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Noise-Induced Barren Plateaus in Variational Quantum Algorithms

arXiv 2007.14384 ↗First posted 28 Jul 2020quant-ph cs.LGcited by 192

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Abstract (arXiv)

Variational Quantum Algorithms (VQAs) may be a path to quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) computers. A natural question is whether noise on NISQ devices places fundamental limitations on VQA performance. We rigorously prove a serious limitation for noisy VQAs, in that the noise causes the training landscape to have a barren plateau (i.e., vanishing gradient). Specifically, for the local Pauli noise considered, we prove that the gradient vanishes exponentially in the number of qubits n if the depth of the ansatz grows linearly with n. These noise-induced barren plateaus (NIBPs) are conceptually different from noise-free barren plateaus, which are linked to random parameter initialization. Our result is formulated for a generic ansatz that includes as special cases the Quantum Alternating Operator Ansatz and the Unitary Coupled Cluster Ansatz, among others. For the former, our numerical heuristics demonstrate the NIBP phenomenon for a realistic hardware noise model.

Key facts. Cited by 192 papers in the map (data through 7 Oct 2026). First posted on arXiv 28 Jul 2020.

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Citing papers per year: 2021: 25; 2022: 38; 2023: 32; 2024: 27; 2025: 30; 2026: 40.

192 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. 2021Equivalence of quantum barren plateaus to cost concentration and narrow gorgescited by 53
  10. 2022Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networkscited by 52
  11. 2022Out-of-distribution generalization for learning quantum dynamicscited by 49
  12. 2023Understanding quantum machine learning also requires rethinking generalizationcited by 48
38 more
  1. 2022Escaping from the Barren Plateau via Gaussian Initializations in Deep Variational Quantum Circuitscited by 42
  2. 2022Equivariant quantum circuits for learning on weighted graphscited by 41
  3. 2024Curriculum reinforcement learning for quantum architecture search under hardware errorscited by 37
  4. 2024KANQAS: Kolmogorov-Arnold Network for Quantum Architecture Searchcited by 36
  5. 2021Recent advances for quantum classifierscited by 35
  6. 2023Trainability barriers and opportunities in quantum generative modelingcited by 35
  7. 2021Subtleties in the trainability of quantum machine learning modelscited by 33
  8. 2023On quantum backpropagation, information reuse, and cheating measurement collapsecited by 32
  9. 2024A comprehensive review of Quantum Machine Learning: from NISQ to Fault Tolerancecited by 32
  10. 2024Quantum Architecture Search: A Surveycited by 31
  11. 2021Analyzing the barren plateau phenomenon in training quantum neural networks with the ZX-calculuscited by 30
  12. 2023Generative quantum machine learning via denoising diffusion probabilistic modelscited by 30
  13. 2023Machine Learning for Anomaly Detection in Particle Physicscited by 29
  14. 2021Entangled Datasets for Quantum Machine Learningcited by 26
  15. 2022QSAN: A Near-term Achievable Quantum Self-Attention Networkcited by 25
  16. 2022Analytic theory for the dynamics of wide quantum neural networkscited by 21
  17. 2021Hybrid Quantum Classical Graph Neural Networks for Particle Track Reconstructioncited by 20
  18. 2022Symmetric Pruning in Quantum Neural Networkscited by 20
  19. 2022Problem-Dependent Power of Quantum Neural Networks on Multi-Class Classificationcited by 20
  20. 2024Learning shallow quantum circuitscited by 20
  21. 2021Variational inference with a quantum computercited by 18
  22. 2023On fundamental aspects of quantum extreme learning machinescited by 18
  23. 2022An exponentially-growing family of universal quantum circuitscited by 17
  24. 2022Stochastic noise can be helpful for variational quantum algorithmscited by 16
  25. 2022Enhancing Quantum Adversarial Robustness by Randomized Encodingscited by 16
  26. 2021A semi-agnostic ansatz with variable structure for quantum machine learningcited by 15
  27. 2021Optimal training of variational quantum algorithms without barren plateauscited by 15
  28. 2023Thermodynamic AI and the fluctuation frontiercited by 15
  29. 2021Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms?cited by 14
  30. 2023Parallel Hybrid Networks: an interplay between quantum and classical neural networkscited by 14
  31. 2023Quantum Kernel Alignment with Stochastic Gradient Descentcited by 14
  32. 2023Quantum Machine Learning on Near-Term Quantum Devices: Current State of Supervised and Unsupervised Techniques for Real-World Applicationscited by 14
  33. 2024Variational quantum simulation: a case study for understanding warm startscited by 14
  34. 2021Learning quantum data with the quantum Earth Mover's distancecited by 13
  35. 2022Avoiding Barren Plateaus with Classical Deep Neural Networkscited by 13
  36. 2022Quantum Neural Network Classifiers: A Tutorialcited by 13
  37. 2022The Complexity of NISQcited by 13
  38. 2022Near-Term Quantum Computing Techniques: Variational Quantum Algorithms, Error Mitigation, Circuit Compilation, Benchmarking and Classical Simulationcited by 13

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