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Trainability of Dissipative Perceptron-Based Quantum Neural Networks

arXiv 2005.12458 ↗First posted 26 May 2020quant-ph cs.LGcited by 56

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Abstract (arXiv)

Several architectures have been proposed for quantum neural networks (QNNs), with the goal of efficiently performing machine learning tasks on quantum data. Rigorous scaling results are urgently needed for specific QNN constructions to understand which, if any, will be trainable at a large scale. Here, we analyze the gradient scaling (and hence the trainability) for a recently proposed architecture that we called dissipative QNNs (DQNNs), where the input qubits of each layer are discarded at the layer's output. We find that DQNNs can exhibit barren plateaus, i.e., gradients that vanish exponentially in the number of qubits. Moreover, we provide quantitative bounds on the scaling of the gradient for DQNNs under different conditions, such as different cost functions and circuit depths, and show that trainability is not always guaranteed.

Key facts. Cited by 56 papers in the map (data through 7 Oct 2026). First posted on arXiv 26 May 2020.

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Citing papers per year: 2021: 18; 2022: 13; 2023: 12; 2024: 3; 2025: 6; 2026: 4.

56 papers.

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  1. 2021Generalization in quantum machine learning from few training datacited by 214
  2. 2023Challenges and Opportunities in Quantum Machine Learningcited by 202
  3. 2021Connecting ansatz expressibility to gradient magnitudes and barren plateauscited by 180
  4. 2024Barren Plateaus in Variational Quantum Computingcited by 130
  5. 2021Theory of overparametrization in quantum neural networkscited by 100
  6. 2022Exponential concentration in quantum kernel methodscited by 89
  7. 2023Does provable absence of barren plateaus imply classical simulability?cited by 78
  8. 2022Theory for Equivariant Quantum Neural Networkscited by 60
  9. 2022Group-Invariant Quantum Machine Learningcited by 56
  10. 2021Equivalence of quantum barren plateaus to cost concentration and narrow gorgescited by 53
  11. 2022Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networkscited by 52
  12. 2023Understanding quantum machine learning also requires rethinking generalizationcited by 48
38 more
  1. 2022Representation Theory for Geometric Quantum Machine Learningcited by 40
  2. 2023Trainability barriers and opportunities in quantum generative modelingcited by 35
  3. 2021Subtleties in the trainability of quantum machine learning modelscited by 33
  4. 2021Analyzing the barren plateau phenomenon in training quantum neural networks with the ZX-calculuscited by 30
  5. 2021Entangled Datasets for Quantum Machine Learningcited by 26
  6. 2021On the statistical complexity of quantum circuitscited by 25
  7. 2022Analytic theory for the dynamics of wide quantum neural networkscited by 21
  8. 2024Learning shallow quantum circuitscited by 20
  9. 2022Enhancing Quantum Adversarial Robustness by Randomized Encodingscited by 16
  10. 2021A semi-agnostic ansatz with variable structure for quantum machine learningcited by 15
  11. 2023Quantum Machine Learning on Near-Term Quantum Devices: Current State of Supervised and Unsupervised Techniques for Real-World Applicationscited by 14
  12. 2021Learning quantum data with the quantum Earth Mover's distancecited by 13
  13. 2021Adaptive shot allocation for fast convergence in variational quantum algorithmscited by 12
  14. 2021Effects of quantum resources on the statistical complexity of quantum circuitscited by 9
  15. 2021Long-time simulations with high fidelity on quantum hardwarecited by 8
  16. 2021A Leap among Quantum Computing and Quantum Neural Networks: A Surveycited by 8
  17. 2022Mitigating barren plateaus of variational quantum eigensolverscited by 8
  18. 2023Quantum Neural Network for Quantum Neural Computingcited by 8
  19. 2021Quantum Machine Learning for Financecited by 7
  20. 2022Inference-Based Quantum Sensingcited by 7
  21. 2023Expressibility-induced Concentration of Quantum Neural Tangent Kernelscited by 7
  22. 2023Time-Warping Invariant Quantum Recurrent Neural Networks via Quantum-Classical Adaptive Gatingcited by 5
  23. 2025TensorHyper-VQC: A Tensor-Train-Guided Hypernetwork for Robust and Scalable Variational Quantum Computingcited by 5
  24. 2021Variational Quantum Classifiers Through the Lens of the Hessiancited by 4
  25. 2022NAPA: Intermediate-level Variational Native-pulse Ansatz for Variational Quantum Algorithmscited by 4
  26. 2022Quark: A Gradient-Free Quantum Learning Framework for Classification Taskscited by 4
  27. 2022The Quantum Path Kernel: a Generalized Quantum Neural Tangent Kernel for Deep Quantum Machine Learningcited by 4
  28. 2023Variational Denoising for Variational Quantum Eigensolvercited by 4
  29. 2022Quantum Capsule Networkscited by 3
  30. 2025Stability and Generalization of Quantum Neural Networkscited by 3
  31. 2021Multi-layer Perceptron Trainability Explained via Variabilitycited by 2
  32. 2021Mitigating Noise-Induced Gradient Vanishing in Variational Quantum Algorithm Trainingcited by 2
  33. 2023Error mitigation of entangled states using brainbox quantum autoencoderscited by 1
  34. 2023Pre-training Tensor-Train Networks Facilitates Machine Learning with Variational Quantum Circuitscited by 1
  35. 2024Leveraging Pre-Trained Neural Networks to Enhance Machine Learning with Variational Quantum Circuitscited by 1
  36. 2023Symbolically integrating tensor networks over various random tensors by the second version of Python RTNIcited by 0
  37. 2025QFDNN: A Resource-Efficient Variational Quantum Feature Deep Neural Networks for Fraud Detection and Loan Predictioncited by 0
  38. 2025Physical models realizing the transformer architecture of large language modelscited by 0

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