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On barren plateaus and cost function locality in variational quantum algorithms

arXiv 2011.10530 ↗First posted 20 Nov 2020quant-ph cond-mat.dis-nn cs.LGcited by 36

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Abstract (arXiv)

Variational quantum algorithms rely on gradient based optimization to iteratively minimize a cost function evaluated by measuring output(s) of a quantum processor. A barren plateau is the phenomenon of exponentially vanishing gradients in sufficiently expressive parametrized quantum circuits. It has been established that the onset of a barren plateau regime depends on the cost function, although the particular behavior has been demonstrated only for certain classes of cost functions. Here we derive a lower bound on the variance of the gradient, which depends mainly on the width of the circuit causal cone of each term in the Pauli decomposition of the cost function. Our result further clarifies the conditions under which barren plateaus can occur.

Key facts. Cited by 36 papers in the map (data through 7 Oct 2026). First posted on arXiv 20 Nov 2020.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 8; 2022: 8; 2023: 10; 2024: 5; 2025: 1; 2026: 4.

36 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. 2023Does provable absence of barren plateaus imply classical simulability?cited by 78
  6. 2021Training Quantum Embedding Kernels on Near-Term Quantum Computerscited by 69
  7. 2022Theory for Equivariant Quantum Neural Networkscited by 60
  8. 2021Equivalence of quantum barren plateaus to cost concentration and narrow gorgescited by 53
  9. 2022Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networkscited by 52
  10. 2022Escaping from the Barren Plateau via Gaussian Initializations in Deep Variational Quantum Circuitscited by 42
  11. 2021Recent advances for quantum classifierscited by 35
  12. 2024A comprehensive review of Quantum Machine Learning: from NISQ to Fault Tolerancecited by 32
24 more
  1. 2022Symmetric Pruning in Quantum Neural Networkscited by 20
  2. 2023On fundamental aspects of quantum extreme learning machinescited by 18
  3. 2022Enhancing Quantum Adversarial Robustness by Randomized Encodingscited by 16
  4. 2022Dynamical simulation via quantum machine learning with provable generalizationcited by 15
  5. 2023Quantum Machine Learning on Near-Term Quantum Devices: Current State of Supervised and Unsupervised Techniques for Real-World Applicationscited by 14
  6. 2023Reduction of finite sampling noise in quantum neural networkscited by 12
  7. 2024Investigating and Mitigating Barren Plateaus in Variational Quantum Circuits: A Surveycited by 9
  8. 2021Long-time simulations with high fidelity on quantum hardwarecited by 8
  9. 2023Expressibility-induced Concentration of Quantum Neural Tangent Kernelscited by 7
  10. 2023The quantum cost function concentration dependency on the parametrization expressivitycited by 6
  11. 2023Fast Quantum Convolutional Neural Networks for Low-Complexity Object Detection in Autonomous Driving Applicationscited by 5
  12. 2021Variational Quantum Classifiers Through the Lens of the Hessiancited by 4
  13. 2024Trainability issues in quantum policy gradientscited by 4
  14. 2021F-Divergences and Cost Function Locality in Generative Modelling with Quantum Circuitscited by 3
  15. 2022Quantum Capsule Networkscited by 3
  16. 2023Quantum Inception Scorecited by 2
  17. 2024Quantum Algorithms for Drone Mission Planningcited by 2
  18. 2026How to find expressible and trainable parameterized quantum circuits?cited by 2
  19. 2022Fundamental limitations on optimization in variational quantum algorithmscited by 1
  20. 2026An architectural capacity ceiling, not a barren plateau: why a fixed-encoding variational quantum circuit cannot fit the Lorenz-63 attractorcited by 1
  21. 2023Improving Parameter Training for VQEs by Sequential Hamiltonian Assemblycited by 0
  22. 2025Connecting phases of matter to the flatness of the loss landscape in analog variational quantum algorithmscited by 0
  23. 2026Empirical Study of Observable Sets in Multiclass Quantum Classificationcited by 0
  24. 2026Trainability Beyond Linearity in Variational Quantum Objectivescited by 0