Can a Quantum Support Vector Machine algorithm be utilized to identify Key Biomarkers from Multi-Omics data of COVID19 patients?

Chansu Yu; Jae U. Jung; Junggu Choi; Kyle L. Jung; Lara Jehi; Serpil C. Erzurum; Suan-Sin Foo; Suzy AA Comhair; Weiqiang Chen

REVIEW 3 major objections 6 minor 5 references

Can a Quantum Support Vector Machine algorithm be utilized to identify Key Biomarkers from Multi-Omics data of COVID19 patients?

T0 review · 3 major / 6 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read Simulated quantum SVM matches classical SVM on COVID-19 biomarker classification while preserving biomarker importance rankings.

desk verdict A clean QSVM-vs-CSVM benchmark on two COVID-19 omics datasets, undermined by an un-nested feature selection step that makes the biomarker-importance claim circular. read the letter →

arxiv 2505.00037 v1 pith:2KSZES64 submitted 2025-04-29 quant-ph cs.LGq-bio.QM

Junggu Choi , Chansu Yu , Kyle L. Jung , Suan-Sin Foo , Weiqiang Chen , Suzy AA Comhair , Serpil C. Erzurum , Lara Jehi

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Jae U. Jung

This is my paper · ORCID

classification quant-phcs.LGq-bio.QM

keywords quantumsupportvectormachineCOVID-19biomarkersmulti-omicsridgeregressionkernelprojectedbiomarkerrankinglongCOVIDclassification

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tests whether a quantum support vector machine trained on ridge-regression-selected proteomic and metabolomic biomarkers can classify COVID-19 status and long-COVID subtypes. Using two independent cohorts, the authors rank hundreds of biomarkers by ridge-regression coefficient magnitude, split them into high- and low-importance groups, and compare classical SVM with several QSVM quantum kernels after PCA reduction to 2–16 dimensions. Across the 16 classification tasks, simulated QSVM models matched or exceeded CSVM in most settings where the comparison was highlighted, and the high-importance biomarker group consistently outperformed the low-importance group in both algorithms. The paper argues this shows QSVM is a viable alternative for small multi-omics classification and preserves the biological signal captured by ridge regression.

What carries the argument

The argument is carried by the kernel-based SVM trained on PCA-reduced biomarker groups. Biomarker importance is defined by the absolute coefficients of a ridge regression with an L2 penalty, which ranks all features and divides them into fixed-size groups. The QSVM replaces the classical RBF or polynomial kernel with four quantum kernels: amplitude encoding, angle encoding, the ZZ feature map, and the projected quantum kernel (PQK), each evaluated at 2, 4, 8, and 16 principal components or qubits. The load-bearing comparison is the AUC difference between Group 1 (top-ranked biomarkers) and Group 4 (bottom-ranked biomarkers) under k-fold cross-validation, with class weights applied to address imbalance.

What would settle it

Rerun the same pipeline with the ridge regression ranking computed only on the training fold (or on a held-out ranking set), and with cross-validation folds defined by individual patient rather than by sample; if the Group-1-versus-Group-4 AUC gap and the QSVM superiority shrink or disappear, the central biomarker-ranking claim would not survive.

Watch

Extended reading notes

Core claim

The central claim is that a QSVM with an appropriate quantum kernel can classify COVID-19 cases from proteomic and metabolomic profiles at least as well as a classical SVM, while preserving the feature-importance ordering produced by ridge regression. On the INCOV healthy-versus-T1 task, angle-encoding and angle-with-PQK kernels produced AUC values of about 0.99, matching or slightly exceeding the best RBF-based CSVM; in long-COVID subtype comparisons and in the Cleveland Clinic dataset, several QSVM configurations also showed higher AUC than CSVM. The authors interpret the consistent Group-1-over-Group-4 gap as evidence that the quantum models retain the biologically meaningful biomarker ranking rather than fitting noise.

Load-bearing premise

The load-bearing premise is that ridge regression's biomarker importance ranking, computed on the full cohort, can be used to define training groups for cross-validated classifiers without leaking information; the paper also assumes repeated samples from the same individual are independent cross-validation units.

Editorial extensions

If this is right

If the central claim holds, QSVM is a drop-in alternative to classical SVM for small multi-omics classification tasks, with no loss in discrimination when the kernel is chosen appropriately.
The angle-encoding and angle-with-PQK kernels appear most consistently competitive, suggesting that feature encoding choice matters more than raw qubit count for these datasets.
The Group-1-versus-Group-4 AUC gap gives a template for validating quantum classifiers against a classical feature-ranking reference before deploying them on new omics data.
Numerical parity in noise-free simulation is a prerequisite for, not evidence of, quantum advantage; the next step implied by the paper is testing on noisy simulators and real hardware.
Classification of long-COVID subtypes is harder (AUC around 0.7) than acute infection detection (AUC above 0.9), so the method's practical value is greater for early diagnosis than for subtype stratification.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The reported biomarker-ranking result likely overstates generalization because the ridge regression ranks features on the full cohort before the train/test split; a nested cross-validation or a separate ranking-only training set would give more honest out-of-sample AUC for the Group-1 group.
Repeated samples from the same Cleveland Clinic patients are treated as independent cross-validation units, so the healthy-versus-COVID AUC differences may be inflated by intra-subject correlation; a leave-one-individual-out evaluation would test this.
If the same experiments were rerun with nested CV and patient-level grouping, the QSVM-versus-CSVM margin might shrink, but the paper's qualitative claim of comparability would likely survive; the strongest testable prediction is that angle-encoding kernels retain an edge over RBF at low PCA dimensions.
The choice of 2–16 principal components means the 'quantum' part operates on a heavily compressed input; an extension would be to compare QSVM with raw biomarker input or with a classical kernel on the same compressed features to isolate what the quantum kernel adds.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Quick take: this is a straightforward application-level benchmark of QSVM kernels against classical SVM on two COVID-19 multi-omics datasets. The numerical comparison is fine as far as it goes, but the paper's headline claim — that QSVM consistently matches or beats CSVM while 'reflecting' ridge-regression importance rankings — overstates what the design supports. The feature-ranking step is done on the full data before cross-validation, so the Group 1 vs Group 4 comparison is in-sample selection, not out-of-sample validation. The authors acknowledge repeated measures in Cleveland Clinic but don't correct for it. And the appendix shows many QSVM conditions at or near chance (amplitude encoding especially), while the main text highlights the best cells. So the consistency claim isn't supported by the full record.

What's genuinely good: the paper is transparent about simulation-only results, releases code on GitHub, and reports full AUC tables in the appendix — that's more than most QML papers do. Testing four quantum kernels (amplitude, angle, ZZ, projected) across two independent cohorts is a legitimate contribution to the QML-for-omics benchmarking conversation, even if no new algorithm or kernel is introduced. The discussion of selected biomarkers (LGALS9, MMP7, quinolinate, etc.) is reasonable and connects to prior biology.

Soft spots, in order of severity. First and load-bearing: the ridge regression ranks biomarkers on the full dataset, then stable groups are selected, then classifiers are trained on those same groups. Labels leak into feature-group construction, so the finding that Group 1 outperforms Group 4 is not a valid negative-control demonstration. This is fixable: put the ranking inside each cross-validation fold (nested feature selection). Second: the Cleveland Clinic dataset includes repeated samples from the same patients; the Discussion notes this but the analysis doesn't split by subject, so CV AUCs are optimistic. Third: no confidence intervals or significance tests; many reported AUC differences are within noise (e.g., 0.709 vs 0.711). Fourth: the main text selects highlighted conditions while the appendix contains many chance-level QSVM results; the abstract's 'consistently' is not accurate. The QSVM-vs-CSVM comparison itself is not circular, and the paper never claims quantum advantage — that's good, because none is shown.

Who it's for: readers interested in whether quantum kernels can be dropped into small biomedical classification problems, and referees wanting a concrete example of how feature-selection leakage can invalidate an otherwise honest benchmark. It deserves a serious referee — the data and code are real, the flaw is identifiable and fixable, and a revised version with nested validation and subject-level splitting could be a solid application note. I'd send it to review, with a request for major revision.

Referee Report

3 major / 6 minor

Summary. The manuscript investigates whether a simulated quantum support vector machine (QSVM) can classify COVID-19 status or long-COVID subtypes from proteomic and metabolomic biomarker panels, and whether the quantum model preserves a ridge-regression-based ranking of biomarker importance. Two datasets are used: the Su et al. INCOV cohort and a Cleveland Clinic cohort. Biomarkers are ranked by ridge-regression coefficients, divided into high- and low-importance groups, and used as inputs to classical SVM and to QSVM with amplitude, angle, ZZ-feature-map, and projected quantum kernels. Performance is measured by AUC under k-fold cross-validation. The authors report that QSVM consistently matched or exceeded CSVM and that high-importance groups outperform low-importance groups.

Significance. If the results were fully supported, the paper would provide a useful empirical data point on quantum-kernel SVM for small multi-omics biomedical datasets, with a biologically grounded biomarker-selection workflow. The study covers multiple quantum embeddings, two independent cohorts, and makes code available at a public repository. The main contribution, however, is an evaluation claim about QSVM viability and biomarker-importance consistency; both are compromised by the evaluation protocol and by selective reporting of the full result tables, as detailed below.

major comments (3)

[Section 3.2 and Section 2.5] The biomarker-importance claim rests on a feature-selection procedure that is not nested inside the cross-validation loop. Ridge regression is applied to each full classification task in Section 3.2 to rank biomarkers and define Group 1 and Group 4; the same groups are then used in Section 2.5 to train and evaluate classifiers under k-fold cross-validation. Because the ridge fit uses the labels of all samples before the folds are formed, the Group 1 versus Group 4 comparison is an in-sample separation rather than an out-of-sample test. The negative control is only valid if the ranking is computed independently of the evaluation folds. This issue is load-bearing for the claim that QSVM 'reflects the importance rankings by ridge regression.' The Cleveland Clinic analysis is further affected by splitting repeated samples from the same patient across folds, as acknowledged in the Discussion but not corrected.
[Appendix B and Section 3.4] The abstract's 'consistently' claim is contradicted by the full results in Appendix B. Many QSVM conditions produce AUC at or near chance, and some below chance: for example, Table B.3 amplitude encoding gives 0.4430, 0.3618, and 0.3175 for Type2 vs. Type1; Table B.4 gives 0.3401 and 0.3011; and Tables B.5–B.8 contain numerous exactly-0.5000 entries (e.g., Tables B.5 and B.6). The main text and Tables 6–11 highlight only the conditions in which QSVM matched or exceeded CSVM, so the reader cannot infer consistent comparable-or-better performance. The authors should report the full distribution of AUC values, a summary statistic across conditions, and a comparison that includes all quantum kernels, not only the favorable bold entries.
[Tables 6–11 and Section 3.4] No uncertainty or significance testing accompanies the performance comparisons. Reported AUC values are averaged over folds without confidence intervals or significance tests, and many apparent QSVM improvements are tiny: for example, Table 6 rows 1–2 show 0.987 vs. 0.987 and 0.985 vs. 0.984, and Table 7 row 1 shows 0.990 vs. 0.989. Given small sample sizes and repeated measures, these differences are within noise. The claim that QSVM 'exceeded' CSVM requires either error bars or a statistical test; at minimum, the comparisons should be described as descriptive rather than as evidence of superiority.

minor comments (6)

[Section 1] The sentence beginning 'However, Despite the use of QML algorithms' contains a capitalization error and is grammatically incomplete; it should be revised to a complete sentence, e.g., 'However, the use of QML algorithms for analyzing multi-omics datasets and identifying COVID-19-related biomarkers remains unexplored.'
[Table 1.1] The entry for the number of long-COVID individuals appears as '1271', which is likely a typo for 127; the table should be checked and the notation 'meta2/proteo3' clarified.
[Section 4.1] The statement that long-COVID subgroup classification 'reaching a maximum AUC of 87% (See Table 6 and Table 7)' cites the wrong tables: Tables 6 and 7 report Healthy vs. T1 comparisons, not T3 subgroup comparisons.
[Section 4.1] The sentence 'angle encoding suppressed CSVM in the proteomic domain' appears to be a typo; 'suppressed' should presumably read 'surpassed'.
[Section 2.4(b)] The displayed quantum kernel formula 'STφ(x)Sφ(x)US' is garbled and should be written as an inner product such as ⟨φ(x)|φ(x')⟩.
[Appendix A] Class-label names are not harmonized across tables: for example, Table A.5 uses 'Naive vs. Inter' and 'Type2 vs. Inter' while Table 4 uses 'Intermediate vs. Naive' and 'Intermediate vs. Type2'; consistent naming would improve reproducibility.

Circularity Check

1 steps flagged · score 6.0 of 10

Ridge-based biomarker ranking is fit on the full cohort and then 'validated' on the same data, making the Group 1 vs Group 4 AUC comparison a fitted input rather than an independent prediction.

fitted input called prediction [Section 2.3, Section 2.5; evaluated in Section 3.3 and Section 4.1]
"Biomarkers were ranked based on the magnitude of their coefficients in the ridge regression model. They were then grouped into distinct subsets reflecting high and low predictive importance. These subsets were subsequently used as input features for both CSVM and QSVM models to evaluate the effect of biomarker relevance on classification performance. ... The classification performance of CSVM and QSVM was evaluated using biomarker groups determined by the ridge regression model."

The biomarker groups are a deterministic function of ridge coefficients fit on the full dataset, and no nested feature-selection loop is described. The same labels that define Group 1 and Group 4 are then used to compute the cross-validated AUC that supposedly confirms the ranking. The paper's negative-control logic requires the ranking to be independent of the evaluation folds, but the Group 1 versus Group 4 comparison is a within-fit rank check: the feature selector has already seen the test labels. Any classifier trained on features preselected by the full-data ridge fit can show a Group1/Group4 AUC gap even without true predictive signal.

full rationale

The central circular step is the biomarker-importance validation. Ridge regression ranks biomarkers on the full cohort, the top and bottom groups are formed from that ranking, and the paper then treats the higher AUC of Group 1 relative to Group 4 as evidence that the models 'reflect the importance rankings by ridge regression.' Because the group definitions and the evaluation labels come from the same samples, this comparison is an in-sample confirmation of the ridge fit rather than an independent prediction. The QSVM-versus-CSVM performance comparison itself is not circular: it is a numerical comparison of kernels on the same preprocessed inputs. The self-citations to the INCOV and Cleveland Clinic datasets are dataset sources, not load-bearing theorems, and do not by themselves raise the circularity score. The appendix's many near-chance QSVM results are a reporting concern, not a circularity issue. Overall, one load-bearing 'prediction' reduces to its own fitting input, so the paper is partially circular.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The analysis rests mainly on methodological choices rather than invented physical entities. No new particles, forces, mediators, or dimensions are introduced. The most consequential assumptions are that ridge coefficient magnitude measures biomarker importance, that group selection can be evaluated on the same data, and that repeated blood samples can be treated as independent in cross-validation.

free parameters (5)

Ridge regression regularization strength lambda = not reported
Equation (1)-(2) defines the L2 penalty, but the value of lambda is not stated. The resulting biomarker rankings depend on it.
SVM regularization parameter C = grid values 0.0001 to 10000; per-condition optima in Appendix A
C is selected by grid search for each task, group, and PCA dimension, then reused for QSVM. This ties QSVM comparison to classically optimized C values.
Projected quantum kernel bandwidth gamma = not reported
Equation (7) includes a bandwidth gamma for the projected quantum kernel, but no value or search procedure is reported.
PCA component count = 2, 4, 8, or 16
The number of principal components is chosen by hand as an experimental sweep and also sets the qubit count for QSVM. The main text emphasizes conditions where QSVM performed well.
Biomarker group size cutoff = not specified; counts shown in Tables 4-5
Section 3.2 creates groups of fixed sizes, but the exact rule for choosing the number of biomarkers in Group 1 and Group 4 is not given.

assumptions (6)

domain assumption Ridge regression coefficient magnitude is a valid biomarker importance measure.
Used throughout Sections 2.3 and 3.2 to construct top and bottom groups; no comparison with other feature selection methods and no formal stability guarantee beyond five repetitions.
domain assumption Biomarker groups can be validated by training classifiers on the same full cohort.
Sections 2.3, 3.2, and 2.5 evaluate Group 1 versus Group 4 without nested or split feature selection, leading to possible in-sample circularity.
domain assumption PCA computed before or within cross-validation does not leak label information.
Section 2.2 and Section 3.3 do not state whether PCA is fitted inside each CV fold; if fitted on the full data, dimensionality reduction can leak label information.
domain assumption Repeated samples from the same patient are independent across cross-validation folds.
Section 3.1 includes repeated measures from Cleveland Clinic patients; the Discussion acknowledges intra-subject correlation but the analysis does not use grouped cross-validation.
domain assumption Noiseless numerical simulation approximates QSVM behavior on real hardware.
Section 5 states all experiments were conducted in an ideal, noise-free environment; no noisy simulation or hardware results are provided.
standard math Standard SVM and quantum kernel mathematics from cited textbooks and papers are correct.
Equations (3)-(7) rely on established SVM, kernel, and quantum embedding results; these are accepted as background rather than derived.

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Cite this review

Pith. "Pith review of Can a Quantum Support Vector Machine algorithm be utilized to identify Key Biomarkers from Multi-Omics data of COVID19 patients?." pith.science (2026). https://pith.science/paper/2KSZES64

@misc{pith2026250500037,
  author       = {Pith},
  title        = {Pith review of: Can a Quantum Support Vector Machine algorithm be utilized to identify Key Biomarkers from Multi-Omics data of COVID19 patients?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2KSZES64}},
  note         = {Machine review of arXiv:2505.00037}
}

read the original abstract

Identifying key biomarkers for COVID-19 from high-dimensional multi-omics data is critical for advancing both diagnostic and pathogenesis research. In this study, we evaluated the applicability of the Quantum Support Vector Machine (QSVM) algorithm for biomarker-based classification of COVID-19. Proteomic and metabolomic biomarkers from two independent datasets were ranked by importance using ridge regression and grouped accordingly. The top- and bottom-ranked biomarker sets were then used to train and evaluate both classical SVM (CSVM) and QSVM models, serving as predictive and negative control inputs, respectively. The QSVM was implemented with multiple quantum kernels, including amplitude encoding, angle encoding, the ZZ feature map, and the projected quantum kernel. Across various experimental settings, QSVM consistently achieved classification performance that was comparable to or exceeded that of CSVM, while reflecting the importance rankings by ridge regression. Although the experiments were conducted in numerical simulation, our findings highlight the potential of QSVM as a promising approach for multi-omics data analysis in biomedical research.

Figures

Figures reproduced from arXiv: 2505.00037 by the authors.

**Figure 1.** The research scheme of this study 2.1 Datasets Two distinct multi-omics datasets were selected and analyzed in this study. First, we utilized the publicly available dataset from Su et al., a longitudinal multi-omics dataset originally introduced to examine biochemical changes associated with long COVID [26]. This dataset comprises two cohorts of patients diagnosed with severe acute respiratory syndrome coronavirus 2… view at source ↗

**Figure 2.** The highlighted classification performance of the CSVM and [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗

**Figure 4.** The highlighted classification performance of the CSVM and QSVM algorithm from metabolomics of the [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗

Figures from the paper (1 more)

**Figure 6.** Figure 6: The highlighted classification performance of the [PITH_FULL_IMAGE:figures/full_fig_p016_6.png]

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Works this paper leans on

5 extracted references · 3 canonical work pages

[3]

A., Marzouk, R

Gameil, M. A., Marzouk, R. E., Elsebaie, A. H., & Rozaik, S. E. (2021). Long-term clinical and biochemical residue after COVID-19 recovery. Egyptian liver journal, 11, 1-8. [4] Li, J., Zhou, Y., Ma, J., Zhang, Q., Shao, J., Liang, S., ... & Wang, C. (2023). The long-term health outcomes, pathophysiological mechanisms and multidisciplinary management of lo...

arXiv 2021
[5]

By ranking biomarker using ridge-regression and grouping them by importance, we evaluated classification performance of both CSVM and QSVM across different experimental conditions

Conclusion In this study, we evaluated the applicability of the QSVM algorithm for identifying key biomarkers associated with COVID-19 detection. By ranking biomarker using ridge-regression and grouping them by importance, we evaluated classification performance of both CSVM and QSVM across different experimental conditions. Using the INCOV and Cleveland ...

work page 2020
[19]

Abbas, A., Sutter, D., Zoufal, C., Lucchi, A., Figalli, A., & Woerner, S. (2021). The power of quantum neural networks. Nature Computational Science, 1(6), 403-409. [20] Enad, H. G., & Mohammed, M. A. (2023). A Review on Artificial Intelligence and Quantum Machine Learning for Heart Disease Diagnosis: Current Techniques, Challenges and Issues, Recent Deve...

work page Pith review arXiv 2021
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Tudisco, A. (2022). Encoding techniques for quantum machine learning (Doctoral dissertation, Politecnico di Torino). [35] Havlíček, V., Córcoles, A. D., Temme, K., Harrow, A. W., Kandala, A., Chow, J. M., & Gambetta, J. M. (2019). Supervised learning with quantum-enhanced feature spaces. Nature, 567(7747), 209-212. [36] Huang, H. Y., Broughton, M., Mohsen...

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arXiv 2021

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.

[1] [3]

A., Marzouk, R

Gameil, M. A., Marzouk, R. E., Elsebaie, A. H., & Rozaik, S. E. (2021). Long-term clinical and biochemical residue after COVID-19 recovery. Egyptian liver journal, 11, 1-8. [4] Li, J., Zhou, Y., Ma, J., Zhang, Q., Shao, J., Liang, S., ... & Wang, C. (2023). The long-term health outcomes, pathophysiological mechanisms and multidisciplinary management of lo...

arXiv 2021

[2] [5]

By ranking biomarker using ridge-regression and grouping them by importance, we evaluated classification performance of both CSVM and QSVM across different experimental conditions

Conclusion In this study, we evaluated the applicability of the QSVM algorithm for identifying key biomarkers associated with COVID-19 detection. By ranking biomarker using ridge-regression and grouping them by importance, we evaluated classification performance of both CSVM and QSVM across different experimental conditions. Using the INCOV and Cleveland ...

work page 2020

[3] [19]

Abbas, A., Sutter, D., Zoufal, C., Lucchi, A., Figalli, A., & Woerner, S. (2021). The power of quantum neural networks. Nature Computational Science, 1(6), 403-409. [20] Enad, H. G., & Mohammed, M. A. (2023). A Review on Artificial Intelligence and Quantum Machine Learning for Heart Disease Diagnosis: Current Techniques, Challenges and Issues, Recent Deve...

work page Pith review arXiv 2021

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Tudisco, A. (2022). Encoding techniques for quantum machine learning (Doctoral dissertation, Politecnico di Torino). [35] Havlíček, V., Córcoles, A. D., Temme, K., Harrow, A. W., Kandala, A., Chow, J. M., & Gambetta, J. M. (2019). Supervised learning with quantum-enhanced feature spaces. Nature, 567(7747), 209-212. [36] Huang, H. Y., Broughton, M., Mohsen...

work page Pith review arXiv 2022

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Bourgin, M., Derosa, L., Silva, C. A. C., Goubet, A. G., Dubuisson, A., Danlos, F. X., ... & Durand, S. (2021). Circulating acetylated polyamines correlate with Covid-19 severity in cancer patients. Aging (Albany NY), 13(17), 20860. [48] Mangge, H., Herrmann, M., Meinitzer, A., Pailer, S., Curcic, P., Sloup, Z., ... & Prüller, F. (2021). Increased kynuren...

arXiv 2021