mlsanityData to 7 Oct 2026

Efficient Learning for Deep Quantum Neural Networks

arXiv 1902.10445 ↗First posted 27 Feb 2019quant-ph cs.GT cs.LGcited by 160

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Abstract (arXiv)

Neural networks enjoy widespread success in both research and industry and, with the imminent advent of quantum technology, it is now a crucial challenge to design quantum neural networks for fully quantum learning tasks. Here we propose the use of quantum neurons as a building block for quantum feed-forward neural networks capable of universal quantum computation. We describe the efficient training of these networks using the fidelity as a cost function and provide both classical and efficient quantum implementations. Our method allows for fast optimisation with reduced memory requirements: the number of qudits required scales with only the width, allowing the optimisation of deep networks. We benchmark our proposal for the quantum task of learning an unknown unitary and find remarkable generalisation behaviour and a striking robustness to noisy training data.

Key facts. Cited by 160 papers in the map (data through 7 Oct 2026). First posted on arXiv 27 Feb 2019.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 38; 2022: 25; 2023: 28; 2024: 20; 2025: 29; 2026: 20.

160 papers.

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  1. 2023Challenges and Opportunities in Quantum Machine Learningcited by 202
  2. 2024Barren Plateaus in Variational Quantum Computingcited by 130
  3. 2021Theory of overparametrization in quantum neural networkscited by 100
  4. 2021QNLP in Practice: Running Compositional Models of Meaning on a Quantum Computercited by 65
  5. 2021Equivalence of quantum barren plateaus to cost concentration and narrow gorgescited by 53
  6. 2021Quantum Federated Learning with Quantum Datacited by 53
  7. 2021lambeq: An Efficient High-Level Python Library for Quantum NLPcited by 43
  8. 2022Recent Advances for Quantum Neural Networks in Generative Learningcited by 39
  9. 2021Recent advances for quantum classifierscited by 35
  10. 2021On Circuit-based Hybrid Quantum Neural Networks for Remote Sensing Imagery Classificationcited by 33
  11. 2021Subtleties in the trainability of quantum machine learning modelscited by 33
  12. 2023A survey on the complexity of learning quantum statescited by 31
38 more
  1. 2022Benchmarking Adversarially Robust Quantum Machine Learning at Scalecited by 28
  2. 2022projUNN: efficient method for training deep networks with unitary matricescited by 27
  3. 2021Entangled Datasets for Quantum Machine Learningcited by 26
  4. 2023Towards quantum enhanced adversarial robustness in machine learningcited by 26
  5. 2021On the statistical complexity of quantum circuitscited by 25
  6. 2021QuantumFed: A Federated Learning Framework for Collaborative Quantum Trainingcited by 22
  7. 2022Analytic theory for the dynamics of wide quantum neural networkscited by 21
  8. 2021Quantum Self-Supervised Learningcited by 20
  9. 2021The dilemma of quantum neural networkscited by 20
  10. 2024Learning shallow quantum circuitscited by 20
  11. 2024FedQNN: Federated Learning using Quantum Neural Networkscited by 20
  12. 2021Deep Reinforcement Learning with Quantum-inspired Experience Replaycited by 18
  13. 2023Beyond Classical Attention: Quantum Attention for Scalable Computationcited by 18
  14. 2024QFNN-FFD: Quantum Federated Neural Network for Financial Fraud Detectioncited by 18
  15. 2022Certified Robustness of Quantum Classifiers against Adversarial Examples through Quantum Noisecited by 17
  16. 2023Deep learning models for price forecasting of financial time series: A review of recent advancements: 2020-2022cited by 16
  17. 2021Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms?cited by 14
  18. 2021Variational Quantum Soft Actor-Criticcited by 14
  19. 2023Quantum Machine Learning on Near-Term Quantum Devices: Current State of Supervised and Unsupervised Techniques for Real-World Applicationscited by 14
  20. 2021Learning quantum data with the quantum Earth Mover's distancecited by 13
  21. 2021Quantum Annealing Formulation for Binary Neural Networkscited by 13
  22. 2022Quantum Neural Network Classifiers: A Tutorialcited by 13
  23. 2022An Invitation to Distributed Quantum Neural Networkscited by 13
  24. 2023Differentiable Quantum Architecture Search for Quantum Reinforcement Learningcited by 13
  25. 2023Reduction of finite sampling noise in quantum neural networkscited by 12
  26. 2022A Hybrid Quantum-Classical Neural Network Architecture for Binary Classificationcited by 11
  27. 2022Quantum activation functions for quantum neural networkscited by 10
  28. 2021Effects of quantum resources on the statistical complexity of quantum circuitscited by 9
  29. 2023Effects of noise on the overparametrization of quantum neural networkscited by 9
  30. 2024Equilibrium Propagation: the Quantum and the Thermal Casescited by 9
  31. 2025QCPINN: Quantum-Classical Physics-Informed Neural Networks for Solving PDEscited by 9
  32. 2021A Leap among Quantum Computing and Quantum Neural Networks: A Surveycited by 8
  33. 2022Toward Physically Realizable Quantum Neural Networkscited by 8
  34. 2023Quantum Neural Network for Quantum Neural Computingcited by 8
  35. 2021Noise-Resilient Quantum Machine Learning for Stability Assessment of Power Systemscited by 7
  36. 2021Quantum Machine Learning for Financecited by 7
  37. 2022Verifying Fairness in Quantum Machine Learningcited by 7
  38. 2023Quantum-Inspired Neural Network Model of Optical Illusionscited by 7

50 most cited of 160 All 160 (JSON)