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Barren plateaus in quantum neural network training landscapes

arXiv 1803.11173 ↗First posted 29 Mar 2018quant-ph cs.LG physics.chem-phcited by 624

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Abstract (arXiv)

Many experimental proposals for noisy intermediate scale quantum devices involve training a parameterized quantum circuit with a classical optimization loop. Such hybrid quantum-classical algorithms are popular for applications in quantum simulation, optimization, and machine learning. Due to its simplicity and hardware efficiency, random circuits are often proposed as initial guesses for exploring the space of quantum states. We show that the exponential dimension of Hilbert space and the gradient estimation complexity make this choice unsuitable for hybrid quantum-classical algorithms run on more than a few qubits. Specifically, we show that for a wide class of reasonable parameterized quantum circuits, the probability that the gradient along any reasonable direction is non-zero to some fixed precision is exponentially small as a function of the number of qubits. We argue that this is related to the 2-design characteristic of random circuits, and that solutions to this problem must be studied.

Key facts. Cited by 624 papers in the map (data through 7 Oct 2026). First posted on arXiv 29 Mar 2018.

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Citing papers per year: 2021: 64; 2022: 91; 2023: 78; 2024: 93; 2025: 126; 2026: 172.

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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. 2021Supervised quantum machine learning models are kernel methodscited by 199
  4. 2021Connecting ansatz expressibility to gradient magnitudes and barren plateauscited by 180
  5. 2024Barren Plateaus in Variational Quantum Computingcited by 130
  6. 2021Theory of overparametrization in quantum neural networkscited by 100
  7. 2021QuantumNAS: Noise-Adaptive Search for Robust Quantum Circuitscited by 97
  8. 2021Quantum machine learning beyond kernel methodscited by 91
  9. 2021The Inductive Bias of Quantum Kernelscited by 90
  10. 2022Exponential concentration in quantum kernel methodscited by 89
  11. 2024Better than classical? The subtle art of benchmarking quantum machine learning modelscited by 82
  12. 2021Noisy intermediate-scale quantum (NISQ) algorithmscited by 79
38 more
  1. 2023Does provable absence of barren plateaus imply classical simulability?cited by 78
  2. 2021Training Quantum Embedding Kernels on Near-Term Quantum Computerscited by 69
  3. 2022Exploiting symmetry in variational quantum machine learningcited by 68
  4. 2022Theory for Equivariant Quantum Neural Networkscited by 60
  5. 2022Group-Invariant Quantum Machine Learningcited by 56
  6. 2021Equivalence of quantum barren plateaus to cost concentration and narrow gorgescited by 53
  7. 2022Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networkscited by 52
  8. 2023Understanding quantum machine learning also requires rethinking generalizationcited by 48
  9. 2022Escaping from the Barren Plateau via Gaussian Initializations in Deep Variational Quantum Circuitscited by 42
  10. 2022Equivariant quantum circuits for learning on weighted graphscited by 41
  11. 2021Enhancing Generative Models via Quantum Correlationscited by 40
  12. 2021Representation Learning via Quantum Neural Tangent Kernelscited by 40
  13. 2022Representation Theory for Geometric Quantum Machine Learningcited by 40
  14. 2022Recent Advances for Quantum Neural Networks in Generative Learningcited by 39
  15. 2021Recent advances for quantum classifierscited by 35
  16. 2023Trainability barriers and opportunities in quantum generative modelingcited by 35
  17. 2022Learning to predict arbitrary quantum processescited by 34
  18. 2021Subtleties in the trainability of quantum machine learning modelscited by 33
  19. 2024Quantum Convolutional Neural Networks are Effectively Classically Simulablecited by 33
  20. 2021Capacity and quantum geometry of parametrized quantum circuitscited by 32
  21. 2022Bandwidth Enables Generalization in Quantum Kernel Modelscited by 32
  22. 2023On quantum backpropagation, information reuse, and cheating measurement collapsecited by 32
  23. 2024A comprehensive review of Quantum Machine Learning: from NISQ to Fault Tolerancecited by 32
  24. 2021Analyzing the barren plateau phenomenon in training quantum neural networks with the ZX-calculuscited by 30
  25. 2021Quantum machine learning of large datasets using randomized measurementscited by 30
  26. 2023Generative quantum machine learning via denoising diffusion probabilistic modelscited by 30
  27. 2021Speeding up Learning Quantum States through Group Equivariant Convolutional Quantum Ans"atzecited by 29
  28. 2021Automatic design of quantum feature mapscited by 27
  29. 2021QTN-VQC: An End-to-End Learning framework for Quantum Neural Networkscited by 27
  30. 2021QuantumNAT: Quantum Noise-Aware Training with Noise Injection, Quantization and Normalizationcited by 27
  31. 2022projUNN: efficient method for training deep networks with unitary matricescited by 27
  32. 2021Entangled Datasets for Quantum Machine Learningcited by 26
  33. 2022Theoretical Error Performance Analysis for Variational Quantum Circuit Based Functional Regressioncited by 26
  34. 2023Towards quantum enhanced adversarial robustness in machine learningcited by 26
  35. 2022QSAN: A Near-term Achievable Quantum Self-Attention Networkcited by 25
  36. 2022Hybrid quantum neural network for drug response predictioncited by 25
  37. 2024On the relation between trainability and dequantization of variational quantum learning modelscited by 24
  38. 2021Exponentially Many Local Minima in Quantum Neural Networkscited by 22

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