mlsanityData to 14 Oct 2026

Training robust and generalizable quantum models

arXiv 2311.11871 ↗First posted 20 Nov 2023quant-ph cs.LG math.OCcited by 21

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Abstract (arXiv)

Adversarial robustness and generalization are both crucial properties of reliable machine learning models. In this paper, we study these properties in the context of quantum machine learning based on Lipschitz bounds. We derive parameter-dependent Lipschitz bounds for quantum models with trainable encoding, showing that the norm of the data encoding has a crucial impact on the robustness against data perturbations. Further, we derive a bound on the generalization error which explicitly involves the parameters of the data encoding. Our theoretical findings give rise to a practical strategy for training robust and generalizable quantum models by regularizing the Lipschitz bound in the cost. Further, we show that, for fixed and non-trainable encodings, as those frequently employed in quantum machine learning, the Lipschitz bound cannot be influenced by tuning the parameters. Thus, trainable encodings are crucial for systematically adapting robustness and generalization during training. The practical implications of our theoretical findings are illustrated with numerical results.

Key facts. Cited by 21 papers in the map (data through 14 Oct 2026). Builds on 39 of its 70 references that are in the map. First posted on arXiv 20 Nov 2023.

Builds on

39 of 70 references.

References · 39

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27 more
  1. 2020The effect of data encoding on the expressive power of variational quantum machine learning modelscited by 333
  2. 2019Parameterized quantum circuits as machine learning modelscited by 332
  3. 2018Regularisation of Neural Networks by Enforcing Lipschitz Continuitycited by 314
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  5. 2018Lipschitz-Margin Training: Scalable Certification of Perturbation Invariance for Deep Neural Networkscited by 195
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 7; 2025: 8; 2026: 5.

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  1. 2024On the relation between trainability and dequantization of variational quantum learning modelscited by 25
  2. 2024A Comparative Analysis of Adversarial Robustness for Quantum and Classical Machine Learning Modelscited by 12
  3. 2024Adversarial Robustness Guarantees for Quantum Classifierscited by 9
  4. 2023Quantum Neural Networks under Depolarization Noise: Exploring White-Box Attacks and Defensescited by 5
  5. 2024Quantum Neural Networks in Practice: A Comparative Study with Classical Models from Standard Data Sets to Industrial Imagescited by 5
  6. 2024QUACK: Quantum Aligned Centroid Kernelcited by 4
  7. 2024Robustness and Generalization in Quantum Reinforcement Learning via Lipschitz Regularizationcited by 4
  8. 2024Adversarial Quantum Machine Learning: An Information-Theoretic Generalization Analysiscited by 3
  9. 2025Predictive control of blast furnace temperature in steelmaking with hybrid depth-infused quantum neural networkscited by 2
  10. 2025On the Generalization of Adversarially Trained Quantum Classifierscited by 1
  11. 2025Entangled Threats: A Unified Kill Chain Model for Quantum Machine Learning Securitycited by 1
  12. 2025Efficient and Accurate Estimation of Lipschitz Constants for Hybrid Quantum-Classical Decision Modelscited by 0
9 more
  1. 2025Detecting underdetermination in parameterized quantum circuitscited by 0
  2. 2025Hybrid quantum recurrent neural network for remaining useful life prediction of turbofan enginescited by 0
  3. 2025The interplay of robustness and generalization in quantum machine learningcited by 0
  4. 2025MediQ-GAN: Quantum-Inspired GAN for High Resolution Medical Image Generationcited by 0
  5. 2026Defending Quantum Classifiers against Adversarial Perturbations through Quantum Autoencoderscited by 0
  6. 2026Quantum Interval Bound Propagation for Certified Training of Quantum Neural Networkscited by 0
  7. 2026Controlled Steering-Based State Preparation for Adversarial-Robust Quantum Machine Learningcited by 0
  8. 2026Mitigating Measurement-Induced Training Instability in Hybrid Quantum Neural Networks for Protein Classificationcited by 0
  9. 2026A Multiclass Quantum Aligned Centroid Kernelcited by 0