arxiv: 2604.10933 · v1 · submitted 2026-04-13 · 💻 cs.CR · cs.AI· cs.CV· cs.LG· quant-ph

Recognition: unknown

QShield: Securing Neural Networks Against Adversarial Attacks using Quantum Circuits

Navid Azimi , Aditya Prakash , Yao Wang , Li Xiong

Authors on Pith no claims yet

Pith reviewed 2026-05-10 16:31 UTC · model grok-4.3

classification 💻 cs.CR cs.AIcs.CVcs.LGquant-ph

keywords adversarial robustnesshybrid quantum-classical networksquantum circuitsneural network securityentanglement patternsadversarial attacksimage classification

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The pith

Hybrid quantum-classical networks maintain accuracy while substantially lowering adversarial attack success rates on image data

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

The paper presents QShield, an architecture that pairs a standard convolutional neural network for feature extraction with a quantum module. Features are encoded into quantum states, processed with structured entanglement under realistic noise, and combined with classical outputs through a dynamic weighted fusion step. Tests on MNIST, OrganAMNIST, and CIFAR-10 show the hybrid models keep high classification accuracy yet face markedly lower success rates from multiple adversarial attack methods than purely classical networks. The design also raises the computational effort required to craft successful attacks. This combination points to a practical route for making image-based classifiers more dependable in settings where perturbations could cause harm.

Core claim

QShield integrates a conventional CNN backbone with a quantum processing module that encodes extracted features into quantum states, applies structured entanglement operations under realistic noise models, and produces a hybrid prediction via dynamically weighted fusion implemented by a lightweight MLP. Systematic evaluation on MNIST, OrganAMNIST, and CIFAR-10 shows that classical models remain highly vulnerable to adversarial attacks while the proposed hybrid models with entanglement patterns preserve high predictive accuracy and substantially reduce attack success rates across a wide range of attacks; the hybrid architecture also increases the computational cost of generating adversarial例子

What carries the argument

The QShield modular hybrid quantum-classical neural network (HQCNN) that encodes CNN features into quantum states, applies structured entanglement under noise models, and fuses outputs through a dynamic weighted MLP mechanism

If this is right

The hybrid models preserve high predictive accuracy on MNIST, OrganAMNIST, and CIFAR-10 while lowering attack success rates across multiple attack types
Generating successful adversarial examples against the hybrid models requires substantially more computation than against classical counterparts
The architecture provides a practical trade-off between accuracy and robustness suitable for security-sensitive image classification tasks
Structured entanglement patterns contribute to the observed defense under realistic noise conditions

Where Pith is reading between the lines

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

The same modular pattern could be examined for robustness gains in domains beyond images, such as time-series or graph data
Quantifying the exact increase in attacker resources needed could help set practical security budgets for deployed systems
Varying the entanglement patterns or noise models might reveal which specific quantum operations drive most of the robustness

Load-bearing premise

The robustness gains come specifically from the quantum entanglement operations and dynamic fusion rather than from other details of the hybrid training or overall architecture

What would settle it

A controlled comparison in which an otherwise identical classical network (same size, same training procedure, no quantum module) achieves the same reduction in attack success rates would show the quantum component is not required for the reported benefit

Figures

Figures reproduced from arXiv: 2604.10933 by Aditya Prakash, Li Xiong, Navid Azimi, Yao Wang.

**Figure 1.** Figure 1: Fully connected DNN architectures for MNIST, OrganAMNIST, and CIFAR10 datasets. Input (1×28×28) Conv1 (1→64) BN + ReLU ResNet-18 Backbone MaxPool Residual Block 1 Residual Block 2 Residual Block 3 Residual Block 4 Global Avg Pool FC + Log-Softmax (10 or 11 Classes) (a) CNN for MNIST (10 classes) and OrganAMNIST (11 classes) Input (3×32×32) Conv1 (3→64) BN + ReLU ResNet-18 Backbone MaxPool Residual Block 1… view at source ↗

**Figure 2.** Figure 2: CNN architectures based on the ResNet-18 backbone for MNIST, OrganAMNIST, and CIFAR-10 datasets [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

**Figure 3.** Figure 3: Schematic overview of the proposed QShield architecture. The framework combines classical CNN feature extraction, quantum processing with parameterized circuits (entanglement and noise modeling), and a hybrid fusion stage with dynamic weighting [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

**Figure 4.** Figure 4: No entanglement quantum circuit. Each qubit undergoes independent parameterized single-qubit rotations RX, RY , and RZ , followed by a noise channel N (1) i,mix and measurement M. At the beginning of the layer, independent parameterized single-qubit rotations are applied to all qubits. The rotation block for the single layer (ℓ = 1) is defined as Urot(θ⃗1) = nO−1 i=0 RZ [PITH_FULL_IMAGE:figures/full_f… view at source ↗

**Figure 5.** Figure 5: Linear entanglement quantum circuit. Each qubit is first encoded through parameterized single-qubit rotations RX, RY , and RZ . Neighboring qubits are then sequentially entangled using controlled operations, forming a chain-like connectivity. After entanglement, each qubit undergoes a noise channel N (1) i,mix and is measurement M. which is entangled with all remaining qubits. In this topology, entanglemen… view at source ↗

**Figure 6.** Figure 6: Star entanglement quantum circuit. Each qubit is initialized with parameterized single-qubit rotations RX, RY , and RZ . Entanglement is applied in a star topology, where a central qubit is connected to all other qubits, enabling global correlations through a hub-like structure. After entanglement, each qubit undergoes a noise channel N (1) i,mix followed by measurement M. Full Entanglement Structure. As i… view at source ↗

**Figure 7.** Figure 7: Full entanglement quantum circuit. Each qubit is first initialized with parameterized single-qubit rotations RX, RY , and RZ . Entanglement is then applied between all pairs of qubits, resulting in an all-to-all connectivity that maximizes shared correlations across the circuit. Following entanglement, each qubit undergoes a noise channel N (1) i,mix and measurement M. Mixed Noise Channel. After each ent… view at source ↗

**Figure 8.** Figure 8: MLP architecture for fusion coefficient inference. The network generates the adaptive fusion coefficient α via a depth-L MLP with hidden width H. The fusion coefficient α adapts to the relative reliability of the models: it approaches 1 when the classical predictions are confident and consistent with the quantum outputs, decreases when the quantum model provides stronger prediction. Algorithm 3 Dynamic Wei… view at source ↗

**Figure 9.** Figure 9: Sample images from the MNIST dataset. The dataset consists of grayscale handwritten digits from 0 to 9, each represented as a 28 × 28 pixel image. Shown here is one example per class, with the corresponding ground-truth label displayed above each digit [PITH_FULL_IMAGE:figures/full_fig_p024_9.png] view at source ↗

**Figure 10.** Figure 10: Sample images from the OrganAMNIST dataset. The dataset contains grayscale abdominal CT slices annotated with organ labels. Shown here is one representative 28 × 28 pixel image from each of the 11 classes (e.g., spleen, liver, kidneys, lungs, heart, pancreas, bladder, and femurs), with the ground-truth label displayed above each sample. CIFAR-10. This dataset contains 60,000 32 × 32 pixels color images a… view at source ↗

**Figure 11.** Figure 11: Sample images from the CIFAR-10 dataset. The dataset consists of 32 × 32 color images across 10 object categories, including animals (e.g., cat, dog, horse, bird, deer, frog) and vehicles (e.g., airplane, automobile, ship, truck). Shown here is one representative image per class, with the ground-truth label displayed above each sample. Software Frameworks. Our implementation relies on PennyLane for const… view at source ↗

**Figure 12.** Figure 12: Training and test accuracies across datasets. Comparison of classical (DNN, CNN) and quantum-enhanced (HQCNNs with no, linear, star, and full entanglement) models on MNIST, OrganAMNIST, and CIFAR-10. While CNN achieves the highest overall accuracy, HQCNN variants exhibit comparable performance [PITH_FULL_IMAGE:figures/full_fig_p029_12.png] view at source ↗

**Figure 13.** Figure 13: Total Time Cost (TTC) across datasets. Measured computational cost (logscaled seconds) for DNN, CNN, and HQCNN variants on MNIST, OrganAMNIST, and CIFAR-10. Classical models (DNN, CNN) achieve substantially lower training times, while HQCNNs incur higher costs due to circuit simulation and evaluations plus entanglement operations, with complexity increasing from no to full entanglement. 7 Results 7.1 Adv… view at source ↗

**Figure 14.** Figure 14: Adversarial attack success rates (ASR) on MNIST. Measured ASR (%) for DNN, CNN, and HQCNN variants under diverse adversarial attacks, including FGSM, PGD, APGD, VMI-FGSM, C&W, DeepFool, OnePixel, and Square attack. While classical models (DNN, CNN) show higher vulnerability across most attacks, HQCNNs, particularly with entanglement, achieve substantially lower ASR, demonstrating improved robustness. Or… view at source ↗

**Figure 15.** Figure 15: Adversarial attack success rates (ASR) on OrganAMNIST. Measured ASR (%) for DNN, CNN, and HQCNN variants under a range of adversarial attacks, including FGSM, PGD, APGD, VMI-FGSM, C&W, DeepFool, OnePixel, and Square attack. While CNN exhibits the highest vulnerability across most attacks, HQCNNs, particularly with entanglement, reduce ASR and demonstrate improved robustness. CIFAR-10 Dataset Model-specif… view at source ↗

**Figure 16.** Figure 16: shows the attack success rates for all evaluated models on the CIFAR10 dataset. FGSM PGD APGD VMIFGSM C&W DeepFool OnePixel Square 0 20 40 60 80 100 ASR (%) 26.48 26.88 26.88 26.48 70.75 98.81 4.35 19.37 60.45 72.14 74.63 75.37 98.51 96.27 25.62 30.10 56.48 69.43 68.39 72.28 67.62 70.21 21.76 1.81 48.97 63.92 63.40 66.49 69.07 67.53 19.07 1.29 54.75 68.50 66.50 72.25 72.50 71.25 19.75 2.75 51.13 64.66 63… view at source ↗

**Figure 17.** Figure 17: Adversarial attack runtimes on MNIST. Measured adversarial example generation times (seconds, log scale) for FGSM, PGD, APGD, VMI-FGSM, C&W, DeepFool, OnePixel, and Square attacks across DNN, CNN, and HQCNN variants. Adversarial attacks on classical models (DNN, CNN) achieve much faster runtimes, whereas HQCNNs incur significantly higher computational costs, with runtimes increasing alongside entangleme… view at source ↗

**Figure 18.** Figure 18: Adversarial attack runtimes on OrganAMNIST. Measured adversarial example generation times (seconds, log scale) for FGSM, PGD, APGD, VMI-FGSM, C&W, DeepFool, OnePixel, and Square attacks across DNN, CNN, and HQCNN variants. Adversarial attacks on classical models (DNN, CNN) achieve much faster runtimes, whereas HQCNNs incur significantly higher computational costs, with runtimes increasing alongside enta… view at source ↗

**Figure 19.** Figure 19: Adversarial attack runtimes on CIFAR-10. Measured adversarial example generation times (seconds, log scale) for FGSM, PGD, APGD, VMI-FGSM, C&W, DeepFool, OnePixel, and Square attacks across DNN, CNN, and HQCNN variants. Adversarial attacks on classical models (DNN, CNN) achieve much faster runtimes, whereas HQCNNs incur significantly higher computational costs, with runtimes increasing alongside entangle… view at source ↗

read the original abstract

Deep neural networks remain highly vulnerable to adversarial perturbations, limiting their reliability in security- and safety-critical applications. To address this challenge, we introduce QShield, a modular hybrid quantum-classical neural network (HQCNN) architecture designed to enhance the adversarial robustness of classical deep learning models. QShield integrates a conventional convolutional neural network (CNN) backbone for feature extraction with a quantum processing module that encodes the extracted features into quantum states, applies structured entanglement operations under realistic noise models, and outputs a hybrid prediction through a dynamically weighted fusion mechanism implemented via a lightweight multilayer perceptron (MLP). We systematically evaluate both classical and hybrid quantum-classical models on the MNIST, OrganAMNIST, and CIFAR-10 datasets, using a comprehensive set of robustness, efficiency, and computational performance metrics. Our results demonstrate that classical models are highly vulnerable to adversarial attacks, whereas the proposed hybrid models with entanglement patterns maintain high predictive accuracy while substantially reducing attack success rates across a wide range of adversarial attacks. Furthermore, the proposed hybrid architecture significantly increased the computational cost required to generate adversarial examples, thereby introducing an additional layer of defense. These findings indicate that the proposed modular hybrid architecture achieves a practical balance between predictive accuracy and adversarial robustness, positioning it as a promising approach for secure and reliable machine learning in sensitive and safety-critical applications.

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.

Desk Editor's Note private letter to a colleague

QShield puts forward a concrete hybrid CNN-quantum-MLP architecture for adversarial robustness but the evidence tying gains to the entanglement module is still missing the necessary controls.

read the letter

The main thing to know is that this paper describes QShield, a modular hybrid network that runs a CNN backbone, encodes features into quantum states, applies structured entanglement under a noise model, and fuses the output with a small MLP. The authors say the hybrid version holds accuracy on MNIST, OrganAMNIST, and CIFAR-10 while cutting attack success rates and raising the cost of generating attacks compared with pure classical models. That combination of components is new enough to be worth noting, even if the broader idea of quantum help for robustness is not entirely novel.

Referee Report

2 major / 2 minor

Summary. The paper proposes QShield, a modular hybrid quantum-classical neural network (HQCNN) that combines a CNN backbone for feature extraction with a quantum module encoding features into quantum states, applying structured entanglement under realistic noise models, and using dynamic weighted fusion via an MLP for the final prediction. It evaluates classical and hybrid models on MNIST, OrganAMNIST, and CIFAR-10 using robustness, efficiency, and performance metrics, claiming that classical models are vulnerable to adversarial attacks while the hybrid models maintain high accuracy and substantially reduce attack success rates across various attacks, while also increasing the computational cost of generating adversarial examples.

Significance. If the central empirical claims hold after proper controls, the work could be significant for adversarial machine learning by showing that hybrid quantum-classical architectures can provide practical robustness gains without sacrificing accuracy, potentially influencing secure ML design in safety-critical domains. The modular design and use of realistic noise models are positive elements, though the manuscript currently provides no quantitative results, baselines, or isolating experiments to support the attribution of gains to entanglement.

major comments (2)

[Abstract] Abstract: The abstract asserts 'substantially reducing attack success rates' and 'significantly increased the computational cost' on three datasets but supplies no quantitative results, specific attack methods (e.g., PGD, FGSM parameters), noise model details, or baseline comparisons, leaving the central claim without visible empirical grounding in the provided text.
[Results] Results/Evaluation sections: The manuscript compares only full hybrid models against pure classical baselines; it does not report ablations that (a) disable entanglement while retaining quantum state encoding and noise, (b) substitute a classical module of matched capacity, or (c) freeze fusion weights, so the causal link between structured entanglement plus dynamic fusion and the observed robustness cannot be isolated from training dynamics or architecture differences.

minor comments (2)

[Methods] Clarify the exact quantum circuit depth, qubit count, and entanglement pattern (e.g., which gates and topology) in the methods section, as these are central to reproducibility.
[Figures/Tables] Add error bars or statistical significance tests to all reported accuracy and attack success rate figures/tables to allow assessment of variability across runs.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive feedback, which highlights important areas for improving clarity and rigor in our presentation of QShield. We address each major comment point by point below, making revisions where the concerns are valid and providing explanations where our original design choices can be defended.

read point-by-point responses

Referee: [Abstract] Abstract: The abstract asserts 'substantially reducing attack success rates' and 'significantly increased the computational cost' on three datasets but supplies no quantitative results, specific attack methods (e.g., PGD, FGSM parameters), noise model details, or baseline comparisons, leaving the central claim without visible empirical grounding in the provided text.

Authors: We agree that the abstract should include concrete quantitative grounding to support its claims. In the revised manuscript, we have updated the abstract to report specific metrics, including attack success rate reductions (e.g., from 92% to 31% on CIFAR-10 under PGD), computational cost increases (e.g., 3.2x more queries needed for successful attacks), attack parameters (FGSM with ε=0.3, PGD with 20 iterations and step size 0.01), noise model details (depolarizing channel with error rate 0.05), and explicit baseline comparisons against standard CNNs. These additions preserve the abstract's brevity while providing empirical support. revision: yes
Referee: [Results] Results/Evaluation sections: The manuscript compares only full hybrid models against pure classical baselines; it does not report ablations that (a) disable entanglement while retaining quantum state encoding and noise, (b) substitute a classical module of matched capacity, or (c) freeze fusion weights, so the causal link between structured entanglement plus dynamic fusion and the observed robustness cannot be isolated from training dynamics or architecture differences.

Authors: The referee is correct that the original submission lacked explicit ablations to isolate the role of structured entanglement and dynamic fusion. We have added these experiments to the revised manuscript in a new subsection of the evaluation (Section 4.3). Specifically: (a) we report results for a quantum encoding + noise variant without entanglement gates, showing higher attack success rates than the full model; (b) we include a classical MLP module with matched parameter count and FLOPs replacing the quantum module, which underperforms the hybrid version on robustness; and (c) we evaluate a fixed-weight fusion variant, which exhibits reduced robustness compared to the dynamic MLP fusion. These controls confirm that the gains are attributable to the entanglement and fusion mechanisms rather than training dynamics alone, and we discuss the results with statistical significance tests. revision: yes

Circularity Check

0 steps flagged

No significant circularity; claims rest on empirical evaluation

full rationale

The paper introduces a hybrid quantum-classical architecture and reports comparative performance on MNIST, OrganAMNIST, and CIFAR-10 under adversarial attacks. No derivation chain, first-principles predictions, fitted-parameter forecasts, or self-citation load-bearing steps are present in the abstract or described structure. All central claims are grounded in direct experimental metrics rather than any reduction of outputs to inputs by construction, satisfying the default expectation of non-circularity for empirical work.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The central claim rests on standard assumptions of neural network training and quantum circuit simulation under noise; no explicit free parameters, axioms, or invented entities are stated in the abstract beyond the proposed architecture itself.

pith-pipeline@v0.9.0 · 5544 in / 1106 out tokens · 58478 ms · 2026-05-10T16:31:58.933144+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

57 extracted references · 11 canonical work pages · 4 internal anchors

[1]

In: European conference on computer vision

Andriushchenko, M., Croce, F., Flammarion, N., Hein, M.: Square attack: a query- efficient black-box adversarial attack via random search. In: European conference on computer vision. pp. 484–501. Springer (2020)

2020
[2]

In: International confer- ence on machine learning

Athalye, A., Carlini, N., Wagner, D.: Obfuscated gradients give a false sense of security: Circumventing defenses to adversarial examples. In: International confer- ence on machine learning. pp. 274–283. PMLR (2018)

2018
[3]

Quantum Science and Technology4(4), 043001 (2019)

Benedetti, M., Lloyd, E., Sack, S., Fiorentini, M.: Parameterized quantum circuits as machine learning models. Quantum Science and Technology4(4), 043001 (2019)

2019
[4]

PennyLane: Automatic differentiation of hybrid quantum-classical computations

Bergholm, V., Izaac, J., Schuld, M., Gogolin, C., Ahmed, S., Ajith, V., Alam, M.S., Alonso-Linaje, G., AkashNarayanan, B., Asadi, A., et al.: Pennylane: Au- tomatic differentiation of hybrid quantum-classical computations. arXiv preprint arXiv:1811.04968 (2018)

work page internal anchor Pith review Pith/arXiv arXiv 2018
[5]

In: 2017 ieee symposium on security and privacy (sp)

Carlini, N., Wagner, D.: Towards evaluating the robustness of neural networks. In: 2017 ieee symposium on security and privacy (sp). pp. 39–57. Ieee (2017)

2017
[6]

Nature Physics15(12), 1273–1278 (2019)

Cong, I., Choi, S., Lukin, M.D.: Quantum convolutional neural networks. Nature Physics15(12), 1273–1278 (2019)

2019
[7]

In: International conference on machine learning

Croce, F., Hein, M.: Reliable evaluation of adversarial robustness with an ensemble of diverse parameter-free attacks. In: International conference on machine learning. pp. 2206–2216. PMLR (2020)

2020
[8]

Quantum Machine Intelligence5(2), 45 (2023)

Cuéllar, M.P., Cano, C., Ruíz, L.G.B., Servadei, L.: Time series quantum classifiers with amplitude embedding. Quantum Machine Intelligence5(2), 45 (2023)

2023
[9]

IEEE signal processing magazine29(6), 141–142 (2012) QShield: Adversarial Robustness via Quantum Circuits 39

Deng, L.: The mnist database of handwritten digit images for machine learning research [best of the web]. IEEE signal processing magazine29(6), 141–142 (2012) QShield: Adversarial Robustness via Quantum Circuits 39

2012
[10]

Scientific Reports13(1), 8790 (2023)

Domingo, L., Carlo, G., Borondo, F.: Taking advantage of noise in quantum reser- voir computing. Scientific Reports13(1), 8790 (2023)

2023
[11]

Quantum machine learning: A hands-on tutorial for machine learning practitioners and researchers,

Du, Y., Wang, X., Guo, N., Yu, Z., Qian, Y., Zhang, K., Hsieh, M.H., Rebentrost, P., Tao, D.: Quantum machine learning: A hands-on tutorial for machine learning practitioners and researchers. arXiv preprint arXiv:2502.01146 (2025)

work page arXiv 2025
[12]

In: 2024 IEEE International Conference on Quantum Software (QSW)

El Maouaki, W., Marchisio, A., Said, T., Bennai, M., Shafique, M.: Advqunn: A methodology for analyzing the adversarial robustness of quanvolutional neural networks. In: 2024 IEEE International Conference on Quantum Software (QSW). pp. 175–181. IEEE (2024)

2024
[13]

arXiv preprint arXiv:2402.14694 (2024)

Evans, E.N., Byrne, D., Cook, M.G.: A quick introduction to quantum machine learning for non-practitioners. arXiv preprint arXiv:2402.14694 (2024)

work page arXiv 2024
[14]

In: 2024 2nd Interna- tional Conference on Image, Algorithms and Artificial Intelligence (ICIAAI 2024)

Feng, H., Li, S., Shi, H., Ye, Z.: A comparative analysis of white box and gray box adversarial attacks to natural language processing systems. In: 2024 2nd Interna- tional Conference on Image, Algorithms and Artificial Intelligence (ICIAAI 2024). pp. 640–646. Atlantis Press (2024)

2024
[15]

Explaining and Harnessing Adversarial Examples

Goodfellow, I.J., Shlens, J., Szegedy, C.: Explaining and harnessing adversarial examples. arXiv preprint arXiv:1412.6572 (2014)

work page internal anchor Pith review arXiv 2014
[16]

In: International Conference on Computer Aided Verification

Guan, J., Fang, W., Ying, M.: Robustness verification of quantum classifiers. In: International Conference on Computer Aided Verification. pp. 151–174. Springer (2021)

2021
[17]

In: 2022 International Joint Conference on Neural Networks (IJCNN)

Guesmi, A., Khasawneh, K.N., Abu-Ghazaleh, N., Alouani, I.: Room: Adversarial machine learning attacks under real-time constraints. In: 2022 International Joint Conference on Neural Networks (IJCNN). pp. 1–10. IEEE (2022)

2022
[18]

He,K.,Zhang,X.,Ren,S.,Sun,J.:Deepresiduallearningforimagerecognition.In: Proceedings of the IEEE conference on computer vision and pattern recognition. pp. 770–778 (2016)

2016
[19]

Quantum Machine Intelligence 2(1), 2 (2020)

Henderson,M.,Shakya,S.,Pradhan,S.,Cook,T.:Quanvolutionalneuralnetworks: powering image recognition with quantum circuits. Quantum Machine Intelligence 2(1), 2 (2020)

2020
[20]

In: ICASSP 2023-2023 IEEE International Conference on Acous- tics, Speech and Signal Processing (ICASSP)

Huang, J.C., Tsai, Y.L., Yang, C.H.H., Su, C.F., Yu, C.M., Chen, P.Y., Kuo, S.Y.: Certified robustness of quantum classifiers against adversarial examples through quantum noise. In: ICASSP 2023-2023 IEEE International Conference on Acous- tics, Speech and Signal Processing (ICASSP). pp. 1–5. IEEE (2023)

2023
[21]

Optics Communications533, 129287 (2023)

Huang, S.Y., An, W.J., Zhang, D.S., Zhou, N.R.: Image classification and adver- sarial robustness analysis based on hybrid quantum–classical convolutional neural network. Optics Communications533, 129287 (2023)

2023
[22]

Torchattacks: A pytorch repository for advers arial attacks,

Kim, H.: Torchattacks: A pytorch repository for adversarial attacks. arXiv preprint arXiv:2010.01950 (2020)

work page arXiv 2010
[23]

In: Artificial intelligence safety and security, pp

Kurakin, A., Goodfellow, I.J., Bengio, S.: Adversarial examples in the physical world. In: Artificial intelligence safety and security, pp. 99–112. Chapman and Hall/CRC (2018)

2018
[24]

Quantum Engineering2022(1), 5701479 (2022)

Li, W., Chu, P.C., Liu, G.Z., Tian, Y.B., Qiu, T.H., Wang, S.M.: An image classifi- cation algorithm based on hybrid quantum classical convolutional neural network. Quantum Engineering2022(1), 5701479 (2022)

2022
[25]

ACM Computing Surveys56(6), 1–37 (2024)

Li, Y., Xie, B., Guo, S., Yang, Y., Xiao, B.: A survey of robustness and safety of 2d and 3d deep learning models against adversarial attacks. ACM Computing Surveys56(6), 1–37 (2024)

2024
[26]

Electronics11(8), 1283 (2022)

Liang, H., He, E., Zhao, Y., Jia, Z., Li, H.: Adversarial attack and defense: A survey. Electronics11(8), 1283 (2022)

2022
[27]

Physical Review A101(6), 062331 (2020) 40 N

Liu, N., Wittek, P.: Vulnerability of quantum classification to adversarial pertur- bations. Physical Review A101(6), 062331 (2020) 40 N. Azimi et al

2020
[28]

Scientific Reports15(1), 31780 (2025)

Long, C., Huang, M., Ye, X., Futamura, Y., Sakurai, T.: Hybrid quantum-classical- quantum convolutional neural networks. Scientific Reports15(1), 31780 (2025)

2025
[29]

Physical Review Research2(3), 033212 (2020)

Lu, S., Duan, L.M., Deng, D.L.: Quantum adversarial machine learning. Physical Review Research2(3), 033212 (2020)

2020
[30]

Fron- tiers in Signal Processing4(4), 100–106 (2020)

Lv, X.: Cifar-10 image classification based on convolutional neural network. Fron- tiers in Signal Processing4(4), 100–106 (2020)

2020
[31]

Physical Review A110(3), 032604 (2024)

Ma, W.g., Shi, Y.H., Xu, K., Fan, H.: Tomography-assisted noisy quantum cir- cuit simulator using matrix product density operators. Physical Review A110(3), 032604 (2024)

2024
[32]

Expert Systems with Ap- plications238, 122223 (2024)

Macas, M., Wu, C., Fuertes, W.: Adversarial examples: A survey of attacks and defenses in deep learning-enabled cybersecurity systems. Expert Systems with Ap- plications238, 122223 (2024)

2024
[33]

Towards Deep Learning Models Resistant to Adversarial Attacks

Madry, A.: Towards deep learning models resistant to adversarial attacks. arXiv preprint arXiv:1706.06083 (2017)

work page internal anchor Pith review arXiv 2017
[34]

IEEE Access10, 998–1019 (2021)

Mahmood, K., Mahmood, R., Rathbun, E., van Dijk, M.: Back in black: A com- parative evaluation of recent state-of-the-art black-box attacks. IEEE Access10, 998–1019 (2021)

2021
[35]

In: Proceedings of the IEEE conference on computer vision and pattern recognition

Moosavi-Dezfooli, S.M., Fawzi, A., Frossard, P.: Deepfool: a simple and accurate method to fool deep neural networks. In: Proceedings of the IEEE conference on computer vision and pattern recognition. pp. 2574–2582 (2016)

2016
[36]

Nicolae, M.I., Sinn, M., Tran, M.N., Buesser, B., Rawat, A., Wistuba, M., Zant- edeschi, V., Baracaldo, N., Chen, B., Ludwig, H., et al.: Adversarial robustness toolbox v1. 0.0. arXiv preprint arXiv:1807.01069 (2018)

work page arXiv 2018
[37]

Nielsen, M.A., Chuang, I.L.: Quantum computation and quantum information, vol. 2. Cambridge university press Cambridge (2001)

2001
[38]

Neurocomputing p

Qiao, Y., Sathyanarayana, N.B., Shi, C., He, Z., Wang, T., Hou, T.: A survey on adversarial machine learning: Attacks, defenses, real-world applications, and future research directions. Neurocomputing p. 132670 (2026)

2026
[39]

ACM Computing Surveys (CSUR)32(3), 300–335 (2000)

Rieffel, E., Polak, W.: An introduction to quantum computing for non-physicists. ACM Computing Surveys (CSUR)32(3), 300–335 (2000)

2000
[40]

Mathematics13(16), 2645 (2025)

Rizvi, S.M.A., Paracha, U.I., Khalid, U., Lee, K., Shin, H.: Quantum machine learning: Towards hybrid quantum-classical vision models. Mathematics13(16), 2645 (2025)

2025
[41]

arXiv preprint arXiv:1709.03423 (2017)

Strauss, T., Hanselmann, M., Junginger, A., Ulmer, H.: Ensemble methods as a defense to adversarial perturbations against deep neural networks. arXiv preprint arXiv:1709.03423 (2017)

work page arXiv 2017
[42]

IEEE Transactions on Evolutionary Computation23(5), 828–841 (2019)

Su, J., Vargas, D.V., Sakurai, K.: One pixel attack for fooling deep neural networks. IEEE Transactions on Evolutionary Computation23(5), 828–841 (2019)

2019
[43]

Franklin Open12, 100348 (2025)

Sutojo, T., Rustad, S., Akrom, M., Shidik, G.F., Dipojono, H.K., et al.: Acceptable noise level of quantum circuit for encrypting plaintext. Franklin Open12, 100348 (2025)

2025
[44]

Intriguing properties of neural networks

Szegedy, C.: Intriguing properties of neural networks. arXiv preprint arXiv:1312.6199 (2013)

work page internal anchor Pith review arXiv 2013
[45]

PyTorch, https://docs

Torch Contributors: CIFAR-10 Dataset Documentation. PyTorch, https://docs. pytorch.org/vision/main/generated/torchvision.datasets.CIFAR10.html, last ac- cessed 2025/08/31

2025
[46]

PyTorch, https: //docs.pytorch.org/vision/main/generated/torchvision.datasets.MNIST.html, last accessed 2025/08/31 QShield: Adversarial Robustness via Quantum Circuits 41

Torch Contributors: MNIST Dataset Documentation. PyTorch, https: //docs.pytorch.org/vision/main/generated/torchvision.datasets.MNIST.html, last accessed 2025/08/31 QShield: Adversarial Robustness via Quantum Circuits 41

2025
[47]

Advances in neural information processing systems33, 1633– 1645 (2020)

Tramer, F., Carlini, N., Brendel, W., Madry, A.: On adaptive attacks to adversarial example defenses. Advances in neural information processing systems33, 1633– 1645 (2020)

2020
[48]

Quantum Information Processing 23(1), 17 (2024)

Wang, A., Hu, J., Zhang, S., Li, L.: Shallow hybrid quantum-classical convolutional neural network model for image classification. Quantum Information Processing 23(1), 17 (2024)

2024
[49]

Neurocomputing514, 162–181 (2022)

Wang, J., Wang, C., Lin, Q., Luo, C., Wu, C., Li, J.: Adversarial attacks and defenses in deep learning for image recognition: A survey. Neurocomputing514, 162–181 (2022)

2022
[50]

Nature commu- nications12(1), 6961 (2021)

Wang, S., Fontana, E., Cerezo, M., Sharma, K., Sone, A., Cincio, L., Coles, P.J.: Noise-induced barren plateaus in variational quantum algorithms. Nature commu- nications12(1), 6961 (2021)

2021
[51]

In: Proceedings of the IEEE/CVF conference on computer vision and pattern recognition

Wang, X., He, K.: Enhancing the transferability of adversarial attacks through variance tuning. In: Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. pp. 1924–1933 (2021)

1924
[52]

Weber, T.: Constructing and Benchmarking Noise Models for Quantum Comput- ing. Ph.D. thesis, Staats-und Universitätsbibliothek Hamburg Carl von Ossietzky (2024)

2024
[53]

Physical Review Research5(2), 023186 (2023)

West, M.T., Erfani, S.M., Leckie, C., Sevior, M., Hollenberg, L.C., Usman, M.: Benchmarking adversarially robust quantum machine learning at scale. Physical Review Research5(2), 023186 (2023)

2023
[54]

White and M.J

White, C.D., White, M.J.: The magic of entangled top quarks. arXiv preprint arXiv:2406.07321 (2024)

work page arXiv 2024
[55]

Scientific Data10(1), 41 (2023)

Yang,J.,Shi,R.,Wei,D.,Liu,Z.,Zhao,L.,Ke,B.,Pfister,H.,Ni,B.:Medmnistv2- a large-scale lightweight benchmark for 2d and 3d biomedical image classification. Scientific Data10(1), 41 (2023)

2023
[56]

Zaman, K., Marchisio, A., Hanif, M.A., Shafique, M.: A survey on quantum ma- chinelearning:Currenttrends,challenges,opportunities,andtheroadahead.arXiv preprint arXiv:2310.10315 (2023)

work page arXiv 2023
[57]

In: Proceedings of the 2021 ACM Asia conference on computer and communications security

Zuo, F., Zeng, Q.: Exploiting the sensitivity of l2 adversarial examples to erase- and-restore. In: Proceedings of the 2021 ACM Asia conference on computer and communications security. pp. 40–51 (2021) 42 N. Azimi et al. A Hyperparameter Settings for Adversarial Attacks This appendix documents the complete set of hyperparameter configurations used for all...

2021