos and infelicities: 'apodt' (Eq. 19), 'Simlarly' (Section 2), 'analogoues' (Section 3.2), 'as as the following' (Eq. 12), 'OrganMNIST' for OrganAMNIST (Section 4, Experiment 6), and a missing closing bracket in Eq. (17): d(FPR(σ).

Circularity Check

0 steps flagged

No circularity: the paper is an empirical feasibility study on external MedMNIST benchmarks; central claims rest on measured results and statistical tests, not on construction.

full rationale

The paper makes no formal derivation claim that could reduce to its inputs. Section 3 constructs the CV and DV circuits from standard Gaussian and discrete-variable gates, and Section 4 reports measured train/validation/test metrics. The central claim of comparable performance is supported by empirical results and by Friedman/Wilcoxon hypothesis tests, not by a derivation from the model definitions. The PCA encoder in Section 3.1 is fitted on the training data only, and the reported test-set metrics are predictions on held-out data, so no fitted parameter is renamed as a prediction. No load-bearing step relies on a self-citation or an imported uniqueness theorem; the cited prior work on CV QML provides background and architecture inspiration, but the proposed circuits, training, and evaluation are self-contained. The observed inconsistencies between Table 3 and the experimental text, and the 'PENDING' code repository, are serious reproducibility and correctness concerns, but they are not circularity: they do not show that any claimed result is equivalent to its inputs by construction. Therefore no circular steps are identified.

Axiom & Free-Parameter Ledger

4 free parameters · 4 axioms · 0 invented entities

The central feasibility claim rests on several modeling choices — especially the aggressive PCA truncation and the choice of a Gaussian-only circuit — that are not independently validated and substantially constrain what the results can say. No new physical entities are postulated; all quantum elements are standard.

free parameters (4)
  • Number of PCA components (k=4) = 4
    Chosen by hand; retains ~60%, ~60%, ~48% variance for Breast, Pneumonia, Organ (Table 1). The PCA axes themselves are fitted to the training set.
  • Trainable circuit and classical-head parameters = 42 per model
    Learned during training using Adam; values are not released (code PENDING), so the fitted parameter values are not auditable.
  • Circuit depth / number of variational layers = 2
    Chosen to keep gradient computation feasible; no sweep or justification.
  • Noise range for robustness test = sigma in [0.1, 1.0] in steps of 0.05
    Ad hoc choice; not tied to a physical noise model.
axioms (4)
  • domain assumption PennyLane's Gaussian backend (with Strawberry Fields plugin) faithfully simulates the CV quantum circuit dynamics.
    Section 3.2 relies on the simulator for all CV results.
  • domain assumption 4 PCA components preserve enough class-discriminative information for classification.
    Section 3.1, Table 1: retained variance is only 48-60%, yet the authors treat the reduced features as sufficient for the feasibility claim.
  • domain assumption Threefold cross-validation F1 scores provide enough statistical power for Friedman/Wilcoxon comparisons.
    Section 4 Experiment 6: with 3 folds, the tests have minimal power; the conclusion 'no difference' is therefore weak.
  • ad hoc to paper Grad-CAM can be meaningfully applied to PCA-reconstructed 4-dimensional inputs through quantum circuits.
    Section 4 Experiment 5: no derivation or validation is given for computing spatial heatmaps from 4 PCA features; the resulting maps are interpreted as clinical attention.

pith-pipeline@v1.3.0-alltime-deepseek · 18437 in / 13237 out tokens · 139399 ms · 2026-08-04T00:14:52.212708+00:00 · methodology

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read the original abstract

Continuous-variable (CV) quantum computing offers a promising framework for scalable quantum machine learning, leveraging optical systems with infinite-dimensional Hilbert spaces. While discrete-variable (DV) quantum neural networks have shown remarkable progress in various computer vision tasks, CV quantum models remain comparatively underexplored. In this work, we present a feasibility study of continuous-variable quantum neural networks (CV-QCNNs) applied to biomedical image classification. Utilizing photonic circuit simulation frameworks, we construct CV quantum circuits composed of Gaussian gates, such as displacement, squeezing, rotation, and beamsplitters to emulate convolutional behavior. Our experiments are conducted on the MedMNIST dataset collection, a set of annotated medical image benchmarks for multiple diagnostic tasks. We evaluate CV-QCNN's performance in terms of classification accuracy, model expressiveness, and resilience to Gaussian noise, comparing against classical CNNs and equivalent DV quantum circuits. This study aims to identify trade-offs between DV and CV paradigms for quantum-enhanced medical imaging. Our results highlight the potential of continuous-variable models and their viability for future computer-aided diagnosis systems.

Figures

Figures reproduced from arXiv: 2511.02051 by Daniel Alejandro Lopez, Miguel Lopez-Montiel, Oscar Castillo, Oscar Montiel.

Figure 1
Figure 1. Figure 1: Comparison between original and PCA-reconstructed images for each dataset. From top to bottom: PneumoniaMNIST, BreastMNIST, and OrganAMNIST. For each dataset, the left image shows an example of the original input, while the right image shows its reconstruction using 4 principal components. Furthermore, [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The proposed 4-mode Continuous-Variable (CV) quantum circuit. Each qumode undergoes displacement (D) for data encoding, followed by rotational (R) and squeezing (S) gates for feature extraction. Beamsplitter (BS) operations entangle adjacent modes analogously to CNOT gates in DV circuits. Finally, the quadrature expectation values ⟨Xˆ⟩ are measured for data decoding. This quantum circuit is implemented as … view at source ↗
Figure 3
Figure 3. Figure 3: The proposed 4-qubit DV quantum circuit, comprised of a set of data encoding Ry(ϕ) gates; a combination of phase Rz(ϕ) and rotational Ry(ϕ) gates for feature extraction that emulate rotational and squeezing gates from CV quantum circuits; CNOT gates that entangle data information, analogous to beam splitter gates in CV quantum systems; and data decoding via expectation values measured on the z-axis. Taking… view at source ↗
Figure 4
Figure 4. Figure 4: Example of how TP, FP, FN, and TN are defined for a given class (here Class B) in a multiclass confusion matrix. The diagonal cell for Class B corresponds to TP, the rest of row B are FN, the rest of column B are FP, and all other cells are TN. After model predictions are finished, classification metrics may be calculated to assess its performance. The accuracy (ACC) represents model performance across all… view at source ↗
Figure 5
Figure 5. Figure 5: Receiver Operating Characteristic (ROC) curve. The red line indicates the ROC curve with threshold points, the dashed gray line represents the main diagonal (random performance), and the shaded blue area corresponds to the area under the ROC curve (AUROC). FPR and TPR are evaluated over each threshold σ [36]. One more important metric that encapsulates classification performance is the area under the compu… view at source ↗
Figure 6
Figure 6. Figure 6: Example Precision–Recall (PR) curve. The blue line indicates the PR curve, the dashed gray line marks the baseline (positive class prevalence, here 0.2), and the shaded area corresponds to the AUPRC. 4 Experiments and Results This section presents four experiments that evaluate the performance, generalization, and robustness of the proposed continuous variable quantum neural network, discrete variable quan… view at source ↗
Figure 7
Figure 7. Figure 7: Performance evaluation of the proposed continuous-variable quantum neural network (CV-QNN) on the PneumoniaMNIST dataset. From left to right: (a) area under the receiver operating characteristic (AUROC), (b) precision–recall (PR) curve, and (c) confusion matrix. precision of 85.34%, and a F1 score of 85.26%. The test set results hold up to what is displayed in the set of plots of [PITH_FULL_IMAGE:figures/… view at source ↗
Figure 8
Figure 8. Figure 8: Performance evaluation of discrete variable neural network on PneumoniaMNIST dataset: (a) AUROC, (b) precision-recall (PR) curve, (c) confusion matrix. To compare the performance of the proposed quantum models, a classical counterpart with an identical architecture and number of parameters is trained and evaluated over the same configuration as the quantum neural networks. For the training and validation s… view at source ↗
Figure 9
Figure 9. Figure 9: Performance evaluation of classical neural network on PneumoniaMNIST dataset: (a) AUROC, (b) precision-recall (PR) curve, (c) confusion matrix [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Performance evaluation of Continuous Variable Quantum Neural Network on OrganAMNIST: (a) AUROC, (b) precision-recall (PR) curve, (c) confusion matrix. class by class evaluation demonstrates that although the model attained high classification performance for the majority classes of “Liver”, “Lung-Left”, and “Lung-Right” by correctly predicting 71.26%, 79.51%, and 84.28% of the class samples respectively, … view at source ↗
Figure 11
Figure 11. Figure 11: Performance evaluation of discrete variable quantum neural network on OrganAMNIST: (a) AUROc, (b) precision-recall (PR) curve, (c) confusion matrix. 12 [PITH_FULL_IMAGE:figures/full_fig_p012_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Performance evaluation of classical neural network on OrganAMNIST: (a) AUROC, (b) precision-recall (PR) curve, (c) confusion matrix [PITH_FULL_IMAGE:figures/full_fig_p013_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Performance evaluation of Continuous Variable Quantum Neural Network on BreastMNIST: (a) AUROC, (b) precision-recall (PR) curve, (c) confusion matrix. Likewise with the PneumoniaMNIST dataset, the classical model is also used as reference to the proposed quantum models. Over the 50 epochs of threefold cross-validation, the classical model attained an average accuracy, recall, and F1 score of 55.25%, and a… view at source ↗
Figure 14
Figure 14. Figure 14: Performance evaluation of discrete variable quantum neural network on BreastMNIST: (a) AUROC, (b) precision-recall (PR) curve, and (c) confusion matrix. The classical model is also trained and evaluated on the BreastMNIST dataset for benchmarking comparison with the proposed models. Similarly to what was obtained on the previous datasets, the classical model showcased a slight advantage over the proposed … view at source ↗
Figure 15
Figure 15. Figure 15: Performance evaluation of classical neural network on BreastMNIST: (a) AUROC, (b) precision-recall (PR) curve, and (c) confusion matrix. Experiment 4: Noise robustness model comparison To assess robustness of the proposed quantum neural networks, we test the trained models on test set classification over different levels of random Gaussian noise. Random Gaussian noise ranging from [0.1, 1.0] with incremen… view at source ↗
Figure 16
Figure 16. Figure 16: Noise robustness comparison between models for every considered dataset of MedMNIST database. Experiment 5: Decision heatmap comparison on all datasets To evaluate the potential clinical interpretability of the proposed quantum neural networks, Grad-CAM heatmaps were computed for each model, as shown in [PITH_FULL_IMAGE:figures/full_fig_p015_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Comparison of Grad-CAM heatmaps across models and datasets. Each row corresponds to a dataset — (a) PneumoniaMNIST, (b) OrganAMNIST, (c) BreastMNIST — and each column compares the Continuous-Variable (CV) QNN, Discrete-Variable (DV) QNN, and classical neural network. Red regions indicate the most influential image areas for model predictions. 21 [PITH_FULL_IMAGE:figures/full_fig_p021_17.png] view at source ↗

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