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REVIEW 3 major objections 6 minor 5 cited by

Robust Decentralized Quantum Kernel Learning for Noisy and Adversarial Environment

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

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Pith's one-line read Decentralized quantum kernel learning remains accurate and reaches consensus even when some nodes are very noisy or adversarial.

desk verdict RDQKL is a modest but honest extension of CDQKL: Eq. (21) checks out, the defense works on the two tested attacks, but the adversarial claim is scoped too broadly and the noisy-node averages are selective. read the letter →

arxiv 2504.13782 v1 pith:KGTCDB4E submitted 2025-04-18 quant-ph cs.DC

Wenxuan Ma , Kuan-Cheng Chen , Shang Yu , Mengxiang Liu , Ruilong Deng This is my paper · ORCID
classification quant-phcs.DC
keywords QuantumKernelLearningDecentralizedAlgorithmDistributedComputingRobustOptimizationAdversarialAttackDepolarizingNoiseAlignmentClippingAggregation
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 aims to show that a decentralized network of quantum computing units can train a quantum kernel classifier reliably even when individual units have very different noise levels, and can additionally be hardened against nodes that deliberately send corrupted updates. The core claim is that under depolarizing noise the noisy kernel has the affine form $K_e = (1-p)K + p/D$, which makes the kernel-alignment gradient of a high-noise node shrink toward zero, so that node neither slows consensus nor perturbs low-noise nodes. On top of this, the paper replaces the weighted-average aggregation rule with a clipping rule and obtains RDQKL, which preserves high classification accuracy under Gaussian and sign-flipping attacks. If the claim holds, decentralized quantum kernel learning becomes viable on heterogeneous near-term hardware and in settings with untrusted participants, rather than only in clean, trusted, centralized settings.

What carries the argument

The load-bearing object is the noisy quantum kernel under global depolarizing noise, $K_e(x,x') = (1-p)K(x,x') + p/D$, which the paper combines with the kernel-alignment loss of Eq. (18). The noise term makes the denominator in the alignment gradient grow, so gradients vanish as $p \to 1$; this is what stops high-noise nodes from damaging the shared model. The other two mechanisms are the doubly stochastic weight matrix $W$ used in weighted-average aggregation, which makes the network behave like SGD on the average parameter, and the clipping rule $\mathrm{Clip}(\theta_{(i,j)},\tau)$ of Eq. (35), which caps the length of any neighbor's update and is the defense against adversarial nodes.

What would settle it

Take the decentralized QKL protocol with one node set to high depolarizing noise and measure the actual kernel matrix elements on hardware; if the noisy kernel deviates from $(1-p)K + p/D$ by more than the shot-noise error, the predicted gradient collapse and consensus protection need not occur. A simpler test is to rerun the experiments with small shot counts $m$: if low-noise nodes' accuracy drops as $m$ decreases, the large-$m$ assumption is doing essential work.

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Extended reading notes

Core claim

The paper's central discovery is that the combination of three ingredients makes decentralized quantum kernel learning robust. First, under global depolarizing noise the noisy kernel is an affine rescaling of the ideal kernel, $K_e(x,x') = (1-p)K(x,x') + p/D$, so the kernel-alignment objective inherits a noise-dependent denominator that shrinks every local gradient as $p$ grows. Second, because the aggregation matrix $W$ is doubly stochastic, the average of the local parameters evolves exactly like a stochastic gradient step on the global loss, so the network reaches consensus even when some local gradients are nearly zero. Third, clipping each neighbor's update before aggregation bounds the influence of any single malicious node, turning the general decentralized QKL into RDQKL. The numerical results on checkerboard and reduced MNIST data show that this design keeps accuracy high under depolarizing noise and under Gaussian and sign-flipping attacks.

Load-bearing premise

The whole robustness analysis assumes that noise acts on each kernel in a simple, uniform way: the measured kernel is a fixed blend of the true kernel and a constant, and that enough measurements are taken so random sampling noise is negligible. If real hardware noise behaves differently, the claimed protection of low-noise nodes breaks.

Editorial extensions

If this is right

  • A connected decentralized QKL network with doubly stochastic weights converges to a common parameter vector even when some nodes are much noisier than others.
  • When a node's depolarizing noise is very high, its local alignment gradient approaches zero, so that node cannot significantly perturb the training of low-noise nodes.
  • With the clipping aggregation rule, the RDQKL variant keeps classification accuracy high under Gaussian and sign-flipping attacks, whereas unguarded decentralized QKL degrades sharply.
  • The clipping threshold $\tau$ controls a trade-off: smaller values detect attacks more aggressively but slow training, while larger values reduce robustness.
  • Decentralized QKL reaches target accuracy in fewer iterations than centralized QKL under normal, relatively high, and quite high noise conditions.

Reading between the lines

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

  • Editorial: If the paper's mechanism is right, a practical deployment could monitor each node's local gradient norm and dynamically deprioritize nodes whose gradients have collapsed from noise, without waiting for consensus to reveal the problem.
  • Editorial: The clipping defense is analyzed for a single malicious node, but the same rule should partially bound the influence of several colluding nodes, since each neighbor's update is capped independently; a multi-attacker analysis would be a natural extension.
  • Editorial: The affine-noise assumption suggests a calibration test: estimate $p$ per node from measured kernel values and correct the kernel matrix before alignment, which could extend the framework's noise range beyond what clipping alone handles.
  • Editorial: The numerical evidence comes from mixed-state simulations; the claim would be directly tested by running RDQKL on real hardware nodes with different error rates.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper proposes RDQKL, a decentralized quantum kernel learning framework that combines weighted-average aggregation with a norm-clipping robust aggregation rule. It analyzes the effect of depolarizing noise on quantum kernel alignment in Section IV-B, derives a noisy gradient expression in Eq. (21), and argues in Section IV-D that nodes with very high noise have vanishing gradients and therefore do not perturb low-noise nodes. The adversarial robustness component in Section IV-E clips received parameter vectors by their norm before aggregation, and the paper evaluates classification accuracy on a checkerboard dataset and a reduced MNIST dataset under heterogeneous noise and under Gaussian and sign-flipping attacks. The empirical results are reported in Tables I and II for ring and fully connected topologies.

Significance. If the central claims were fully established, the framework would be a useful step toward practical decentralized quantum machine learning under hardware noise and adversarial nodes. The paper provides an explicit depolarizing noise model, a derivation of the noisy kernel gradient (Eq. 21), a public code repository, and experiments on two network topologies. However, the noise-robustness argument is only heuristic, the adversarial evaluation is limited to two non-adaptive attacks with a single malicious node, and some reported results exclude the high-noise node, so the main claims are only partially supported at present.

major comments (3)
  1. [Section IV-B and IV-D] The central noise-robustness claim rests on the informal proposition in Section IV-B that high noise shrinks the gradient of the quantum kernel alignment. This proposition is not proved, and its implicit assumptions—balanced labels, bounded kernel derivatives, and negligible shot noise via Section III-C4—are not validated or quantified. Moreover, the step from gradient shrinkage in Eq. (21) to the Section IV-D conclusion that high-noise units "will not significantly affect" low-noise units is not made rigorous: no bound is given on the influence of a node with noise level p_i on the consensus parameter error or on the final classification accuracy. Please provide a formal statement with a proof, or explicitly label the claim as a heuristic and temper the conclusions accordingly.
  2. [Section IV-E and Section V] The adversarial-robustness claim is not established by the experiments. The clipping rule in Eq. (35) passes any vector with norm at most τ unchanged, and the thresholds τ=0.5 and τ=0.05 are fixed and publicly stated in Section V-A. An adversary aware of τ can scale the sign-flipping attack of Eq. (34) so that its norm is below τ, rendering the defense ineffective. The experiments only test the unscaled attacks of Eqs. (33)-(34) with a single malicious node, so they do not support the abstract's claim of mitigation "across multiple nodes." No sensitivity analysis over τ and no test against scaled or adaptive attacks are provided.
  3. [Tables I and II] The "Quite High Noise" rows in both tables report accuracies as "avg. w/o node2", excluding the node with the highest noise level. This selection hides the performance on the node that is most affected by the very condition the robustness claim concerns, and it is not justified in the text. The "Relatively High Noise" row in Table I also mixes "avg. w/o node2" for Score1 and Score2 with "avg. w/ node2" for Score3, which makes the table difficult to interpret. Please report per-node results or averages over all nodes, together with an explanation of any exclusions.
minor comments (6)
  1. [Fig. 2 caption] The caption says "Hardman gate"; this should read "Hadamard gate".
  2. [Table I] The row label "Sign-flippin Attack" is a typo and should read "Sign-flipping Attack".
  3. [Section II, last paragraph] The phrase "a more simpler and general strategy" is grammatically incorrect; it should be "a simpler and more general strategy".
  4. [Equation (24)] The stochastic gradient in Eq. (24) uses an index p over samples, but the sampling distribution over the local dataset D_i is not defined; please specify how the q_i samples are drawn.
  5. [Section V-A] The threshold values τ=0.5 for Gaussian attacks and τ=0.05 for sign-flipping attacks are introduced without justification; a brief rationale or a small sensitivity study would help the reader assess how sensitive the reported robustness is to this hyperparameter.
  6. [Algorithm 1, line 10] The notation θ^{(k+1/2)}_{(i,j)} for the parameter vector received from neighbor j is never formally defined; please define it consistently with the aggregation rule in Eq. (25).

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the noise analysis is a direct derivative under the stated depolarizing model and the clipping defense is evaluated against explicit attacks, not fitted to the headline outcome.

full rationale

The paper's derivation chain is self-contained rather than circular. The noisy-kernel relation K_e = (1-p)K + p/D (Eq. 14) is an explicit model assumption, and Eq. (21) is a parameter-free derivative of the alignment objective under that assumption; the gradient-shrinkage conclusion as p -> 1 follows algebraically from the enlarged denominator, with no fitted quantity. The consensus analysis (Eqs. 29-32) is a standard doubly-stochastic averaging argument, and the adversarial mechanism (Eqs. 35-36) is an explicit clipping algorithm whose thresholds are declared hyperparameters rather than parameters fitted to reproduce the reported accuracies; the experiments compare RDQKL against no-defense baselines for Gaussian and sign-flipping attacks. Self-citations [39] and [40] are contextual motivation for decentralized QKL and are not load-bearing for the central claims. The m-large and global-depolarizing assumptions make the robustness statement conditional, but conditionality is an assumption, not circularity. No 'prediction' was found to reduce by construction to its own inputs.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The central derivation relies on a specific depolarizing noise model, a balanced-dataset assumption, bounded kernel gradients, and a doubly stochastic mixing matrix. No invented physical entities are introduced. The only hand-chosen numeric parameters are the two clipping thresholds, set per attack type.

free parameters (2)
  • clipping threshold tau for Gaussian attack = 0.5
    Chosen by hand for Gaussian attack; no sensitivity analysis is provided. The threshold directly controls the defense strength.
  • clipping threshold tau for Sign-flipping attack = 0.05
    Chosen by hand for Sign-flipping attack, different from the Gaussian case. The authors do not justify the choice or study its sensitivity.
assumptions (5)
  • domain assumption Global depolarizing noise model: the noisy kernel satisfies K_e = (1-p)K + p/D
    Used in Eq. (14) and throughout Sections IV-B and IV-D to derive gradient behavior. The effective p is computed as p = 1 - (1-p_tilde)^{2L} (Eq. 10), taken from [22].
  • domain assumption The number of measurement shots m is large enough that shot noise is negligible
    Section III-C4 explicitly states 'we assume that m is large enough'. Finite-shot estimation error is not included in the analysis.
  • domain assumption Balanced dataset: sum_i y_i = 0
    Used in the derivation of Eq. (21) for the noisy alignment gradient; the constant p/D term cancels in the numerator only if labels sum to zero.
  • domain assumption Bounded kernel gradients: partial K_ij(theta) / partial theta_t is bounded
    Invoked in Section IV-B to argue the noisy gradient shrinks as p increases. No proof is given for the specific variational circuit in Fig. 2.
  • standard math Weight matrix W is doubly stochastic and rho(W - 11^T/N) < 1
    Used in Section IV-D for consensus convergence; standard conditions for decentralized optimization, inherited from [54].

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Cite this review

Pith. "Pith review of Robust Decentralized Quantum Kernel Learning for Noisy and Adversarial Environment." pith.science (2026). https://pith.science/paper/KGTCDB4E

@misc{pith2026250413782,
  author       = {Pith},
  title        = {Pith review of: Robust Decentralized Quantum Kernel Learning for Noisy and Adversarial Environment},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KGTCDB4E}},
  note         = {Machine review of arXiv:2504.13782}
}
read the original abstract

This paper proposes a general decentralized framework for quantum kernel learning (QKL). It has robustness against quantum noise and can also be designed to defend adversarial information attacks forming a robust approach named RDQKL. We analyze the impact of noise on QKL and study the robustness of decentralized QKL to the noise. By integrating robust decentralized optimization techniques, our method is able to mitigate the impact of malicious data injections across multiple nodes. Experimental results demonstrate that our approach maintains high accuracy under noisy quantum operations and effectively counter adversarial modifications, offering a promising pathway towards the future practical, scalable and secure quantum machine learning (QML).

Figures

Figures reproduced from arXiv: 2504.13782 by the authors.

Figure 1
Figure 1. A schematic overview of the application scenario. Multiple quantum [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. A quantum feature mapping circuit under noise with variational parameters. The circuit can be sequentially divided into a superposition layer, an [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Quantum kernel alignment value during the training process under [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: The checkerboard data is within a 1x1-sized region, divided into a total [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: The MNIST dataset is reduced in dimension to a 1x1-sized region [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

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Reference graph

Works this paper leans on

58 extracted references · 26 canonical work pages · cited by 5 Pith papers

  1. [1]

    Learning to optimize variational quantum circuits to solve combina- torial problems,

    S. Khairy, R. Shaydulin, L. Cincio, Y . Alexeev, and P. Balaprakash, “Learning to optimize variational quantum circuits to solve combina- torial problems,” in Proceedings of the AAAI conference on artificial intelligence, vol. 34, pp. 2367–2375, 2020

    work page 2020

  2. [2]

    Quantum approximate optimization algorithm: Performance, mechanism, and im- plementation on near-term devices,

    L. Zhou, S.-T. Wang, S. Choi, H. Pichler, and M. D. Lukin, “Quantum approximate optimization algorithm: Performance, mechanism, and im- plementation on near-term devices,” Physical Review X , vol. 10, no. 2, p. 021067, 2020

    2020

  3. [3]

    Resource-efficient compilation of distributed quantum circuits for solving large-scale wireless communication network problems,

    K.-C. Chen, F. Burt, S. Yu, C.-Y . Liu, M.-H. Hsieh, and K. K. Le- ung, “Resource-efficient compilation of distributed quantum circuits for solving large-scale wireless communication network problems,” arXiv preprint arXiv:2501.10242, 2025

    arXiv 2025

  4. [4]

    Noise- aware distributed quantum approximate optimization algorithm on near- term quantum hardware,

    K.-C. Chen, X. Xu, F. Burt, C.-Y . Liu, S. Yu, and K. K. Leung, “Noise- aware distributed quantum approximate optimization algorithm on near- term quantum hardware,” in 2024 IEEE International Conference on Quantum Computing and Engineering (QCE) , vol. 2, pp. 144–149, IEEE, 2024

    2024

  5. [5]

    Self-verifying variational quantum simulation of lattice models,

    C. Kokail, C. Maier, R. van Bijnen, T. Brydges, M. K. Joshi, P. Jurcevic, C. A. Muschik, P. Silvi, R. Blatt, C. F. Roos, et al. , “Self-verifying variational quantum simulation of lattice models,” Nature, vol. 569, no. 7756, pp. 355–360, 2019

    work page 2019

  6. [6]

    The variational quantum eigensolver: a review of methods and best practices,

    J. Tilly, H. Chen, S. Cao, D. Picozzi, K. Setia, Y . Li, E. Grant, L. Wossnig, I. Rungger, G. H. Booth, et al., “The variational quantum eigensolver: a review of methods and best practices,” Physics Reports, vol. 986, pp. 1–128, 2022

    2022

  7. [7]

    Quantum- classical-quantum workflow in quantum-hpc middleware with gpu ac- celeration,

    K.-C. Chen, X. Li, X. Xu, Y .-Y . Wang, and C.-Y . Liu, “Quantum- classical-quantum workflow in quantum-hpc middleware with gpu ac- celeration,” in 2024 International Conference on Quantum Communica- tions, Networking, and Computing (QCNC) , pp. 304–311, IEEE, 2024

    2024

  8. [8]

    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 Sci- ence, vol. 1, no. 6, pp. 403–409, 2021

    2021

Show all 58 references
  1. [9]

    Shedding light on the future: Exploring quantum neural networks through optics,

    S. Yu, Z. Jia, A. Zhang, E. Mer, Z. Li, V . Crescimanna, K.-C. Chen, R. B. Patel, I. A. Walmsley, and D. Kaszlikowski, “Shedding light on the future: Exploring quantum neural networks through optics,” Advanced Quantum Technologies, p. 2400074, 2024

    2024

  2. [10]

    Quan- tum machine learning regression optimisation for full-scale sewage sludge anaerobic digestion,

    Y . Mohamed, A. Elghadban, H. I. Lei, A. A. Shih, and P.-H. Lee, “Quan- tum machine learning regression optimisation for full-scale sewage sludge anaerobic digestion,” npj Clean Water, vol. 8, no. 1, p. 17, 2025

    2025

  3. [11]

    Quan- tum computing for climate resilience and sustainability challenges,

    K. T. M. Ho, K.-C. Chen, L. Lee, F. Burt, S. Yu, and P.-H. Lee, “Quan- tum computing for climate resilience and sustainability challenges,” in 2024 IEEE International Conference on Quantum Computing and Engineering (QCE), vol. 2, pp. 262–267, IEEE, 2024

    2024

  4. [12]

    Quantum-train long short- term memory: Application on flood prediction problem,

    C.-H. A. Lin, C.-Y . Liu, and K.-C. Chen, “Quantum-train long short- term memory: Application on flood prediction problem,” in 2024 IEEE International Conference on Quantum Computing and Engineering (QCE), vol. 2, pp. 268–273, IEEE, 2024

    2024

  5. [13]

    A universal programmable gaussian boson sampler for drug discovery,

    S. Yu, Z.-P. Zhong, Y . Fang, R. B. Patel, Q.-P. Li, W. Liu, Z. Li, L. Xu, S. Sagona-Stophel, E. Mer, et al. , “A universal programmable gaussian boson sampler for drug discovery,” Nature Computational Science, vol. 3, no. 10, pp. 839–848, 2023

    2023

  6. [14]

    Potential of quantum com- puting for drug discovery,

    Y . Cao, J. Romero, and A. Aspuru-Guzik, “Potential of quantum com- puting for drug discovery,” IBM Journal of Research and Development , vol. 62, no. 6, pp. 6–1, 2018

    2018

  7. [15]

    Quantum machine learning,

    J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, “Quantum machine learning,” Nature, vol. 549, no. 7671, pp. 195–202, 2017

    2017

  8. [16]

    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, no. 7747, pp. 209–212, 2019

    2019

  9. [17]

    Validating large-scale quantum ma- chine learning: Efficient simulation of quantum support vector machines using tensor networks,

    K.-C. Chen, T.-Y . Li, Y .-Y . Wang, S. See, C.-C. Wang, R. Wille, N.-Y . Chen, A.-C. Yang, and C.-Y . Lin, “Validating large-scale quantum ma- chine learning: Efficient simulation of quantum support vector machines using tensor networks,” Machine Learning: Science and Technol...

    2024

  10. [18]

    Quantum-enhanced support vector machine for large-scale multi-class stellar classification,

    K.-C. Chen, X. Xu, H. Makhanov, H.-H. Chung, and C.-Y . Liu, “Quantum-enhanced support vector machine for large-scale multi-class stellar classification,” in International Conference on Intelligent Com- puting, pp. 155–168, Springer, 2024

    2024

  11. [19]

    Power of data in quantum machine learning,

    H.-Y . Huang, M. Broughton, M. Mohseni, R. Babbush, S. Boixo, H. Neven, and J. R. McClean, “Power of data in quantum machine learning,” Nature communications, vol. 12, no. 1, p. 2631, 2021

    2021

  12. [20]

    Training quantum embedding kernels on near-term quantum computers,

    T. Hubregtsen, D. Wierichs, E. Gil-Fuster, P.-J. H. Derks, P. K. Faehrmann, and J. J. Meyer, “Training quantum embedding kernels on near-term quantum computers,” Physical Review A , vol. 106, no. 4, p. 042431, 2022

    2022

  13. [21]

    Exponential con- centration in quantum kernel methods,

    S. Thanasilp, S. Wang, M. Cerezo, and Z. Holmes, “Exponential con- centration in quantum kernel methods,” Nature communications, vol. 15, no. 1, p. 5200, 2024

    2024

  14. [22]

    Power characterization of noisy quantum kernels,

    Y . Wang, B. Qi, X. Wang, T. Liu, and D. Dong, “Power characterization of noisy quantum kernels,” IEEE Transactions on Neural Networks and Learning Systems, 2025

    2025

  15. [23]

    Communication-efficient learning of deep networks from decentralized data,

    B. McMahan, E. Moore, D. Ramage, S. Hampson, and B. A. y Arcas, “Communication-efficient learning of deep networks from decentralized data,” in Artificial intelligence and statistics , pp. 1273–1282, PMLR, 2017

    2017

  16. [24]

    Distributed subgradient methods for multi- agent optimization,

    A. Nedic and A. Ozdaglar, “Distributed subgradient methods for multi- agent optimization,” IEEE Transactions on Automatic Control , vol. 54, no. 1, pp. 48–61, 2009

    2009

  17. [25]

    Large scale distributed deep networks,

    J. Dean, G. Corrado, R. Monga, K. Chen, M. Devin, M. Mao, M. Ran- zato, A. Senior, P. Tucker, K. Yang, et al., “Large scale distributed deep networks,” Advances in neural information processing systems , vol. 25, 2012

    2012

  18. [26]

    A survey on federated learning,

    C. Zhang, Y . Xie, H. Bai, B. Yu, W. Li, and Y . Gao, “A survey on federated learning,” Knowledge-Based Systems , vol. 216, p. 106775, 2021

    2021

  19. [27]

    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

    2019

  20. [28]

    A rigorous and robust quantum speed-up in supervised machine learning,

    Y . Liu, S. Arunachalam, and K. Temme, “A rigorous and robust quantum speed-up in supervised machine learning,” Nature Physics, vol. 17, no. 9, pp. 1013–1017, 2021

    2021

  21. [29]

    Quantum tangent kernel,

    N. Shirai, K. Kubo, K. Mitarai, and K. Fujii, “Quantum tangent kernel,” Physical Review Research, vol. 6, no. 3, p. 033179, 2024

    2024

  22. [30]

    Qksan: A quantum kernel self-attention network,

    R.-X. Zhao, J. Shi, and X. Li, “Qksan: A quantum kernel self-attention network,” IEEE Transactions on Pattern Analysis and Machine Intelli- gence, 2024

    2024

  23. [31]

    Quantum kernel-based long short- term memory,

    Y .-C. Hsu, T.-Y . Li, and K.-C. Chen, “Quantum kernel-based long short- term memory,” arXiv preprint arXiv:2411.13225 , 2024

    2024 arXiv

  24. [32]

    Quantum kernel- based long short-term memory for climate time-series forecasting,

    Y .-C. Hsu, N.-Y . Chen, T.-Y . Li, K.-C. Chen, et al., “Quantum kernel- based long short-term memory for climate time-series forecasting,”arXiv preprint arXiv:2412.08851, 2024

    2024 arXiv

  25. [33]

    Challenges and opportunities in quantum machine learning,

    M. Cerezo, G. Verdon, H.-Y . Huang, L. Cincio, and P. J. Coles, “Challenges and opportunities in quantum machine learning,” Nature computational science, vol. 2, no. 9, pp. 567–576, 2022

    2022

  26. [34]

    Noisy intermediate-scale quantum computers,

    B. Cheng, X.-H. Deng, X. Gu, Y . He, G. Hu, P. Huang, J. Li, B.-C. Lin, D. Lu, Y . Lu, et al. , “Noisy intermediate-scale quantum computers,” Frontiers of Physics, vol. 18, no. 2, p. 21308, 2023

    2023

  27. [35]

    Barren plateaus in variational quantum computing,

    M. Larocca, S. Thanasilp, S. Wang, K. Sharma, J. Biamonte, P. J. Coles, L. Cincio, J. R. McClean, Z. Holmes, and M. Cerezo, “Barren plateaus in variational quantum computing,” Nature Reviews Physics , pp. 1–16, 2025

    2025

  28. [36]

    The complexity of quantum support vector machines,

    G. Gentinetta, A. Thomsen, D. Sutter, and S. Woerner, “The complexity of quantum support vector machines,” Quantum, vol. 8, p. 1225, 2024

    2024

  29. [37]

    Quantum kernel alignment with stochastic gradient descent,

    G. Gentinetta, D. Sutter, C. Zoufal, B. Fuller, and S. Woerner, “Quantum kernel alignment with stochastic gradient descent,” in 2023 IEEE Inter- national Conference on Quantum Computing and Engineering (QCE) , vol. 1, pp. 256–262, IEEE, 2023

    2023

  30. [38]

    Efficient parameter optimisation for quantum kernel alignment: A sub-sampling approach in variational training,

    M. E. Sahin, B. C. Symons, P. Pati, F. Minhas, D. Millar, M. Gabrani, S. Mensa, and J. L. Robertus, “Efficient parameter optimisation for quantum kernel alignment: A sub-sampling approach in variational training,” Quantum, vol. 8, p. 1502, 2024

    2024

  31. [39]

    CDQKL: Consensus-based distributed quantum kernel learning,

    W. Ma, M. Liu, and R. Deng, “CDQKL: Consensus-based distributed quantum kernel learning,” in 2024 International Conference on Quantum Communications, Networking, and Computing (QCNC) , pp. 33–40, IEEE, 2024

    2024

  32. [40]

    Consensus-based distributed quantum kernel learning for speech recognition,

    K.-C. Chen, W. Ma, and X. Xu, “Consensus-based distributed quantum kernel learning for speech recognition,” arXiv preprint arXiv:2409.05770, 2024

    2024 arXiv

  33. [41]

    Transitioning from federated learn- ing to quantum federated learning in internet of things: A comprehensive survey,

    C. Qiao, M. Li, Y . Liu, and Z. Tian, “Transitioning from federated learn- ing to quantum federated learning in internet of things: A comprehensive survey,” IEEE Communications Surveys & Tutorials , 2024

    2024

  34. [42]

    Defending against byzantine attacks in quantum federated learning,

    Q. Xia, Z. Tao, and Q. Li, “Defending against byzantine attacks in quantum federated learning,” in 2021 17th International Conference on Mobility, Sensing and Networking (MSN) , pp. 145–152, IEEE, 2021

    2021

  35. [43]

    Byzantine-resilient decentralized stochas- tic optimization with robust aggregation rules,

    Z. Wu, T. Chen, and Q. Ling, “Byzantine-resilient decentralized stochas- tic optimization with robust aggregation rules,” IEEE transactions on signal processing, vol. 71, pp. 3179–3195, 2023

    2023

  36. [44]

    Distributed training for multi-layer neural networks by consensus,

    B. Liu, Z. Ding, and C. Lv, “Distributed training for multi-layer neural networks by consensus,” IEEE transactions on neural networks and learning systems, vol. 31, no. 5, pp. 1771–1778, 2019

    2019

  37. [45]

    Quantum advantage and noise re- duction in distributed quantum computing,

    J. Avron, O. Casper, and I. Rozen, “Quantum advantage and noise re- duction in distributed quantum computing,” Physical Review A, vol. 104, no. 5, p. 052404, 2021

    2021

  38. [46]

    Quantum-enabled distributed transient stability assessment of power systems,

    S. Yu, Y . Zhou, and L. Wang, “Quantum-enabled distributed transient stability assessment of power systems,” in 2024 IEEE International Conference on Quantum Computing and Engineering (QCE) , vol. 1, pp. 593–599, IEEE, 2024

    2024

  39. [47]

    Securing reset operations in nisq quan- tum computers,

    A. Mi, S. Deng, and J. Szefer, “Securing reset operations in nisq quan- tum computers,” in Proceedings of the 2022 ACM SIGSAC Conference on Computer and Communications Security , pp. 2279–2293, 2022

    2022

  40. [48]

    Evaluating efficacy of model steal- ing attacks and defenses on quantum neural networks,

    S. Kundu, D. Kundu, and S. Ghosh, “Evaluating efficacy of model steal- ing attacks and defenses on quantum neural networks,” in Proceedings of the Great Lakes Symposium on VLSI 2024 , pp. 556–559, 2024

    2024

  41. [49]

    Qdoor: Exploiting ap- proximate synthesis for backdoor attacks in quantum neural networks,

    C. Chu, F. Chen, P. Richerme, and L. Jiang, “Qdoor: Exploiting ap- proximate synthesis for backdoor attacks in quantum neural networks,” in 2023 IEEE International Conference on Quantum Computing and Engineering (QCE), vol. 1, pp. 1098–1106, IEEE, 2023

    2023

  42. [50]

    Adversarial poisoning attack on quantum machine learning models,

    S. Kundu and S. Ghosh, “Adversarial poisoning attack on quantum machine learning models,” arXiv preprint arXiv:2411.14412 , 2024

    2024 arXiv

  43. [51]

    Auction-based trustwor- thy and resilient quantum distributed learning,

    H. Lee, S. B. Son, S. Y .-C. Chen, and S. Park, “Auction-based trustwor- thy and resilient quantum distributed learning,” IEEE Internet of Things Journal, 2025

    2025

  44. [52]

    Byzantine-robust decentralized learning via clippedgossip,

    L. He, S. P. Karimireddy, and M. Jaggi, “Byzantine-robust decentralized learning via clippedgossip,” arXiv preprint arXiv:2202.01545 , 2022

    2022 arXiv

  45. [53]

    Stochastic noise can be helpful for variational quantum algorithms,

    J. Liu, F. Wilde, A. A. Mele, L. Jiang, and J. Eisert, “Stochastic noise can be helpful for variational quantum algorithms,” arXiv preprint arXiv:2210.06723, 2022

    2022 arXiv

  46. [54]

    Tutorial on dynamic average consensus: The problem, its applications, and the algorithms,

    S. S. Kia, B. Van Scoy, J. Cortes, R. A. Freeman, K. M. Lynch, and S. Martinez, “Tutorial on dynamic average consensus: The problem, its applications, and the algorithms,” IEEE Control Systems Magazine , vol. 39, no. 3, pp. 40–72, 2019

    2019

  47. [55]

    Pennylane: Automatic differentiation of hybrid quantum-classical com- putations,

    V . Bergholm, J. Izaac, M. Schuld, C. Gogolin, S. Ahmed, V . Ajith, M. S. Alam, G. Alonso-Linaje, B. AkashNarayanan, A. Asadi, et al. , “Pennylane: Automatic differentiation of hybrid quantum-classical com- putations,” arXiv preprint arXiv:1811.04968 , 2018

    2018 arXiv

  48. [56]

    Grid-metaverse: The path from digital twins and prototype tests on dc microgrids,

    W. Ma, M. Liu, G. Hong, S. Yang, and R. Deng, “Grid-metaverse: The path from digital twins and prototype tests on dc microgrids,” in 2023 IEEE International Conference on Metaverse Computing, Networking and Applications (MetaCom) , pp. 290–296, IEEE, 2023

    2023

  49. [57]

    Vulnerability of machine learning approaches applied in iot-based smart grid: A review,

    Z. Zhang, M. Liu, M. Sun, R. Deng, P. Cheng, D. Niyato, M.-Y . Chow, and J. Chen, “Vulnerability of machine learning approaches applied in iot-based smart grid: A review,”IEEE Internet of Things Journal, vol. 11, no. 11, pp. 18951–18975, 2024

    2024

  50. [58]

    Enhancing cyber-resiliency of der-based smart grid: A survey,

    M. Liu, F. Teng, Z. Zhang, P. Ge, M. Sun, R. Deng, P. Cheng, and J. Chen, “Enhancing cyber-resiliency of der-based smart grid: A survey,” IEEE Transactions on Smart Grid , vol. 15, no. 5, pp. 4998–5030, 2024

    2024

Pith tools

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