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Quantum Kernel Advantage over Classical Collapse in Medical Foundation Model Embeddings

Sebastian Cajas Ordóñez, Felipe Ocampo Osorio, Dax Enshan Koh, Rafi Al Attrach, Aldo Marzullo, Ariel Guerra-Adames, J. Alejandro Andrade, Siong Thye Goh, Chi-Yu Chen, Rahul Gorijavolu, Xue Yang, Noah Dane Hebdon, Leo Anthony Celi

arXiv:2604.24597v1quant-phcs.AI

TL;DR

The paper tests whether quantum kernels extract discriminative structure missed by classical kernels in imbalanced insurance classification from frozen chest-radiograph embeddings. Using identical PCA-q features, it finds QSVM consistently outperforms untuned linear and tuned RBF baselines under noiseless simulation, while classical collapse is structurally linked to low-rank representations.

  • Problem

    Insurance prediction tests whether quantum feature maps can extract discriminative structure that classical kernels miss in a clinically grounded, class-imbalanced task with subtle distributed signal.

  • Method

    The study compares QSVM with classical SVMs using identical PCA-q features from frozen embeddings of three medical foundation models across qubit counts and embedding seeds.

  • Results

    QSVM wins all 18 Tier-1 minority-class F1 comparisons and all seven Tier-2 comparisons, while linear SVM collapses to F1 = 0 on 90–100% of seeds.

  • Takeaways & Limitations

    The results indicate that QSVM performance is not explained by effective rank alone, with quantum spectral structure contributing to collapse resistance and predictive performance.

  • Takeaways & Limitations

    The comparison includes noiseless simulation and relies on prior knowledge of the quantum kernel when setting the RBF bandwidth γ∗, which is unavailable at deployment.

Abstract

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We provide evidence of quantum kernel advantage under noiseless simulation in binary insurance classification on MIMIC-CXR chest radiographs using quantum support vector machines (QSVM) with frozen embeddings from three medical foundation models (MedSigLIP-448, RAD-DINO, ViT-patch32). We propose a two-tier fair comparison framework in which both classifiers receive identical PCA-q features. At Tier 1 (untuned QSVM vs. untuned linear SVM, C = 1 both sides), QSVM wins minority-class F1 in all 18 tested configurations (17 at p < 0.001, 1 at p < 0.01). The classical linear kernel collapses to majority-class prediction on 90-100% of seeds at every qubit count, while QSVM maintains non-trivial recall. At q = 11 (MedSigLIP-448 plateau center), QSVM achieves mean F1 = 0.343 vs. classical F1 = 0.050 (F1 gain = +0.293, p < 0.001) without hyperparameter tuning. Under Tier 2 (untuned QSVM vs. C-tuned RBF SVM), QSVM wins all seven tested configurations (mean gain +0.068, max +0.112). Eigenspectrum analysis reveals quantum kernel effective rank reaches 69.80 at q = 11, far exceeding linear kernel rank, while classical collapse remains C-invariant. A full qubit sweep reveals architecture-dependent concentration onset across models. Code: https://github.com/sebasmos/qml-medimage

I. INTRODUCTION

The paper tests whether quantum kernels provide an empirical advantage for difficult, imbalanced medical-imaging classification, using frozen foundation-model embeddings and controlled classical comparisons. Across models and qubit counts, QSVM consistently outperforms linear and tuned RBF baselines, while analyses link classical collapse to low effective rank and reveal architecture-dependent behavior.

  • Contributions: QSVM beats an equally untuned linear SVM on minority-class F1 in all 18 model×qubit configurations.Seventeen comparisons reach p < 0.001 and one reaches p < 0.01 across 10 embedding seeds.
  • Contributions: QSVM also wins all seven comparisons against the best C-tuned RBF kernel at equal PCA dimensionality.The reported mean gain is +0.068.
  • Structural explanation: The linear kernel has effective rank 3.77–5.85 versus N = 1,896 training samples, providing a structural explanation for its collapse.The paper characterizes this collapse as dimensionality-driven rather than a hyperparameter-tuning failure.
  • Structural explanation: A rank-matched RBF experiment shows that QSVM’s advantage extends beyond effective rank, with QSVM outperforming at all four tested qubit counts.This comparison suggests that quantum-kernel spectral structure contributes beyond rank alone.
  • Design rules: Trace normalization is necessary for non-zero QSVM F1, 1-DOF angle encoding outperforms 3-DOF encoding, and deeper re-uploading degrades performance at q = 8.The reported bottleneck in the deeper-circuit experiment is sample size rather than circuit capacity.
  • Architecture-dependent concentration: A q sweep reveals architecture-dependent concentration: MedSigLIP-448 peaks at q = 11 then collapses at q = 16, whereas RAD-DINO and ViT-patch32 improve monotonically.The multi-seed MedSigLIP-448 mean at q = 16 is 0.377, a Tier-1 win.

III. METHODS

The study uses MIMIC-CXR-JPG chest radiographs to classify insurance status in a strongly imbalanced binary task. It restricts analysis to the DT9 stratum and evaluates minority-class F1 as the primary metric.

  • Dataset and task: MIMIC-CXR contains approximately 61,000 patients, while the study uses MIMIC-CXR-JPG restricted to the DT9 preprocessing stratum.Insurance type is linked from hospital admission records to each study.
  • Scope boundary: The non-collapse Tier-1 advantage for q≥10 has been validated only on DT9, so confirming it on additional strata remains future work.The preprocessing mapping is identical across strata, but the reported validation scope remains limited.
  • Dataset and task: The resulting dataset contains approximately 2,371 samples, with 1,896 training examples split using an 80/10/10 train-validation-test ratio.The split uses a fixed random seed.
  • Dataset and task: Medicaid/Medicare is the majority class at 69.6%, while Private insurance is the minority class at 30.4%.The classification target is binary.
  • Evaluation: Minority-class F1 is the primary metric because a majority-class predictor achieves accuracy ≈0.697 but minority-class F1 = 0.Accuracy and AUC are reported as secondary metrics.

B. Embeddings and Preprocessing

The preprocessing and circuit pipeline standardizes frozen foundation-model embeddings, compresses them to q dimensions, rescales them for angle encoding, and applies a fixed 1-DOF quantum circuit for kernel computation.

  • Embedding models: The study uses frozen CLS-token embeddings from MedSigLIP-448, RAD-DINO, and ViT-patch32-cls.Their embedding dimensions are 448, 768, and 768 respectively.
  • Embedding models: CLS-token pooling is the primary strategy, with ViT-patch32-GAP evaluated separately as a pooling ablation.The GAP variant is reported across 10 seeds.
  • Preprocessing: All embeddings undergo StandardScaler normalization, PCA reduction to q dimensions, and MinMaxScaler rescaling to [−1, 1].The tested qubit counts are q ∈{2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 16}.
  • Quantum circuit: The BSP circuit assigns one parameterized Ry rotation to each qubit, encoding one PCA component per qubit.The circuit uses ring entanglement through CNOT operations.
  • Quantum circuit: The encoding block is repeated with data re-uploading depth reps, fixed at reps = 1 in the primary experiments.Each repetition re-encodes the full input vector.
  • Kernel computation: The quantum kernel is evaluated with compute–uncompute and trace normalization before SVM training.The normalized training kernel is scaled to unit trace, and the test-train block uses the same training trace.

D. Fair Comparison Framework

The paper defines a two-tier framework that controls dimensionality and hyperparameters while comparing QSVM with linear and tuned RBF SVM baselines. Tier 1 is the primary claim, whereas Tier 2 tests QSVM against a tuned classical alternative.

  • Tier 1: The fair fight: Tier 1 compares untuned QSVM and untuned linear SVM using C = 1 and identical PCA-q dimensionality.Neither classifier is cross-validated, isolating performance under identical hyperparameter choices.
  • Tier 2: The stretched goal: Tier 2 compares untuned QSVM with a C-tuned RBF SVM at the same PCA-q dimensionality.The RBF search uses C ∈ {0.01, 0.1, 1, 10, 100} with sklearn’s default γ scale.
  • Validation: QSVM wins minority-class F1 in all 18 Tier-1 configurations, with 17 results at p < 0.001 and one at p < 0.01.The comparison spans three models and eight measured qubit counts across 10 embedding seeds.

F. Reproducibility

The reported experiments use multi-seed validation and representative confusion-matrix analysis, with code and configurations released for reproduction. Results show persistent QSVM gains over classical baselines under the stated comparisons.

  • Reproducibility: The released repository includes source code, SLURM configurations, analysis scripts, and a master script covering embedding loading through figure and table generation.A single-model full qubit sweep requires approximately 12 GPU-hours on an NVIDIA H100; classical baselines complete in minutes on CPU.
  • Multi-seed validation: 10 independent embedding seeds reveal that classical linear SVM collapse is pervasive across models and qubit counts.Collapse occurs on 100% of seeds in several low-dimensional regimes and on 9 of 10 seeds even where single-seed results appeared non-collapsed.
  • Representative operating point: At q = 11, QSVM achieves mean F1 = 0.343 versus classical F1 = 0.050, for a ∆F1 of +0.293 with p < 0.001.Both classifiers use C = 1 without hyperparameter tuning; QSVM remains above F1 = 0.1 on 8 of 10 seeds.
  • Representative operating point: A representative q = 11 QSVM run achieves minority-class precision 0.639, recall 0.542, and F1 = 0.586.The confusion matrix contains N = 238 test samples and uses MedSigLIP-448, C = 1, trace normalization, and seed 0.
  • Reproducibility: Table IV reports Tier-2 QSVM-versus-RBF comparisons as mean ± std over 10 embedding seeds, with ∆F1 defined as the mean QSVM F1 minus mean best-classical F1.QSVM wins minority-class F1 on all seven configurations.

C. Classical Kernel Collapse Analysis

PCA-q compression structurally limits the linear kernel to a low-rank subspace, while the quantum kernel retains greater effective rank and discriminative structure. Additional feature-selection results indicate that the advantage is not specific to PCA geometry.

  • Rank limitation: After PCA reduction to q dimensions, the linear kernel has at most q non-zero eigenvalues among N = 1,896 training samples.This rank limitation constrains the classical representation to the PCA subspace.
  • Collapse mechanism: With effective rank ≈q ≪N, classical SVM often defaults to majority-class prediction regardless of C because within-class and between-class kernel similarities are nearly indistinguishable.Table VI identifies low variance and within-class ≈ between-class variance as the absence of usable discriminative signal.
  • Quantum rank expansion: The quantum feature map operates in a 2^q-dimensional Hilbert space, exceeding the q-dimensional subspace accessible to the linear kernel.The measured higher effective rank of KQ is presented as the structural explanation for non-trivial QSVM F1 where the classical kernel collapses.
  • Quantum rank expansion: At q = 4 and q = 6, quantum-kernel effective ranks are 6.86 and 13.94 versus linear-kernel ranks 3.77 and 5.53.These correspond to 1.82× and 2.52× the linear values; at q = 11, the multi-seed quantum effective rank reaches 69.80.
  • Eigenspectrum evidence: At q = 6, the MedSigLIP-448 linear kernel has exactly six positive eigenvalues and effective rank 5.53 out of 1,896 training samples.The eigenspectrum confirms collapse to a six-dimensional subspace.
  • Feature-selection sensitivity: Using mutual-information ranking or kernel PCA, classical F1 remains below corresponding QSVM F1 at q = 4 and q = 6 for all three models.The reported results support the conclusion that the advantage holds across all three dimensionality-reduction methods.

V. ABLATION STUDIES

Ablations show that QSVM performance depends on normalization, qubit count, circuit architecture, and embedding model. More qubits or circuit depth do not uniformly improve performance, and concentration onset varies by model.

  • Kernel normalization: Trace normalization achieves the best q = 8 QSVM F1, while Frobenius normalization collapses F1 to 0 on all three models.Unnormalized and cosine normalization are intermediate, and the experiment uses reps = 1 and C = 1.
  • Qubit scaling: MedSigLIP-448 forms a QSVM F1 plateau from q = 9 to q = 12, whereas its seed-0 F1 drops to 0.173 at q = 16.The multi-seed mean at q = 16 remains 0.377 and still wins Tier 1, indicating seed-dependent rather than structural collapse.
  • Qubit scaling: RAD-DINO and ViT-patch32 improve more monotonically through q = 16, reaching F1 = 0.524 and F1 = 0.520 respectively.At q = 10, they reach F1 = 0.488 and F1 = 0.478, respectively.
  • Model dependence: At q = 16, MedSigLIP-448 is more susceptible to kernel concentration than RAD-DINO or ViT-patch32.The per-model variation indicates architecture-dependent concentration onset across embeddings.
  • Circuit depth: Increasing data re-uploading depth from reps = 1 to reps = 2 at q = 8 reduces accuracy from 0.756 to 0.727, a drop of −0.029.The reps = 3 condition was cancelled, and greater circuit expressivity did not reliably improve performance at this sample size.
  • Circuit architecture: The 3-DOF circuit uniformly collapses in the q = 8, reps = 1, trace-normalized comparison.The corresponding 1-DOF versus 3-DOF experiment uses C = 1 and seed 0.

C. Circuit Depth: 1-DOF vs. 3-DOF

At q = 8, the 1-DOF angle-encoding circuit substantially outperforms the over-parameterized 3-DOF variant, while high-qubit behavior depends on kernel measurement and normalization choices. Projected kernels can recover performance when fidelity measurements concentrate, but the optimal regime remains model- and qubit-dependent.

  • C. Circuit Depth: 1-DOF vs. 3-DOF: Accuracy drops to 0.33–0.39 and F1 to 0.19–0.39 with 3-DOF encoding, whereas 1-DOF achieves accuracy 0.735–0.756 and F1 0.388–0.543 at q = 8.The 3-DOF circuit uses Rz-Ry-Rz rotations, compared with one Ry parameter per qubit for 1-DOF.
  • E. Projected Quantum Kernel at q = 16: Projected-kernel F1 rises from 0.173 with fidelity q = 16 to 0.396, a gain of +0.223.The projected kernel uses Pauli-Z expectation vectors and an RBF kernel rather than pairwise fidelity measurements.
  • E. Projected Quantum Kernel at q = 16: The projected kernel does not surpass the MedSigLIP-448 fidelity peak of F1 = 0.586 at q = 11, leaving the optimal regime at q ≤11.Generalization across seeds and models remains an open question.
  • Normalization and Kernel Structure: Trace normalization is necessary for non-zero QSVM F1, whereas Frobenius normalization collapses performance to zero across models.The linear-kernel collapse is attributed to dimensionality and remains invariant across C values from 0.01 to 100.
  • Kernel Structure: The quantum kernel can reach effective rank up to 4^q, unlike the linear kernel’s effective rank q, enabling non-zero QSVM F1 in the same PCA subspace.This rank difference is presented as the structural basis for the observed separation between quantum and classical kernels.

B. The q=11 Tier-1 Win: Closing the Quantum Advantage Gap

The q = 11 MedSigLIP-448 configuration forms the clearest Tier-1 quantum advantage window, with gains linked to effective-rank growth before high-qubit concentration. The advantage varies across embedding models and raises fairness concerns because the task captures latent socioeconomic structure in radiographs.

  • B. The q=11 Tier-1 Win: Closing the Quantum Advantage Gap: At q = 11, MedSigLIP-448 QSVM reaches mean F1 = 0.343 ± 0.170 versus classical F1 = 0.050 ± 0.159, a gain of +0.293 with p < 0.001.Both classifiers use C = 1 and identical PCA-11 features; QSVM wins across all 10 embedding seeds.
  • B. The q=11 Tier-1 Win: Closing the Quantum Advantage Gap: The q = 9–12 plateau is a clean Tier-1 window, including seed-0 F1 = 0.552 at q = 9 while classical PCA-9 collapses to F1 = 0.The seed-0 curve peaks at q = 11 and collapses at q = 16, making qubit count a tunable design variable.
  • Cross-Model Behavior: MedSigLIP-448 outperforms RAD-DINO and ViT-patch32 in the quantum setting, reaching multi-seed mean F1 = 0.343 ± 0.170 at q = 11.The reported ordering follows the models’ medical-domain alignment, with ViT-patch32 weakest.
  • Cross-Model Behavior: RAD-DINO and ViT-patch32-cls improve monotonically through q = 16, while only MedSigLIP-448 shows a peak-then-collapse pattern.This suggests concentration onset depends on embedding structure rather than solely on circuit depth or qubit count.
  • Eigenspectrum Mechanism: Effective rank grows from 6.86 at q = 4 to 13.94 at q = 6 and 43.04 at q = 11, tracking seed-0 F1 improvement from 0.488 to 0.504 to 0.586.Beyond q = 11, eigenvalues flatten, effective rank saturates, and discriminative signal is lost as F1 collapses at q = 16.
  • Fairness Implications: Higher effective rank helps QSVM avoid majority-class collapse but may also increase sensitivity to subtle spurious socioeconomic structure in radiographs.The paper therefore calls for interpretability and auditing before clinical deployment.
  • Fairness Implications: Whether the q = 11 signal reflects clinically meaningful variation or amplified demographic confounding remains unresolved.The paper identifies projected kernels, attention localization, and counterfactual auditing as candidate methods for future investigation.

F. Limitations

The evidence is limited to noiseless simulation, one MIMIC-CXR insurance task, and SVM-based comparisons, with possible spurious-signal and preprocessing-specific effects. Rank-matched RBF results further indicate that quantum-kernel performance depends on spectral structure beyond effective rank alone.

  • Scope boundaries: Noiseless Statevector simulation limits the claim to circuit capacity rather than demonstrated advantage on physical quantum hardware.Real hardware may differ because of gate errors, decoherence, connectivity, and readout noise.
  • Scope boundaries: Insurance prediction may exploit acquisition artifacts, institutional patterns, or demographic proxies rather than clinically causal signal.The authors therefore interpret the result as improved separability in representation space, not evidence of clinical utility.
  • Baseline scope: The comparison is limited to SVM-based baselines, while neural networks could exhibit different failure modes and set a stronger classical ceiling.Extending evaluation beyond kernel methods remains open.
  • Evaluation scope: DT9-specific preprocessing means the non-collapse Tier-1 advantage remains unconfirmed across other preprocessing strata.Multi-strata validation is needed to assess generalization of this comparison.
  • Mechanistic qualification: Rank-matched RBF outperforms neither QSVM nor its collapse resistance, showing that effective rank alone does not explain the advantage.At q = 4, rank-matched RBF collapses on 3/10 seeds versus QSVM’s 2/10; across tested qubit counts, QSVM leads by 0.056–0.115 mean F1.
  • Design constraints: Trace normalization is necessary for meaningful QSVM F1, whereas Frobenius normalization collapses F1 to zero across models.The ablations also favor 1-DOF encoding over 3-DOF encoding and warn that deeper re-uploading can degrade performance.
  • Scaling boundary: At q = 16, concentration suggests that scaling QSVM beyond the tested regime requires more than simply adding qubits.The qubit-count performance curve can also be non-monotonic across seeds.

Appendix A: Supplementary Figures

Appendix A supplies supplementary figures and pooling analyses under DT9 preprocessing, primarily documenting kernel spectra, kernel matrices, PCA geometry, and ViT-patch32 pooling robustness.

  • Supplementary setup: All supplementary experiments use DT9 preprocessing, seed 0, and trace normalization unless otherwise noted.
  • Supplementary figures: Figure 6 compares quantum-kernel eigenvalue spectra across three embedding models at q = 4 and q = 6.These spectra complement the MedSigLIP-448 spectrum shown in the main text.
  • Supplementary figures: Figure 9 presents quantum-kernel matrices for all three models at q = 4 and q = 6.
  • Supplementary figures: Figure 10 shows PCA-compressed training data at q = 4 and q = 6, where substantial class overlap provides a geometric explanation for linear-kernel collapse.
  • Pooling ablation: CLS and GAP pooling produce nearly identical QSVM performance at q ≥10, with differences no larger than 0.003.Both variants use 768-dimensional embeddings, and CLS is slightly higher on average across all q.

6. ViT-patch16-cls Patch-Size Ablation

The patch-size ablation compares ViT-patch16-cls with the main ViT-patch32-cls baseline and finds substantially lower QSVM minority-class F1 for patch16 across tested qubit counts.

  • Ablation design: ViT-patch16-cls uses 768-dimensional CLS embeddings from the same frozen ViT backbone, differing from patch32 only in spatial patch resolution.Patch16 produces four times more tokens before CLS pooling.
  • Kernel structure: Quantum-kernel effective rank exceeds linear-kernel rank across all three embedding models at q = 4 and q = 6.
  • Kernel structure: At q = 11, MedSigLIP-448’s quantum-kernel effective rank reaches 43.04 for seed 0, with a multi-seed mean of 69.80.
  • Kernel structure: Higher qubit counts produce richer off-diagonal kernel structure, consistent with increased effective rank.
  • Patch-size results: ΔF1 ≈−0.24 at q = 16 and −0.28 at q = 8 for ViT-patch16-cls relative to ViT-patch32-cls.Patch16 is lower at every tested qubit count.
  • Patch-size interpretation: The patch16 performance gap is attributed to additional redundancy or noise in the low-dimensional PCA subspace, making class separation harder.
  • Visualization caveat: PCA projections of MedSigLIP-448 capture only 21.8% explained variance in two dimensions, indicating that the 2D view omits higher-dimensional structure.
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