Pith. sign in

REVIEW 5 major objections 4 minor 40 references

QSVM-RQNN: Low-Qubit Recurrent Quantum Similarity Learning for Condition Monitoring and Fault Classification

T0 review · 5 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A three-qubit quantum classifier matches or beats larger quantum models on fault diagnosis.

desk verdict A coherent low-qubit QML pipeline with honest reporting, but the empirical state-of-the-art claim is not supported by the paper's own statistics; worth refereeing with major revision. read the letter →

arxiv 2608.09652 v1 pith:W5QKZBN7 submitted 2026-08-10 quant-ph

Amit S. Patel , Himanshu R. Patel , Bikash K. Behera This is my paper · ORCID
classification quant-ph MSC 81P6868T05
keywords quantummachinelearningrecurrentneuralnetworksupportvectorcentroidsimilarityfaultdiagnosisconditionmonitoringclassimbalanceQSMOTE
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

The paper argues that fault classification on noisy quantum hardware does not require wide circuits: by reducing each sample to eight principal components, splitting them into four timesteps, and feeding them through a fixed three-qubit recurrent circuit whose parameters are shared across timesteps, a classifier can match or beat larger quantum models. The two proposed variants, QSVM-RQNN-V1 and QSVM-RQNN-V2, differ in where centroid-based quantum similarity enters, but both keep the qubit count fixed at three and the trainable parameters at 12–14. Across four industrial fault datasets, the authors report that QSVM-RQNN-V1 achieves the best average rank among nine quantum classifiers and the highest F1 scores on two of the four datasets, with the largest gains on minority fault classes after QSMOTE balancing. The authors claim this is the first unified framework combining centroid-based quantum similarity learning, recurrent quantum processing, and class balancing in a low-qubit architecture.

What carries the argument

The load-bearing identity is the squared fidelity between an encoded input segment and a class-centroid segment, $P_c^{(t)}=|\langle 000| U_{\mathrm{enc}}(c_c^{(t)})^\dagger U_{\mathrm{enc}}(z^{(t)}) |000\rangle|^2$, which replaces an explicit $N\times N$ quantum kernel matrix with two centroid comparisons per timestep. This similarity is either used after a full recurrent pass (V1) or fed as input features to a recurrent classifier (V2). The recurrent block is a fixed three-qubit circuit, $U_{\mathrm{RQNN}}=U_{\mathrm{Ent}}U_{RZ}U_{RY}$, whose parameters are reused across all timesteps, giving $P=2Ln_q=12$ parameters for V1 and $7L=14$ for V2. PCA reduction to $d_r=8$ features and partition into $T=4$ timesteps keeps the encoding fixed at three qubits.

What would settle it

Run each of the nine models on the same PCA-reduced features across, say, 30 independent QSMOTE resamplings and random initializations, and compute the distribution of F1 differences between QSVM-RQNN-V1 and the next-best model (RQNN-V1 or QSVM-QNN). If the 95% confidence interval of the difference contains zero, or if a simple classical baseline such as a random forest on the same eight PCA features matches or exceeds the quantum models' F1, then the claimed advantage is not established.

Watch

Extended reading notes

Core claim

The central claim is that integrating centroid-based quantum similarity learning with recurrent quantum representation learning yields a resource-efficient classifier that is competitive with, and in several cases better than, standalone QSVM, QNN, QCNN, RQNN, and hybrid QSVM-QNN and QSVM-QCNN models. In QSVM-RQNN-V1, the input and the class centroid are jointly encoded at each timestep and processed by the shared recurrent circuit; classification uses the normalized probabilities of measuring the all-zero state after the full sequence. In QSVM-RQNN-V2, per-timestep quantum overlaps with two centroids are computed first and fed to a three-qubit recurrent classifier with softmax output. On the CWRUBD and EFDD datasets, V1 attains the highest post-QSMOTE F1 scores (0.9183 and 0.6993), and V1 has the best average Friedman rank (2.750) across all four datasets, although the Friedman test does not reach significance (p = 0.1382). The architecture also shows gradual, rather than abrupt, F1 degradation under six quantum noise channels.

Load-bearing premise

The state-of-the-art claim rests on the assumption that selecting the best-performing encoding for each model and dataset, combined with a single QSMOTE-generated balanced set, produces stable and fair performance estimates; the paper's own Friedman test (p = 0.1382) and its admission that QSMOTE generates different datasets across runs leave this assumption unresolved.

Editorial extensions

If this is right

  • If correct, high-dimensional industrial data can be classified on NISQ devices using a fixed three-qubit circuit, since only the sequence length changes with input dimensionality.
  • The centroid-similarity mechanism removes the need to build and invert a quantum kernel matrix, reducing similarity cost from $O(N^2)$ to $O(T)$ per sample.
  • Recurrent parameter sharing keeps trainable parameters constant in sequence length, mitigating the optimization and noise issues of deep wide circuits.
  • The consistent recall gains after QSMOTE suggest that quantum classifiers can be made usable on imbalanced fault datasets without enlarging the circuit.
  • The noise-robustness curves indicate that phase-damping and phase-flip channels barely degrade F1, which is relevant for realistic hardware operation.

Reading between the lines

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

  • A testable extension is to replace the fixed centroids with learned or adaptive prototypes, which could improve V1's similarity signal on datasets where the class-conditional distributions are multimodal.
  • Because the paper reports the best of four encodings per model and dataset, and QSMOTE is stochastic, the precise F1 gaps are likely smaller than the tables suggest; a repeated-seed study with confidence intervals would settle which rankings are real.
  • The same centroid-similarity-plus-recurrent scheme could be applied to regression or anomaly detection, where the positive class is rare and the centroid of normal operation is well defined.
  • The fixed three-qubit register bounds the entangling capability, so for datasets with strong feature interactions a wider register with the same recurrent sharing would be the next natural comparison.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 4 minor

Summary. The paper proposes QSVM-RQNN, a hybrid quantum-classical framework for binary fault classification that combines PCA-based dimensionality reduction, QSMOTE class balancing, centroid-based quantum similarity scores, and a fixed three-qubit recurrent quantum circuit with shared parameters. Two variants are presented: V1 uses class-conditioned recurrent similarity scores with threshold-based classification, and V2 feeds timestep-wise overlap features into a recurrent quantum classifier with Softmax outputs. The framework is evaluated on four public benchmark datasets against QSVM, QNN, QCNN, QSVM-QNN, QSVM-QCNN, and RQNN baselines, with additional noise-robustness, ablation, efficiency, and ranking analyses. The central claim is that the proposed architecture achieves competitive and, in several cases, state-of-the-art performance while using only 12-14 trainable parameters and three qubits.

Significance. If the performance claim were statistically established, the paper would make a useful contribution to resource-efficient quantum machine learning for imbalanced industrial condition monitoring. The architectural idea of integrating centroid-based similarity learning with parameter-shared recurrent processing on a fixed three-qubit circuit is clearly presented, with explicit circuit equations, pseudocode for both variants, and a complexity analysis that correctly identifies O(L) forward cost and O(KNT L) training cost. The inclusion of recall and false-negative metrics, noise-channel robustness experiments, and an ablation study are appropriate strengths. However, the central empirical claim currently rests on single-run, best-of-four encoding selections and a non-significant cross-dataset statistical test, so the significance of the reported performance advantage is not yet established.

major comments (5)
  1. [Section IV-D and Tables III-VI] The evaluation protocol selects 'the best-performing data encoding strategy for each model based on classification performance' without describing a nested validation procedure for that selection. Each reported row in Tables III-VI is therefore a maximum over four encoding choices, which inflates all models and makes the observed F1 differences unreliable as estimates of true model performance. The encoding-selection step should be performed inside cross-validation or on a validation split that is never used for the final test metric; otherwise the central comparison is biased by selection on the test set.
  2. [Sections IV-H, IV-I and Tables III-X] QSMOTE is explicitly acknowledged to be stochastic, and the robustness and ablation experiments use independently generated balanced datasets with no reported seeds or repeated runs. The same default configuration of QSVM-RQNN-V1 yields materially different F1 scores across tables: 0.7632 on SPID in Table III versus 0.7561 in Table IX and 0.7945 in Table X, and 0.9183 on CWRUBD in Table IV versus 0.9670 in Table IX. These differences show that the main-table results are single draws from a stochastic pipeline, yet no confidence intervals, repeated trials, or seed-controlled reproductions are reported. Gaps as small as 0.0064 F1 on EFDD cannot be distinguished from this sampling noise.
  3. [Section IV-J, Table XIII] The Friedman test over the four post-QSMOTE F1 values gives p=0.1382, which the paper itself acknowledges is not significant. The subsequent ranking discussion nevertheless uses the average ranks (QSVM-RQNN-V1 at 2.750) to support the claim of consistent superiority. With only four datasets and a non-significant omnibus test, the ranking ordering is not statistically supported. The authors should either temper the consistency claim, add repeated-run data that permits paired comparisons, or include additional datasets to achieve adequate statistical power.
  4. [Section III-E, Eqs. (36)-(44)] The central recurrent circuit definition is internally inconsistent. Equation (37) defines |psi_t> = U_RQNN(Theta)|psi_t^(0)> with |psi_t^(0)> = U_enc(z^(t))|000>, which describes independent per-timestep processing with no dependence on |psi_{t-1}>. Equation (44), by contrast, defines |psi_t> = [product of recurrent layers] U_enc(xi^(t)) |psi_{t-1}>, which is the genuine recurrent update used in Algorithms 1 and 2. The manuscript should reconcile these equations; as written, the mathematical definition of the purported recurrent architecture is ambiguous.
  5. [Section III-F and Section III-G] The name 'QSVM' is used for a method that computes centroid-state overlaps and never performs support-vector optimization or kernel-matrix construction. This is a terminology and conceptual-accuracy issue: the method is closer to a quantum nearest-centroid or fidelity-based similarity classifier. The authors should either rename the component or explicitly state that 'QSVM' is used only as a similarity-estimation heuristic, not as a support vector machine.
minor comments (4)
  1. [Section IV-B] The preprocessing description states that features are 'standardized and reduced to eight-dimensional representation using PCA' but does not explicitly state whether the PCA transformation is fitted on the training split only. The authors should clarify this to rule out test information leaking through the PCA projection.
  2. [Section IV-D] The hyperparameter section reports random_state=42 for variational models but gives no equivalent reproducibility control for QSMOTE or for the COBYLA initialization and threshold selection. A complete seed specification, or repeated-seed reporting, would substantially improve reproducibility.
  3. [Section IV-H] The noise-robustness analysis is restricted to the two proposed variants, while baseline models are not evaluated under the same noise conditions. The discussion should state this asymmetry explicitly in the main text rather than only in the narrative.
  4. [Tables IX-XII] The ablation tables do not report the encoding strategy used for each configuration, so it is unclear whether the best encoding was re-selected for each T and L or held fixed from the main experiments. This should be stated.

Circularity Check

0 steps flagged · score 2.0 of 10

No circular derivation: the QSVM-RQNN pipeline is self-contained and empirically evaluated; only minor non-load-bearing self-citations exist.

full rationale

The paper's contribution is an empirical architecture: PCA preprocessing, QSMOTE balancing, centroid-based similarity (Eqs. 25-35), a shared-parameter recurrent circuit (Eqs. 36-44), and two decision rules (Eqs. 48-55 and 59-70) are all defined from first principles within the paper and trained on a training split with COBYLA while test metrics are reported on held-out data. The central state-of-the-art claim is therefore a benchmark comparison, not a derivation that assumes its own conclusion. The self-citations to QSMOTE [21] and QSVM-QNN [22], both co-authored by B. K. Behera, are used respectively as a preprocessing tool and as a comparison baseline; neither supplies the load-bearing evidence for the new architecture. The non-significant Friedman test (p=0.1382) and the best-of-four encoding selection in Section IV-D are methodological/statistical weaknesses that could inflate apparent gains, but they do not make the reported F1 values equal by construction to a fitted input. Accordingly, no concrete circular step can be exhibited, and the appropriate score is 2 for the minor, non-load-bearing self-citations.

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

The paper contributes a pipeline architecture rather than a derivation. The central performance claim depends on hand-selected hyperparameters (d_r = 8, T = 4, L = 2), post hoc encoding choice, stochastic QSMOTE, and the assumption that quantum overlap with class centroids and the chosen baselines define a meaningful state-of-the-art comparison. No new physical entities are introduced.

free parameters (5)
  • Trainable recurrent parameters Theta (V1: 12, V2: 14) = COBYLA-optimized
    Learned from training data via the weighted negative log-likelihood objective and central to each classifier.
  • Best encoding per dataset and model = raw, arctan, arccos, or arcsin as reported in Tables III-VI
    Chosen by best classification performance among four encodings; post hoc selection affects the reported metrics.
  • Decision threshold tau = Validation F1-optimized threshold
    Selected per dataset on the validation split as part of the decision rule in Equation (54).
  • PCA dimension d_r, timesteps T, recurrent depth L = 8, 4, 2
    Fixed by hand in Sections III-C and IV-D; ablations show the optimal T and L vary by dataset, so the default is not universally justified.
  • QSMOTE oversampling parameters = not specified
    The stochastic oversampling procedure is not parameterized in the paper, yet it changes the balanced dataset between independent executions.
assumptions (5)
  • ad hoc to paper PCA-reduced dimension d_r = 8 preserves enough discriminative information for fault diagnosis.
    The choice is fixed by hand with no comparison across reduced dimensions or evidence that the discarded variance is not class-discriminative.
  • domain assumption Squared fidelity between an encoded sample and a class centroid is a useful similarity measure for classification.
    Used in Equations (29) and (59); it is a standard overlap measure, but no justification shows it is discriminative for these datasets.
  • domain assumption QSMOTE generates valid synthetic minority samples in the PCA-reduced feature space.
    Adopted from reference [21] without local validation on these four datasets, and the paper states the results depend on stochastic oversampling.
  • domain assumption Classical statevector simulation faithfully represents the proposed circuits.
    All results come from simulation; no real hardware validation is reported, and device noise is modeled only through hand-picked channels.
  • domain assumption The chosen quantum and hybrid quantum models are representative baselines for a state-of-the-art comparison.
    The comparison is limited to quantum models; no classical SVM, random forest, CNN, or LSTM baselines are included.

how reviews work

0 comments
Cite this review

Pith. "Pith review of QSVM-RQNN: Low-Qubit Recurrent Quantum Similarity Learning for Condition Monitoring and Fault Classification." pith.science (2026). https://pith.science/paper/W5QKZBN7

@misc{pith2026260809652,
  author       = {Pith},
  title        = {Pith review of: QSVM-RQNN: Low-Qubit Recurrent Quantum Similarity Learning for Condition Monitoring and Fault Classification},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/W5QKZBN7}},
  note         = {Machine review of arXiv:2608.09652}
}
read the original abstract

In the Noisy Intermediate-Scale Quantum (NISQ) era, limited qubit availability and hardware noise constrain the practical deployment of quantum machine learning (QML). Existing quantum neural network (QNN) and quantum convolutional neural network (QCNN) architectures often require increasing quantum resources as the input dimension grows, limiting scalability on near-term devices. We propose QSVM-RQNN, a low-qubit framework integrating centroid-based Quantum Support Vector Machine (QSVM) similarity learning with Recurrent Quantum Neural Networks (RQNNs) for fault classification. The framework reduces the feature space using principal component analysis (PCA), partitions the reduced representation into sequential timesteps, and processes them using a compact three-qubit recurrent quantum architecture with shared parameters. Two complementary variants are developed: QSVM-RQNN-V1 performs class-conditioned joint quantum encoding of input and centroid segments, whereas QSVM-RQNN-V2 performs recurrent learning over timestep-wise quantum similarity representations. Experimental evaluation on multiple fault diagnosis datasets shows competitive and, in several cases, state-of-the-art performance compared with QSVM, QNN, QCNN, QSVM-QNN, QSVM-QCNN, and RQNN models. The proposed architectures provide favorable performance-efficiency trade-offs, improved recall, and enhanced fault detection on highly imbalanced datasets. These results demonstrate that integrating centroid-based quantum similarity learning with low-qubit recurrent representation learning provides an effective and scalable approach to condition monitoring and fault classification on resource-constrained NISQ devices.

Figures

Figures reproduced from arXiv: 2608.09652 by the authors.

Figure 1
Figure 1. Conceptual overview of the proposed QSVM-RQNN framework. High-dimensional industrial data are first transformed into compact [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Overall workflow of the proposed QSVM-RQNN framework. The pipeline consists of data preprocessing (normalization, PCA, and [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Architectural comparison of the proposed QSVM-RQNN variants. (a) [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Noise robustness analysis of the proposed QSVM-RQNN variants on the SPID dataset after QSMOTE. The F1-score is evaluated [PITH_FULL_IMAGE:figures/full_fig_p020_4.png]
Figure 5
Figure 5. Figure 5: Noise robustness analysis of the proposed QSVM-RQNN variants on the CWRUBD dataset after QSMOTE. The F1-score is evaluated [PITH_FULL_IMAGE:figures/full_fig_p020_5.png]
Figure 6
Figure 6. Figure 6: Robustness analysis of the proposed QSVM-RQNN architectures on the EFDD dataset after QSMOTE under six quantum noise [PITH_FULL_IMAGE:figures/full_fig_p021_6.png]
Figure 7
Figure 7. Figure 7: Noise robustness analysis of the proposed QSVM-RQNN variants on the IFDD dataset after QSMOTE. The F1-score is evaluated [PITH_FULL_IMAGE:figures/full_fig_p021_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

40 extracted references · 21 canonical work pages

  1. [1]

    A cyber-physical systems architecture for industry 4.0-based manufacturing systems,

    J. Lee, B. Bagheri, and H.-A. Kao, “A cyber-physical systems architecture for industry 4.0-based manufacturing systems,” Manufacturing Letters, vol. 3, pp. 18–23, 2015. [Online]. Available: https://doi.org/10.1016/j.mfglet.2014.12.001

    doi:10.1016/j.mfglet.2014.12.001 2015

  2. [2]

    A review of deep learning-based fault diagnosis techniques for axlebox bearings in rail vehicles,

    L. Wu and X. Sun, “A review of deep learning-based fault diagnosis techniques for axlebox bearings in rail vehicles,” in2025 IEEE International Conference on Intelligent Rail Transportation (ICIRT). Beijing, China: IEEE, 2025, conference held October 11–12, 2025. [Online]. Available: https://ieeexplore.ieee.org/document/11216733

    work page arXiv 2025

  3. [3]

    Industrial big data in an industry 4.0 environment: Challenges, schemes, and applications for predictive maintenance,

    J. Yan, Y . Meng, L. Lu, and L. Li, “Industrial big data in an industry 4.0 environment: Challenges, schemes, and applications for predictive maintenance,”IEEE Access, vol. 5, pp. 23 484–23 491, 2017. [Online]. Available: https://ieeexplore.ieee.org/document/8085101

    work page arXiv 2017

  4. [4]

    Deep learning,

    Y . LeCun, Y . Bengio, and G. Hinton, “Deep learning,”Nature, vol. 521, pp. 436–444, 2015. [Online]. Available: https://doi.org/10.1038/ nature14539

    work page 2015

  5. [5]

    Goodfellow, Y

    I. Goodfellow, Y . Bengio, and A. Courville,Deep Learning. Cambridge, MA: MIT Press, 2016. [Online]. Available: https: //www.deeplearningbook.org

    work page 2016

  6. [6]

    Deep learning in medical ultrasound image analysis: A review,

    Y . Wang, X. Ge, H. Ma, S. Qi, G. Zhang, and Y . Yao, “Deep learning in medical ultrasound image analysis: A review,” IEEE Access, vol. 9, pp. 54 310–54 324, 2021. [Online]. Available: https://ieeexplore.ieee.org/document/9395635

    work page arXiv 2021

  7. [7]

    M. A. Nielsen and I. L. Chuang,Quantum Computation and Quantum Information. Cambridge University Press, 2010. [Online]. Available: https://doi.org/10.1017/CBO9780511976667

    doi:10.1017/cbo9780511976667 2010

  8. [8]

    Quantum Computing in the NISQ era and beyond,

    J. Preskill, “Quantum Computing in the NISQ era and beyond,” Quantum, vol. 2, p. 79, Aug. 2018. [Online]. Available: https: //doi.org/10.22331/q-2018-08-06-79

    doi:10.22331/q-2018-08-06-79 2018

Show all 40 references
  1. [9]

    An introduction to quantum machine learning,

    M. Schuld, I. Sinayskiy, and F. Petruccione, “An introduction to quantum machine learning,”Contemporary Physics, vol. 56, no. 2, pp. 172–185, 2015. [Online]. Available: https://doi.org/10.1080/00107514. 2014.964942

    2015

  2. [10]

    Quantum machine learning,

    J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, “Quantum machine learning,”Nature, vol. 549, pp. 195–202,

  3. [11]

    Schuld and F

    M. Schuld and F. Petruccione,Machine Learning with Quantum Computers. Springer, 2021. [Online]. Available: https://doi.org/10. 1007/978-3-030-83098-4

    2021

  4. [12]

    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, pp. 625–644, 2021. [Online]. Available: https: //doi.org/10.1038/s42254-021-00348-9

    2021 doi

  5. [13]

    Classification with quantum neural networks on near term processors,

    E. Farhi and H. Neven, “Classification with quantum neural networks on near term processors,”arXiv preprint arXiv:1802.06002, 2018. [Online]. Available: https://doi.org/10.48550/arXiv.1802.06002

    2018 doi arXiv

  6. [14]

    Quantum convolutional neural networks,

    I. Cong, S. Choi, and M. Lukin, “Quantum convolutional neural networks,”Nature Physics, vol. 15, pp. 1273–1278, 2019. [Online]. Available: https://doi.org/10.1038/s41567-019-0648-8

    2019 doi

  7. [15]

    Supervised learning with quantum- enhanced feature spaces,

    V . Havl ´ıˇcek, A. D. C ´orcoles, K. Temme, A. W. Harrow, A. Kandala, J. M. Chow, and J. M. Gambetta, “Supervised learning with quantum- enhanced feature spaces,”Nature, vol. 567, pp. 209–212, 2019. [Online]. Available: https://doi.org/10.1038/s41586-019-0980-2

    2019 doi

  8. [16]

    Quantum machine learning in feature hilbert spaces,

    M. Schuld and N. Killoran, “Quantum machine learning in feature hilbert spaces,”Physical Review Letters, vol. 122, no. 4, p. 040504, 2019. [Online]. Available: https://doi.org/10.1103/PhysRevLett.122.040504

    2019 doi

  9. [17]

    Circuit-centric quantum classifiers,

    M. Schuld, A. Bocharov, K. Svore, and N. Wiebe, “Circuit-centric quantum classifiers,”Physical Review A, vol. 101, p. 032308, 2020. [Online]. Available: https://doi.org/10.1103/PhysRevA.101.032308

    2020 doi

  10. [18]

    Barren plateaus in quantum neural network training landscapes,

    J. R. McClean, S. Boixo, R. Smelyanskiy, R. Babbush, and H. Neven, “Barren plateaus in quantum neural network training landscapes,” Nature Communications, vol. 9, p. 4812, 2018. [Online]. Available: https://doi.org/10.1038/s41467-018-07090-4

    2018 doi

  11. [19]

    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, p. 808, 2020. [Online]. Available: https://doi.org/10.1038/s41467-020-14454-2

    2020 doi

  12. [20]

    The power of quantum neural networks,

    A. Abbas, D. Sutter, C. Zoufal, A. Lucchi, A. Figalli, and S. Woerner, “The power of quantum neural networks,”Nature Computational Science, vol. 1, pp. 403–409, 2021. [Online]. Available: https://doi.org/10.1038/s43588-021-00084-1

    2021 doi

  13. [21]

    A quantum approach to synthetic minority oversampling technique (smote),

    N. Mohanty, B. K. Behera, C. Ferrie, and P. Dash, “A quantum approach to synthetic minority oversampling technique (smote),”Quantum Machine Intelligence, vol. 7, no. 1, p. 38, 2025. [Online]. Available: https://link.springer.com/article/10.1007/s42484-025-00248-6

    2025 doi

  14. [22]

    QSVM-QNN: Quantum support vector machine based quantum neural network learning algorithm for brain–computer interfacing systems,

    B. K. Behera, S. Al-Kuwari, and A. Farouk, “QSVM-QNN: Quantum support vector machine based quantum neural network learning algorithm for brain–computer interfacing systems,”IEEE Transactions on Artificial Intelligence, vol. 7, no. 1, pp. 308–320, 2025. [Online]. Available: htt...

    2025

  15. [23]

    Support-vector networks,

    C. Cortes and V . Vapnik, “Support-vector networks,”Machine Learning, vol. 20, pp. 273–297, 1995. [Online]. Available: https: //doi.org/10.1007/BF00994018

    1995 doi

  16. [24]

    An overview of statistical learning theory,

    V . N. Vapnik, “An overview of statistical learning theory,”IEEE Transactions on Neural Networks, vol. 10, no. 5, pp. 988–999, Sep

  17. [25]

    Support vector machine in machine condition monitoring and fault diagnosis,

    A. Widodo and B.-S. Yang, “Support vector machine in machine condition monitoring and fault diagnosis,”Mechanical Systems and Signal Processing, vol. 21, no. 6, pp. 2560–2574, 2007. [Online]. Available: https://doi.org/10.1016/j.ymssp.2006.12.007

    2007 doi

  18. [26]

    Fault diagnosis of rolling bearings based on GA-SVM model,

    W. Zhao, Y . Lv, J. Xiao, and Y . Li, “Fault diagnosis of rolling bearings based on GA-SVM model,” in2021 Global Reliability and Prognostics and Health Management (PHM-Nanjing). Nanjing, China: IEEE, 2021, conference held October 15–17, 2021. [Online]. Available: https://ieeex...

    2021

  19. [27]

    Quantum support vector machine for big data classification,

    P. Rebentrost, M. Mohseni, and S. Lloyd, “Quantum support vector machine for big data classification,”Physical Review Letters, vol. 113, p. 130503, 2014. [Online]. Available: https://doi.org/10.1103/ PhysRevLett.113.130503

    2014

  20. [28]

    Rolling bearing fault diagnosis based on quantum ls-svm,

    Y . Li, L. Song, Q. Sun, H. Xu, X. Li, Z. Fang, and W. Yao, “Rolling bearing fault diagnosis based on quantum ls-svm,”EPJ Quantum Technology, vol. 9, p. 18, 2022. [Online]. Available: https://doi.org/10.1140/epjqt/s40507-022-00137-y

    2022 doi

  21. [29]

    An advanced quantum support vector machine for power quality disturbance detection and identification,

    Q.-L. Wang, Y . Jin, X.-H. Li, Y . Li, Y .-C. Li, K.-J. Zhang, H. Liu, and L. Cheng, “An advanced quantum support vector machine for power quality disturbance detection and identification,” EPJ Quantum Technology, vol. 11, p. 70, 2024. [Online]. Available: https://doi.org/10.1...

    2024 doi

  22. [30]

    Solving industrial fault diagnosis problems with quantum computers,

    A. Diedrich, S. Windmann, and O. Niggemann, “Solving industrial fault diagnosis problems with quantum computers,”Quantum Machine Intelligence, vol. 6, p. 66, 2024. [Online]. Available: https://doi.org/10. 1007/s42484-024-00184-x

    2024

  23. [31]

    From quantum feature maps to quantum reservoir computing: Perspectives and applications,

    C. Gyurik, F. Wudarski, E. Philip, A. Sannia, H. Sadeghi, O. Kyriienko, D. Venturelli, and A. A. Gentile, “From quantum feature maps to quantum reservoir computing: Perspectives and applications,” arXiv preprint arXiv:2510.01797, 2025. [Online]. Available: https: //doi.org/10....

    doi

  24. [32]

    Harnessing disordered quantum dynamics for machine learning,

    K. Fujii and K. Nakajima, “Harnessing disordered quantum dynamics for machine learning,”Physical Review Applied, vol. 8, no. 2, p. 024030,

  25. [33]

    Solar panel images dataset,

    P. Afroz, “Solar panel images dataset,” https://www.kaggle.com/datasets/ pythonafroz/solar-panel-images, 2023, accessed: 2025-09-01

    2023

  26. [34]

    Cwru bearing datasets,

    brjapon, “Cwru bearing datasets,” https://www.kaggle.com/datasets/ brjapon/cwru-bearing-datasets, kaggle dataset. Accessed: 2025-09-26

    2025

  27. [35]

    Available: https://doi.org/10.1103/PhysRevApplied.8

    [Online]. Available: https://doi.org/10.1103/PhysRevApplied.8. 024030

    doi

  28. [36]

    Industrial fault detection dataset,

    Programmer3, “Industrial fault detection dataset,” https://www.kaggle. com/datasets/programmer3/industrial-fault-detection-dataset, 2024, ac- cessed: October 2025

    2024

  29. [37]

    Analysis of the vehicle routing problem solved via hybrid quantum algorithms in the presence of noisy channels,

    N. Mohanty, B. K. Behera, and C. Ferrie, “Analysis of the vehicle routing problem solved via hybrid quantum algorithms in the presence of noisy channels,”IEEE Transactions on Quantum Engineering, vol. 4, pp. 1–14, 2023. [Online]. Available: https: //ieeexplore.ieee.org/documen...

    2023

  30. [38]

    Engine failure detection dataset,

    ziya07, “Engine failure detection dataset,” https://www.kaggle.com/ datasets/ziya07/engine-failure-detection-dataset, kaggle dataset. Ac- cessed: 2025-09-30

    2025

  31. [1999]

    Available: https://doi.org/10.1109/72.788640

    [Online]. Available: https://doi.org/10.1109/72.788640

    doi

  32. [2017]

    Available: https://www.nature.com/articles/nature23474

    [Online]. Available: https://www.nature.com/articles/nature23474

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.