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arxiv: 2606.21570 · v1 · pith:OOYPP2ARnew · submitted 2026-06-19 · 🪐 quant-ph

A Correlation Aware Quantum Feature Map for Variational Quantum Classification

Murat Kurt This is my paper

Pith reviewed 2026-06-26 13:40 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum feature mapvariational quantum classifiercorrelation aware encodingquantum machine learningcontrolled quantum gatesfeature dependenciesSpearman correlationKendall Tau
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The pith

Integrating classical feature correlations via controlled gates improves variational quantum classification accuracy.

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

The paper proposes building quantum feature maps that detect pairs of strongly correlated features in the input data and encode those dependencies by adding controlled gates to the circuit. This is tested inside a variational quantum classifier on three standard datasets for medical diagnosis, credit scoring, and student outcomes. The author shows that maps using rank correlations such as Spearman and Kendall Tau produce higher accuracy than fixed, correlation-blind encodings. A sympathetic reader would care because most current quantum encodings treat every feature independently, so a simple classical check on dependencies could yield better quantum states for the same circuit depth. If the approach holds, it offers a direct way to translate known data structure into the quantum representation without redesigning the entire model.

Core claim

The Correlation Aware Quantum Feature Map constructs the encoding circuit by first computing classical correlation scores between every pair of features, then inserting controlled quantum gates only for those pairs whose score exceeds a chosen threshold; when this map is used inside a variational quantum classifier the resulting decision boundaries separate classes more effectively than standard product-state or fixed-angle feature maps on the tested datasets.

What carries the argument

The Correlation Aware Quantum Feature Map (CAQFM), which selects high-correlation feature pairs from classical measures and adds controlled gates to entangle their encoded qubits.

If this is right

  • Spearman and Kendall Tau variants of CAQFM outperform standard quantum feature maps on all three benchmark datasets.
  • The added controlled gates produce quantum representations that reflect data dependencies and therefore support higher predictive performance in the variational classifier.
  • The method works for multiple correlation measures, with rank-based ones giving the largest gains.
  • The approach requires only classical preprocessing before the quantum circuit is built.

Where Pith is reading between the lines

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

  • The same correlation-driven gate selection could be tried in other variational quantum algorithms that rely on feature encoding.
  • Replacing the fixed threshold with a trainable parameter might remove one source of manual tuning.
  • The idea links classical feature-interaction detection directly to the structure of the quantum circuit.

Load-bearing premise

That a single fixed threshold on any classical correlation score will reliably select dependencies that improve class separation in the quantum state without adding circuit noise or overfitting.

What would settle it

If the Spearman-based CAQFM is run on the breast-cancer dataset and its test accuracy is no higher than the accuracy obtained with the standard angle-encoding feature map, the central claim is falsified.

Figures

Figures reproduced from arXiv: 2606.21570 by Murat Kurt.

Figure 1
Figure 1. Figure 1: Training accuracy values throughout the epochs for the Breast Cancer dataset. [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Training loss values throughout the epochs for the Breast Cancer dataset. [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Test accuracy values throughout the epochs for the Breast Cancer dataset. [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Test loss values throughout the epochs for the Breast Cancer dataset. [PITH_FULL_IMAGE:figures/full_fig_p012_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Training accuracy values throughout the epochs for the Credit Default dataset. [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Training loss values throughout the epochs for the Credit Default dataset. [PITH_FULL_IMAGE:figures/full_fig_p014_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Test accuracy values throughout the epochs for the Credit Default dataset. [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Test loss values throughout the epochs for the Credit Default dataset. [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Training accuracy values throughout the epochs for the Student Placement dataset. [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Training loss values throughout the epochs for the Student Placement dataset. [PITH_FULL_IMAGE:figures/full_fig_p017_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Test accuracy values throughout the epochs for the Student Placement dataset. [PITH_FULL_IMAGE:figures/full_fig_p017_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Test loss values throughout the epochs for the Student Placement dataset. [PITH_FULL_IMAGE:figures/full_fig_p018_12.png] view at source ↗
read the original abstract

Quantum machine learning has emerged as a promising research area for learning complex data patterns. However, most existing quantum feature maps employ fixed encoding strategies that do not explicitly consider the relationships among features within a dataset. In this study, we propose a Correlation Aware Quantum Feature Map (CAQFM) which integrates feature dependencies into the quantum encoding process. The proposed approach utilizes Pearson, Spearman, Kendall Tau, Mutual Information, and Distance Correlation measures to identify relationships among features. Dependencies exceeding a predefined threshold are incorporated into the quantum circuit through controlled quantum gates, enabling the construction of richer quantum representations that better reflect the underlying structure of the data. The proposed method is evaluated using a Variational Quantum Classifier (VQC) on three benchmark datasets, namely breast cancer diagnosis, credit default prediction, and student placement classification. Simulation results demonstrate that correlation based quantum encoding can improve classification performance compared to conventional encoding strategies. In particular, the Spearman and Kendall Tau based CAQFM variants achieved the highest predictive performance and consistently outperformed standard quantum feature maps. The findings indicate that incorporating dependency information from classical data into quantum feature maps facilitates the generation of more discriminative quantum representations and enhances the effectiveness of variational quantum classifiers.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The manuscript proposes a Correlation Aware Quantum Feature Map (CAQFM) for variational quantum classification. It identifies feature dependencies in classical data using Pearson, Spearman, Kendall Tau, Mutual Information, and Distance Correlation measures, then incorporates dependencies above a single predefined threshold into the quantum circuit via controlled gates. The resulting encodings are evaluated in a VQC on three benchmark datasets (breast cancer diagnosis, credit default prediction, student placement), with the claim that Spearman- and Kendall-Tau-based variants achieve the highest performance and consistently outperform standard quantum feature maps.

Significance. If the performance claims are substantiated with reproducible threshold selection and statistical validation, the approach could meaningfully advance quantum feature map design by explicitly encoding classical feature correlations, potentially yielding more discriminative quantum states for VQC tasks across multiple domains.

major comments (2)
  1. Abstract: the headline claim that 'Spearman and Kendall Tau based CAQFM variants achieved the highest predictive performance and consistently outperformed standard quantum feature maps' cannot be evaluated, as the text supplies neither numerical accuracies, standard deviations, nor any statistical significance tests.
  2. Abstract (method description): the central mechanism depends on a 'predefined threshold' applied to the correlation measures, yet no numerical value, selection procedure, or cross-dataset consistency check is stated; without this, the reported superiority cannot be distinguished from post-hoc hyperparameter tuning.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment below and will revise the paper to improve clarity and reproducibility.

read point-by-point responses

  1. Referee: Abstract: the headline claim that 'Spearman and Kendall Tau based CAQFM variants achieved the highest predictive performance and consistently outperformed standard quantum feature maps' cannot be evaluated, as the text supplies neither numerical accuracies, standard deviations, nor any statistical significance tests.

    Authors: We agree that the abstract should be self-contained with quantitative support for the headline claim. In the revised manuscript we will add the mean classification accuracies and standard deviations (from repeated simulation runs) for the top-performing CAQFM variants versus the standard feature maps, together with the results of the statistical significance tests we performed. revision: yes

  2. Referee: Abstract (method description): the central mechanism depends on a 'predefined threshold' applied to the correlation measures, yet no numerical value, selection procedure, or cross-dataset consistency check is stated; without this, the reported superiority cannot be distinguished from post-hoc hyperparameter tuning.

    Authors: We acknowledge the omission. The revised abstract and methods section will explicitly state the numerical threshold value used, the criterion and validation procedure by which it was selected, and confirmation that the same value was applied uniformly across all three datasets. These additions will make the experimental protocol fully reproducible and demonstrate that the threshold was not tuned post-hoc on a per-dataset basis. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper defines CAQFM by applying standard correlation statistics (Pearson, Spearman, Kendall Tau, etc.) to classical features and inserting controlled gates for pairs exceeding a fixed threshold. Performance is then measured empirically on three external benchmark datasets using a standard VQC. No equation reduces a claimed result to a fitted parameter defined from the same data, no self-citation supplies a uniqueness theorem, and the threshold is stated as predefined rather than optimized on the reported metrics. The central claim therefore rests on observable classification accuracy rather than on any definitional or self-referential step.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that classical correlation thresholds translate directly into useful quantum circuit modifications; one free parameter (the threshold) is introduced without reported sensitivity analysis.

free parameters (1)
  • predefined threshold
    Value above which a feature dependency triggers insertion of a controlled gate; no specific value or selection method given in abstract.
axioms (1)
  • domain assumption Controlled quantum gates can encode classical feature dependencies into quantum states in a way that improves classifier performance
    Invoked when the abstract states that dependencies are incorporated through controlled gates to build richer representations.

pith-pipeline@v0.9.1-grok · 5726 in / 1156 out tokens · 26539 ms · 2026-06-26T13:40:28.740446+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

40 extracted references · 20 canonical work pages

  1. [1]

    The Computer as a Physical System: A Microscopic Quantum Mechanical Hamil- tonianModelofComputersasRepresentedbyTuringMachines,

    P. Benioff, “The Computer as a Physical System: A Microscopic Quantum Mechanical Hamil- tonianModelofComputersasRepresentedbyTuringMachines,”Journal of Statistical Physics, 22(5), 563–591, 1980

    1980

  2. [2]

    Simulating Physics with Computers,

    R. P. Feynman, “Simulating Physics with Computers,”International Journal of Theoretical Physics, 21(6–7), 467–488, 1982

    1982

  3. [3]

    Quantum Theory, the Church–Turing Principle and the Universal Quantum Computer,

    D. Deutsch, “Quantum Theory, the Church–Turing Principle and the Universal Quantum Computer,”Proceedings of the Royal Society of London A, 400(1818), 97–117, 1985. 20

    1985

  4. [4]

    Quantum Information and Computation,

    C. H. Bennett, “Quantum Information and Computation,”Physics Today, 48(10), 24–30, 1995

    1995

  5. [5]

    Quantum Computing in the NISQ Era and Beyond,

    J. Preskill, “Quantum Computing in the NISQ Era and Beyond,”Quantum, 2, 79, 2018

    2018

  6. [6]

    NISQ Computers: A Path to Quantum Supremacy,

    M. AbuGhanem and H. Eleuch, “NISQ Computers: A Path to Quantum Supremacy,”IEEE Access, 12, 102941–102961, 2023

    2023

  7. [7]

    Quantum Artificial Intelligence: Enhancing Machine Learning with Quantum Com- puting,

    A. Lohia, “Quantum Artificial Intelligence: Enhancing Machine Learning with Quantum Com- puting,”Journal of Quantum Science and Technology, 1(2), 6–15, 2024

    2024

  8. [8]

    Quantum Artificial Intelligence: A Brief Survey,

    M. Klusch, J. Laessig, D. Muessig, A. Macaluso and F. K. Wilhelm, “Quantum Artificial Intelligence: A Brief Survey,”KI – Kuenstliche Intelligenz, 38(4), 509–520, 2024

    2024

  9. [9]

    Quantum Artificial Intelligence: A Survey,

    G. Acampora, A. Chiatto, R. Schiattarella and A. Vitiello, “Quantum Artificial Intelligence: A Survey,”Computer Science Review, 59, 100807, 2025

    2025

  10. [10]

    Survey of Encoding Techniques for Quantum Machine Learning,

    S. Sharma and R. N., “Survey of Encoding Techniques for Quantum Machine Learning,” Cybernetics and Physics, 13(2), 2024

    2024

  11. [11]

    Quantum Data Encoding: A Comparative Analysis of Classical-to- Quantum Mapping Techniques and Their Impact on Machine Learning Accuracy,

    M. Rath and H. Date, “Quantum Data Encoding: A Comparative Analysis of Classical-to- Quantum Mapping Techniques and Their Impact on Machine Learning Accuracy,”EPJ Quan- tum Technology, vol. 11, no. 1, p. 72, 2024

    2024

  12. [12]

    Beyond Bits: A Review of Quantum Embedding Techniques for Efficient Information Processing,

    M. A. Khan, M. N. Aman, and B. Sikdar, “Beyond Bits: A Review of Quantum Embedding Techniques for Efficient Information Processing,”IEEE Access, vol. 12, pp. 46118–46137, 2024. doi: 10.1109/ACCESS.2024.3382150

    work page doi:10.1109/access.2024.3382150 2024

  13. [13]

    Data Encoding Patterns for Quantum Computing,

    M. Weigold, J. Barzen, F. Leymann, and M. Salm, “Data Encoding Patterns for Quantum Computing,” inProceedings of the Pattern Languages of Programs Conference (PLoP), 2022, Article 2

    2022

  14. [14]

    Modeling Feature Maps for Quantum Machine Learning,

    N. Singh and S. R. Pokhrel, “Modeling Feature Maps for Quantum Machine Learning,”arXiv preprint arXiv:2501.08205, 2025

    arXiv 2025

  15. [15]

    Quantum Support Vector Machines for Classification and Regression on a Trapped-Ion Quantum Computer,

    T. Suzuki, T. Hasebe, and T. Miyazaki, “Quantum Support Vector Machines for Classification and Regression on a Trapped-Ion Quantum Computer,”Quantum Machine Intelligence, vol. 6, pp. 1–14, 2024. doi: 10.1007/s42484-024-00165-0

    work page doi:10.1007/s42484-024-00165-0 2024

  16. [16]

    The Effect of Linear Discriminant Analysis and Quantum Feature Maps on QSVM Performance for Obesity Diagnosis,

    Z. Ozpolat, O. Yildirim, and M. Karabatak, “The Effect of Linear Discriminant Analysis and Quantum Feature Maps on QSVM Performance for Obesity Diagnosis,”Balkan Journal of Electrical and Computer Engineering, 2024. doi: 10.17694/bajece.1475896

    work page doi:10.17694/bajece.1475896 2024

  17. [17]

    Experimental Kernel-Based Quantum Machine Learning in Finite Feature Space,

    K. Bartkiewicz, C. Gneiting, A. Cernoch, K. Jirakova, K. Lemr, and F. Nori, “Experimental Kernel-Based Quantum Machine Learning in Finite Feature Space,”Scientific Reports, vol. 10, no. 1, p. 12356, 2020. doi: 10.1038/s41598-020-68911-5

    work page doi:10.1038/s41598-020-68911-5 2020

  18. [18]

    Investigating Quantum Feature Maps in Quan- tumSupportVectorMachinesforLungCancerClassification,

    A. Toufah, M. A. Kadim, and M. Y. El Hafidi, “Investigating Quantum Feature Maps in Quan- tumSupportVectorMachinesforLungCancerClassification,”Journal of Artificial Intelligence Research and Innovation, vol. 1, no. 1, pp. 100–110, 2025. doi: 10.29328/journal.jairi.1001012

    work page doi:10.29328/journal.jairi.1001012 2025

  19. [19]

    Comparative Performance Analysis of Quantum Machine Learning Architectures for Credit Card Fraud Detection,

    M. El Alami, N. Innan, M. Shafique, and M. Bennai, “Comparative Performance Analysis of Quantum Machine Learning Architectures for Credit Card Fraud Detection,”Applied Intelli- gence, vol. 56, p. 83, 2026. doi: 10.1007/s10489-026-07110-7. 21

    work page doi:10.1007/s10489-026-07110-7 2026

  20. [20]

    Practical Application of Quantum Neural Network to Materials Informatics,

    H. Hirai, “Practical Application of Quantum Neural Network to Materials Informatics,”Sci- entific Reports, vol. 14, p. 8583, 2024. doi: 10.1038/s41598-024-59276-0

    work page doi:10.1038/s41598-024-59276-0 2024

  21. [21]

    A Hybrid Quantum-Classical Neural Network Architecture for Binary Classification,

    D. Arthur and P. Date, “A Hybrid Quantum-Classical Neural Network Architecture for Binary Classification,”arXiv preprint arXiv:2201.01820, 2022

    arXiv 2022

  22. [22]

    Quantum Machine Learning—An Overview,

    K. A. Tychola, T. Kalampokas, and G. A. Papakostas, “Quantum Machine Learning—An Overview,”Electronics, vol. 13, no. 3, p. 560, 2024. doi: 10.3390/electronics13030560

    work page doi:10.3390/electronics13030560 2024

  23. [23]

    A Survey on Quantum Machine Learning Applications in Medicine and Healthcare,

    R. Idzikowski, M. A. Kucharski, K. Pempera, and M. Jaroszczuk, “A Survey on Quantum Machine Learning Applications in Medicine and Healthcare,”Applied Sciences, vol. 16, no. 3, p. 1630, 2026. doi: 10.3390/app16031630

    work page doi:10.3390/app16031630 2026

  24. [24]

    Advancing EEG Signal Analysis with Quantum Machine Learn- ing,

    S. A. Murray and E. Parsons, “Advancing EEG Signal Analysis with Quantum Machine Learn- ing,”arXiv preprint arXiv:2409.11462, 2024

    arXiv 2024

  25. [25]

    Forging the Future: Strategic Approaches to Quantum AI Integration for Industry Transformation,

    M.-L. How and S.-M. Cheah, “Forging the Future: Strategic Approaches to Quantum AI Integration for Industry Transformation,”AI, vol. 5, no. 1, pp. 290–323, 2024. doi: 10.3390/ai5010015

    work page doi:10.3390/ai5010015 2024

  26. [26]

    Future Use of Quantum Artificial Intelligence in Military Do- mains,

    M. Bures and P. Frantis, “Future Use of Quantum Artificial Intelligence in Military Do- mains,” in2024 International Conference on Military Technologies (ICMT), pp. 1–6, 2024. doi: 10.1109/ICMT60383.2024.10579948

    work page doi:10.1109/icmt60383.2024.10579948 2024

  27. [27]

    The proof and measurement of association between two 11 things,

    C. Spearman, “The Proof and Measurement of Association Between Two Things,”The Amer- ican Journal of Psychology, vol. 15, no. 1, pp. 72–101, 1904. doi: 10.2307/1412159

    work page doi:10.2307/1412159 1904

  28. [28]

    Comparing the Pearson and Spearman Correlation Coefficients Across Distributions and Sample Sizes: A Tutorial Using Simulations and Empirical Data,

    J. C. F. de Winter, S. D. Gosling, and J. Potter, “Comparing the Pearson and Spearman Correlation Coefficients Across Distributions and Sample Sizes: A Tutorial Using Simulations and Empirical Data,”Psychological Methods, vol. 21, no. 3, pp. 273–290, 2016

    2016

  29. [29]

    On the Kendall Correlation Coefficient,

    A. Stepanov, “On the Kendall Correlation Coefficient,”arXiv preprint, 2015

    2015

  30. [30]

    Mutual Information: A Way to Quantify Correlations,

    M. Tisoc and J. V. Beltran, “Mutual Information: A Way to Quantify Correlations,”Revista Brasileira de Ensino de Física, vol. 44, p. e20220055, 2022. doi: 10.1590/1806-9126-RBEF- 2022-0055

    work page doi:10.1590/1806-9126-rbef- 2022

  31. [31]

    On Relationships Between the Pearson and the Distance Correlation Coefficients,

    D. Edelmann, T. F. Mori, and G. J. Szekely, “On Relationships Between the Pearson and the Distance Correlation Coefficients,”Statistics Probability Letters, vol. 169, p. 108960, 2021. doi: 10.1016/j.spl.2020.108960

    work page doi:10.1016/j.spl.2020.108960 2021

  32. [32]

    Variational quantum algorithms,

    M. Cerezo, A. Arrasmith, R. Babbush, S. C. Benjamin, S. Endo, K. Fujii, J. R. McClean, K. Mitarai, X. Yuan, L. Cincio, and P. J. Coles, “Variational Quantum Algorithms,”Nature Reviews Physics, vol. 3, no. 9, pp. 625–644, 2021. doi: 10.1038/s42254-021-00348-9

    work page doi:10.1038/s42254-021-00348-9 2021

  33. [33]

    Variational Quantum Algorithms: Fundamental Concepts, Applications and Challenges,

    H. Qi, S. Xiao, Z. Liu, C. Gong, and A. Gani, “Variational Quantum Algorithms: Fundamental Concepts, Applications and Challenges,”Quantum Information Processing, vol. 23, no. 6, p. 224, 2024. doi: 10.1007/s11128-024-04438-2

    work page doi:10.1007/s11128-024-04438-2 2024

  34. [34]

    Hambye, M

    S. Endo, J. Sun, Y. Li, S. C. Benjamin, and X. Yuan, “Variational Quantum Simulation of Gen- eral Processes,”Physical Review Letters, vol. 125, no. 1, p. 010501, 2020. doi: 10.1103/Phys- RevLett.125.010501. 22

    work page doi:10.1103/phys- 2020

  35. [35]

    Towards Efficient Ansatz Architecture for Variational Quantum Algorithms,

    A. Wu, G. Li, Y. Wang, B. Feng, Y. Ding, and Y. Xie, “Towards Efficient Ansatz Architecture for Variational Quantum Algorithms,”arXiv preprint arXiv:2111.13730, 2021

    arXiv 2021

  36. [36]

    When do neural networks outperform kernel methods?*

    J. Qin, “Review of Ansatz Designing Techniques for Variational Quantum Algorithms,”Jour- nal of Physics: Conference Series, vol. 2634, no. 1, p. 012043, 2023. doi: 10.1088/1742- 6596/2634/1/012043

    work page doi:10.1088/1742- 2023

  37. [37]

    Variational Quantum Classifier for Binary Classification: Real vs Synthetic Dataset,

    D. Maheshwari, D. Sierra-Sosa, and B. Garcia-Zapirain, “Variational Quantum Classifier for Binary Classification: Real vs Synthetic Dataset,”IEEE Access, vol. 10, pp. 3705–3715, 2022. doi: 10.1109/ACCESS.2021.3139323

    work page doi:10.1109/access.2021.3139323 2022

  38. [38]

    A Review of Quantum Neural Networks: Methods, Models, Dilemma,

    R. Zhao and S. Wang, “A Review of Quantum Neural Networks: Methods, Models, Dilemma,” arXiv preprint arXiv:2109.01840, 2021

    arXiv 2021

  39. [39]

    The Quest for a Quantum Neural Network,

    M. Schuld, I. Sinayskiy, and F. Petruccione, “The Quest for a Quantum Neural Network,” Quantum Information Processing, vol. 13, pp. 2567–2586, 2014

    2014

  40. [40]

    Training Deep Quantum Neural Networks,

    K. Beer, D. Bondarenko, T. Farrelly, T. J. Osborne, R. Salzmann, D. Scheiermann, and R. Wolf, “Training Deep Quantum Neural Networks,”Nature Communications, vol. 11, no. 1, p. 808, 2020. doi: 10.1038/s41467-020-14454-2. 23

    work page doi:10.1038/s41467-020-14454-2 2020