mlsanityData to 14 Oct 2026

Out-of-distribution generalization for learning quantum dynamics

arXiv 2204.10268 ↗First posted 21 Apr 2022quant-ph cs.LG stat.MLcited by 49

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Abstract (arXiv)

Generalization bounds are a critical tool to assess the training data requirements of Quantum Machine Learning (QML). Recent work has established guarantees for in-distribution generalization of quantum neural networks (QNNs), where training and testing data are drawn from the same data distribution. However, there are currently no results on out-of-distribution generalization in QML, where we require a trained model to perform well even on data drawn from a different distribution to the training distribution. Here, we prove out-of-distribution generalization for the task of learning an unknown unitary. In particular, we show that one can learn the action of a unitary on entangled states having trained only product states. Since product states can be prepared using only single-qubit gates, this advances the prospects of learning quantum dynamics on near term quantum hardware, and further opens up new methods for both the classical and quantum compilation of quantum circuits.

Key facts. Cited by 49 papers in the map (data through 14 Oct 2026). Builds on 27 of its 96 references that are in the map. First posted on arXiv 21 Apr 2022.

Builds on

27 of 96 references.

References · 27

  1. 2019Invariant Risk Minimizationcited by 1,854
  2. 2021Towards Out-Of-Distribution Generalization: A Surveycited by 436
  3. 2020The power of quantum neural networkscited by 379
  4. 2020Power of data in quantum machine learningcited by 338
  5. 2016Quantum Machine Learningcited by 326
  6. 2020A rigorous and robust quantum speed-up in supervised machine learningcited by 271
  7. 2020Predicting Many Properties of a Quantum System from Very Few Measurementscited by 233
  8. 2021Generalization in quantum machine learning from few training datacited by 216
  9. 2020Noise-Induced Barren Plateaus in Variational Quantum Algorithmscited by 193
  10. 2021Quantum advantage in learning from experimentscited by 188
  11. 2021Information-theoretic bounds on quantum advantage in machine learningcited by 96
  12. 2021Towards a Theoretical Framework of Out-of-Distribution Generalizationcited by 94
15 more
  1. 2021Provably efficient machine learning for quantum many-body problemscited by 91
  2. 2021Encoding-dependent generalization bounds for parametrized quantum circuitscited by 82
  3. 2021Out of Distribution Generalization in Machine Learningcited by 60
  4. 2021Exponential separations between learning with and without quantum memorycited by 52
  5. 2020Pseudo-dimension of quantum circuitscited by 30
  6. 2020Reformulation of the No-Free-Lunch Theorem for Entangled Data Setscited by 28
  7. 2021On the statistical complexity of quantum circuitscited by 25
  8. 2021Structural risk minimization for quantum linear classifierscited by 24
  9. 2018Sample Efficient Algorithms for Learning Quantum Channels in PAC Model and the Approximate State Discrimination Problemcited by 16
  10. 2020Learning models of quantum systems from experimentscited by 16
  11. 2021A Hierarchy for Replica Quantum Advantagecited by 16
  12. 2021Sample Complexity of Learning Parametric Quantum Circuitscited by 15
  13. 2019Machine Learning Phase Transitions with a Quantum Processorcited by 13
  14. 2021Revisiting dequantization and quantum advantage in learning taskscited by 12
  15. 2020Binary Classification with Classical Instances and Quantum Labelscited by 5

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 5; 2023: 14; 2024: 15; 2025: 9; 2026: 6.

49 papers.

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  1. 2023Challenges and Opportunities in Quantum Machine Learningcited by 203
  2. 2022Exponential concentration in quantum kernel methodscited by 90
  3. 2022Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networkscited by 52
  4. 2023Understanding quantum machine learning also requires rethinking generalizationcited by 49
  5. 2023Trainability barriers and opportunities in quantum generative modelingcited by 36
  6. 2022Learning to predict arbitrary quantum processescited by 35
  7. 2023A survey on the complexity of learning quantum statescited by 32
  8. 2023Generative quantum machine learning via denoising diffusion probabilistic modelscited by 30
  9. 2022Learning Quantum Processes and Hamiltonians via the Pauli Transfer Matrixcited by 23
  10. 2023Improved machine learning algorithm for predicting ground state propertiescited by 22
  11. 2024Learning shallow quantum circuitscited by 20
  12. 2022Power and limitations of single-qubit native quantum neural networkscited by 19
37 more
  1. 2023Learning quantum states and unitaries of bounded gate complexitycited by 15
  2. 2024Variational quantum simulation: a case study for understanding warm startscited by 14
  3. 2023The power and limitations of learning quantum dynamics incoherentlycited by 12
  4. 2025A Primer on Quantum Machine Learningcited by 12
  5. 2025Generative quantum advantage for classical and quantum problemscited by 11
  6. 2023Generalization of Quantum Machine Learning Models Using Quantum Fisher Information Metriccited by 10
  7. 2024Quantum Gradient Class Activation Map for Model Interpretabilitycited by 9
  8. 2023Expressibility-induced Concentration of Quantum Neural Tangent Kernelscited by 7
  9. 2024Certifying almost all quantum states with few single-qubit measurementscited by 7
  10. 2024Predicting Ground State Properties: Constant Sample Complexity and Deep Learning Algorithmscited by 7
  11. 2024Generalization Error Bound for Quantum Machine Learning in NISQ Era -- A Surveycited by 7
  12. 2025Quantum-Informed Machine Learning for Predicting Spatiotemporal Chaos with Practical Quantum Advantagecited by 7
  13. 2023Classical Verification of Quantum Learningcited by 6
  14. 2024Hamiltonian Property Testingcited by 6
  15. 2023Transition Role of Entangled Data in Quantum Machine Learningcited by 5
  16. 2023Quantum Next Generation Reservoir Computing: An Efficient Quantum Algorithm for Forecasting Quantum Dynamicscited by 5
  17. 2023Learning unitaries with quantum statistical queriescited by 5
  18. 2025Quantum Flow Matchingcited by 4
  19. 2024Adversarial Quantum Machine Learning: An Information-Theoretic Generalization Analysiscited by 3
  20. 2024Scalable quantum dynamics compilation via quantum machine learningcited by 3
  21. 2024Exact gradients for linear optics with single photonscited by 3
  22. 2025Role of scrambling and noise in temporal information processing with quantum systemscited by 3
  23. 2024Harnessing Quantum Support Vector Machines for Cross-Domain Classification of Quantum Statescited by 2
  24. 2024Learning to Classify Quantum Phases of Matter with a Few Measurementscited by 2
  25. 2025Hybrid Quantum-Classical Learning for Multiclass Image Classificationcited by 2
  26. 2026A PAC-Bayesian approach to generalization for quantum modelscited by 2
  27. 2024Data-Dependent Generalization Bounds for Parameterized Quantum Models Under Noisecited by 1
  28. 2025Stochastic Quantum Spiking Neural Networks with Quantum Memory and Local Learningcited by 1
  29. 2025Taming Barren Plateaus in Arbitrary Parameterized Quantum Circuits without Sacrificing Expressibilitycited by 1
  30. 2026Quantum Circuit Pre-Synthesis: Learning Local Edits to Reduce T-countcited by 1
  31. 2026Quantum Circuit-Based Learning Models: Bridging Quantum Computing and Machine Learningcited by 1
  32. 2026Q-Bridge: Code Translation for Quantum Machine Learning via LLMscited by 1
  33. 2024Hybrid Classical-Quantum architecture for vectorised image classification of hand-written sketchescited by 0
  34. 2024Few measurement shots challenge generalization in learning to classify entanglementcited by 0
  35. 2025The interplay of robustness and generalization in quantum machine learningcited by 0
  36. 2026Multitask Learning for Earth Observation Data Classification with Hybrid Quantum Networkcited by 0
  37. 2026A Theory of Finite-Noise Optima and Generalization in Quantum Machine Learningcited by 0