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Parameterized quantum circuits as machine learning models

arXiv 1906.07682 ↗First posted 18 Jun 2019quant-ph cs.LGcited by 330

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Abstract (arXiv)

Hybrid quantum-classical systems make it possible to utilize existing quantum computers to their fullest extent. Within this framework, parameterized quantum circuits can be regarded as machine learning models with remarkable expressive power. This Review presents the components of these models and discusses their application to a variety of data-driven tasks, such as supervised learning and generative modeling. With an increasing number of experimental demonstrations carried out on actual quantum hardware and with software being actively developed, this rapidly growing field is poised to have a broad spectrum of real-world applications.

Key facts. Cited by 330 papers in the map (data through 7 Oct 2026). First posted on arXiv 18 Jun 2019.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 60; 2022: 56; 2023: 51; 2024: 42; 2025: 63; 2026: 58.

330 papers.

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  1. 2021Supervised quantum machine learning models are kernel methodscited by 199
  2. 2021Theory of overparametrization in quantum neural networkscited by 100
  3. 2021QuantumNAS: Noise-Adaptive Search for Robust Quantum Circuitscited by 97
  4. 2021Quantum machine learning beyond kernel methodscited by 91
  5. 2021Parametrized quantum policies for reinforcement learningcited by 87
  6. 2021Federated Quantum Machine Learningcited by 82
  7. 2021Encoding-dependent generalization bounds for parametrized quantum circuitscited by 81
  8. 2021Noisy intermediate-scale quantum (NISQ) algorithmscited by 79
  9. 2021Reinforcement learning for optimization of variational quantum circuit architecturescited by 76
  10. 2022Exploiting symmetry in variational quantum machine learningcited by 68
  11. 2021QNLP in Practice: Running Compositional Models of Meaning on a Quantum Computercited by 65
  12. 2021Quantum Architecture Search via Deep Reinforcement Learningcited by 58
38 more
  1. 2021Quantum Federated Learning with Quantum Datacited by 53
  2. 2021Variational Quantum Reinforcement Learning via Evolutionary Optimizationcited by 50
  3. 2022A Survey on Quantum Reinforcement Learningcited by 50
  4. 2023Understanding quantum machine learning also requires rethinking generalizationcited by 48
  5. 2021Towards understanding the power of quantum kernels in the NISQ eracited by 43
  6. 2022Escaping from the Barren Plateau via Gaussian Initializations in Deep Variational Quantum Circuitscited by 42
  7. 2022Quantum Self-Attention Neural Networks for Text Classificationcited by 42
  8. 2022Equivariant quantum circuits for learning on weighted graphscited by 41
  9. 2022Recent Advances for Quantum Neural Networks in Generative Learningcited by 39
  10. 2022Systematic Literature Review: Quantum Machine Learning and its applicationscited by 32
  11. 2023On quantum backpropagation, information reuse, and cheating measurement collapsecited by 32
  12. 2023Shadows of quantum machine learningcited by 31
  13. 2021Analyzing the barren plateau phenomenon in training quantum neural networks with the ZX-calculuscited by 30
  14. 2021Quantum machine learning with differential privacycited by 30
  15. 2023Tensor Networks Meet Neural Networks: A Survey and Future Perspectivescited by 29
  16. 2023A Survey on Quantum Machine Learning: Current Trends, Challenges, Opportunities, and the Road Aheadcited by 29
  17. 2023Machine Learning for Anomaly Detection in Particle Physicscited by 29
  18. 2021Automatic design of quantum feature mapscited by 27
  19. 2021QTN-VQC: An End-to-End Learning framework for Quantum Neural Networkscited by 27
  20. 2022Theoretical Error Performance Analysis for Variational Quantum Circuit Based Functional Regressioncited by 26
  21. 2022QSAN: A Near-term Achievable Quantum Self-Attention Networkcited by 25
  22. 2021Structural risk minimization for quantum linear classifierscited by 24
  23. 2023Quantum Recurrent Neural Networks for Sequential Learningcited by 24
  24. 2024On the relation between trainability and dequantization of variational quantum learning modelscited by 24
  25. 2021Exponentially Many Local Minima in Quantum Neural Networkscited by 22
  26. 2021Quantum Architecture Search via Continual Reinforcement Learningcited by 22
  27. 2022Hybrid Quantum-Classical Generative Adversarial Network for High Resolution Image Generationcited by 22
  28. 2023Let Quantum Neural Networks Choose Their Own Frequenciescited by 22
  29. 2023Potential and limitations of random Fourier features for dequantizing quantum machine learningcited by 22
  30. 2021Hybrid Quantum-Classical Graph Convolutional Networkcited by 21
  31. 2022Quantum Policy Gradient Algorithm with Optimized Action Decodingcited by 21
  32. 2023Training robust and generalizable quantum modelscited by 21
  33. 2021Quantum Self-Supervised Learningcited by 20
  34. 2021The dilemma of quantum neural networkscited by 20
  35. 2021Hybrid Quantum Classical Graph Neural Networks for Particle Track Reconstructioncited by 20
  36. 2022Problem-Dependent Power of Quantum Neural Networks on Multi-Class Classificationcited by 20
  37. 2024Learning shallow quantum circuitscited by 20
  38. 2021Style-based quantum generative adversarial networks for Monte Carlo eventscited by 19

50 most cited of 330 All 330 (JSON)