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An end-to-end trainable hybrid classical-quantum classifier

arXiv 2102.02416 ↗First posted 4 Feb 2021quant-ph cs.LGcited by 49

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Abstract (arXiv)

We introduce a hybrid model combining a quantum-inspired tensor network and a variational quantum circuit to perform supervised learning tasks. This architecture allows for the classical and quantum parts of the model to be trained simultaneously, providing an end-to-end training framework. We show that compared to the principal component analysis, a tensor network based on the matrix product state with low bond dimensions performs better as a feature extractor for the input data of the variational quantum circuit in the binary and ternary classification of MNIST and Fashion-MNIST datasets. The architecture is highly adaptable and the classical-quantum boundary can be adjusted according the availability of the quantum resource by exploiting the correspondence between tensor networks and quantum circuits.

Key facts. Cited by 49 papers in the map (data through 7 Oct 2026). Builds on 13 of its 26 references that are in the map. First posted on arXiv 4 Feb 2021.

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13 of 26 references.

References · 13

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  2. 2014Very Deep Convolutional Networks for Large-Scale Image Recognitioncited by 15,267
  3. 2017Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithmscited by 4,283
  4. 2014Going Deeper with Convolutionscited by 4,231
  5. 2015Tensorizing Neural Networkscited by 246
  6. 2015On the Expressive Power of Deep Learning: A Tensor Analysiscited by 97
  7. 2020Reinforcement Learning with Quantum Variational Circuitscited by 74
  8. 2016Supervised Learning with Quantum-Inspired Tensor Networkscited by 35
  9. 2018From probabilistic graphical models to generalized tensor networks for supervised learningcited by 31
  10. 2019TensorNetwork for Machine Learningcited by 29
  11. 2020Hybrid quantum-classical classifier based on tensor network and variational quantum circuitcited by 26
  12. 2017Deep Learning and Quantum Entanglement: Fundamental Connections with Implications to Network Designcited by 22
1 more
  1. 2015Matrix Product State for Feature Extraction of Higher-Order Tensorscited by 6

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 4; 2022: 8; 2023: 10; 2024: 11; 2025: 10; 2026: 6.

49 papers.

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  1. 2021Federated Quantum Machine Learningcited by 82
  2. 2021Variational Quantum Reinforcement Learning via Evolutionary Optimizationcited by 50
  3. 2022A Survey on Quantum Reinforcement Learningcited by 50
  4. 2022Theoretical Error Performance Analysis for Variational Quantum Circuit Based Functional Regressioncited by 26
  5. 2022Quantum deep recurrent reinforcement learningcited by 23
  6. 2024Learning to Program Variational Quantum Circuits with Fast Weightscited by 23
  7. 2021Quantum Architecture Search via Continual Reinforcement Learningcited by 22
  8. 2022Problem-Dependent Power of Quantum Neural Networks on Multi-Class Classificationcited by 20
  9. 2023Asynchronous training of quantum reinforcement learningcited by 20
  10. 2023Federated Quantum Machine Learning with Differential Privacycited by 17
  11. 2023Tensor networks for quantum machine learningcited by 16
  12. 2025Learning to Measure Quantum Neural Networkscited by 15
37 more
  1. 2022Federated Quantum Natural Gradient Descent for Quantum Federated Learningcited by 14
  2. 2023Optimizing Quantum Federated Learning Based on Federated Quantum Natural Gradient Descentcited by 14
  3. 2023Efficient quantum recurrent reinforcement learning via quantum reservoir computingcited by 14
  4. 2024Quantum-Train-Based Distributed Multi-Agent Reinforcement Learningcited by 14
  5. 2021Variational Quanvolutional Neural Networks with enhanced image encodingcited by 13
  6. 2024Differentiable Quantum Architecture Search in Asynchronous Quantum Reinforcement Learningcited by 13
  7. 2024Quantum Machine Learning Architecture Search via Deep Reinforcement Learningcited by 12
  8. 2022A Hybrid Quantum-Classical Neural Network Architecture for Binary Classificationcited by 11
  9. 2024Quantum Advantage Actor-Critic for Reinforcement Learningcited by 9
  10. 2024Quantum Gradient Class Activation Map for Model Interpretabilitycited by 9
  11. 2024Evolutionary Optimization for Designing Variational Quantum Circuits with High Model Capacitycited by 9
  12. 2023Quantum Federated Learning With Quantum Networkscited by 8
  13. 2024An Introduction to Quantum Reinforcement Learning (QRL)cited by 7
  14. 2025Adaptive Non-local Observable on Quantum Neural Networkscited by 7
  15. 2025Differentiable Quantum Architecture Search in Quantum-Enhanced Neural Network Parameter Generationcited by 7
  16. 2025Learning to Program Quantum Measurements for Machine Learningcited by 7
  17. 2025TensorHyper-VQC: A Tensor-Train-Guided Hypernetwork for Robust and Scalable Variational Quantum Computingcited by 5
  18. 2022Random Quantum Neural Networks (RQNN) for Noisy Image Recognitioncited by 4
  19. 2023Post-variational quantum neural networkscited by 3
  20. 2025Transfer Learning Analysis of Variational Quantum Circuitscited by 3
  21. 2025Introduction to Quantum Machine Learning and Quantum Architecture Searchcited by 3
  22. 2023Quantum deep Q learning with distributed prioritized experience replaycited by 2
  23. 2024Quantum Machine Learning: An Interplay Between Quantum Computing and Machine Learningcited by 2
  24. 2023Quantum Imitation Learningcited by 1
  25. 2023Pre-training Tensor-Train Networks Facilitates Machine Learning with Variational Quantum Circuitscited by 1
  26. 2024A Quantum-Classical Collaborative Training Architecture Based on Quantum State Fidelitycited by 1
  27. 2025VQC-MLPNet: An Unconventional Hybrid Quantum-Classical Architecture for Scalable and Robust Quantum Machine Learningcited by 1
  28. 2025Neural Architecture Search for Quantum Autoencoderscited by 1
  29. 2026Fedcompass: Federated Clustered and Periodic Aggregation Framework for Hybrid Classical-Quantum Modelscited by 1
  30. 2022An Efficient Binary Harris Hawks Optimization based on Quantum SVM for Cancer Classification Taskscited by 0
  31. 2024Expanding the Horizon: Enabling Hybrid Quantum Transfer Learning for Long-Tailed Chest X-Ray Classificationcited by 0
  32. 2025An Efficient Quantum Classifier Based on Hamiltonian Representationscited by 0
  33. 2026Random-Matrix-Induced Simplicity Bias in Over-parameterized Variational Quantum Circuitscited by 0
  34. 2026Quantum LEGO Learning: A Modular Design Principle for Hybrid Artificial Intelligencecited by 0
  35. 2026Quantum-inspired tensor networks in machine learning modelscited by 0
  36. 2026Diagonal Adaptive Non-local Observables on Quantum Neural Networkscited by 0
  37. 2026Hybrid Variational Quantum-Classical Framework with Adaptive Weighting and Efficiency Assessmentcited by 0