mlsanityData to 14 Oct 2026

Equivalence of quantum barren plateaus to cost concentration and narrow gorges

arXiv 2104.05868 ↗First posted 12 Apr 2021quant-ph cs.LGcited by 53

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Abstract (arXiv)

Optimizing parameterized quantum circuits (PQCs) is the leading approach to make use of near-term quantum computers. However, very little is known about the cost function landscape for PQCs, which hinders progress towards quantum-aware optimizers. In this work, we investigate the connection between three different landscape features that have been observed for PQCs: (1) exponentially vanishing gradients (called barren plateaus), (2) exponential cost concentration about the mean, and (3) the exponential narrowness of minina (called narrow gorges). We analytically prove that these three phenomena occur together, i.e., when one occurs then so do the other two. A key implication of this result is that one can numerically diagnose barren plateaus via cost differences rather than via the computationally more expensive gradients. More broadly, our work shows that quantum mechanics rules out certain cost landscapes (which otherwise would be mathematically possible), and hence our results are interesting from a quantum foundations perspective.

Key facts. Cited by 53 papers in the map (data through 14 Oct 2026). Builds on 19 of its 68 references that are in the map. First posted on arXiv 12 Apr 2021.

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19 of 68 references.

References · 19

  1. 2020Variational Quantum Algorithmscited by 692
  2. 2018Barren plateaus in quantum neural network training landscapescited by 630
  3. 2020The power of quantum neural networkscited by 379
  4. 2020Noise-Induced Barren Plateaus in Variational Quantum Algorithmscited by 193
  5. 2021Connecting ansatz expressibility to gradient magnitudes and barren plateauscited by 180
  6. 2019Efficient Learning for Deep Quantum Neural Networkscited by 161
  7. 2020Absence of Barren Plateaus in Quantum Convolutional Neural Networkscited by 125
  8. 2019Quantum Natural Gradientcited by 106
  9. 2020Entanglement Induced Barren Plateauscited by 101
  10. 2020Layerwise learning for quantum neural networkscited by 88
  11. 2020Effect of barren plateaus on gradient-free optimizationcited by 80
  12. 2021Noisy intermediate-scale quantum (NISQ) algorithmscited by 79
7 more
  1. 2020TensorFlow Quantum: A Software Framework for Quantum Machine Learningcited by 72
  2. 2019Stochastic gradient descent for hybrid quantum-classical optimizationcited by 59
  3. 2019Learning to learn with quantum neural networks via classical neural networkscited by 56
  4. 2020Trainability of Dissipative Perceptron-Based Quantum Neural Networkscited by 56
  5. 2020On barren plateaus and cost function locality in variational quantum algorithmscited by 36
  6. 2019Low-depth gradient measurements can improve convergence in variational hybrid quantum-classical algorithmscited by 31
  7. 2021Quantum Optimization for Training Quantum Neural Networkscited by 6

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 8; 2022: 13; 2023: 6; 2024: 11; 2025: 10; 2026: 5.

53 papers.

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  1. 2023Challenges and Opportunities in Quantum Machine Learningcited by 203
  2. 2024Barren Plateaus in Variational Quantum Computingcited by 133
  3. 2021Theory of overparametrization in quantum neural networkscited by 100
  4. 2022Exponential concentration in quantum kernel methodscited by 90
  5. 2023Does provable absence of barren plateaus imply classical simulability?cited by 80
  6. 2022Theory for Equivariant Quantum Neural Networkscited by 62
  7. 2022Group-Invariant Quantum Machine Learningcited by 56
  8. 2022Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networkscited by 52
  9. 2022Representation Theory for Geometric Quantum Machine Learningcited by 40
  10. 2022Recent Advances for Quantum Neural Networks in Generative Learningcited by 39
  11. 2024Quantum Convolutional Neural Networks are Effectively Classically Simulablecited by 37
  12. 2023Trainability barriers and opportunities in quantum generative modelingcited by 36
38 more
  1. 2021Subtleties in the trainability of quantum machine learning modelscited by 33
  2. 2024A comprehensive review of Quantum Machine Learning: from NISQ to Fault Tolerancecited by 32
  3. 2021Entangled Datasets for Quantum Machine Learningcited by 27
  4. 2024On the relation between trainability and dequantization of variational quantum learning modelscited by 25
  5. 2022Problem-Dependent Power of Quantum Neural Networks on Multi-Class Classificationcited by 20
  6. 2023On fundamental aspects of quantum extreme learning machinescited by 18
  7. 2022Enhancing Quantum Adversarial Robustness by Randomized Encodingscited by 17
  8. 2021Optimal training of variational quantum algorithms without barren plateauscited by 16
  9. 2024Variational quantum simulation: a case study for understanding warm startscited by 14
  10. 2021Graph neural network initialisation of quantum approximate optimisationcited by 13
  11. 2021Adaptive shot allocation for fast convergence in variational quantum algorithmscited by 12
  12. 2023Quantum neural networks form Gaussian processescited by 12
  13. 2024Quantum Boltzmann machine learning of ground-state energiescited by 12
  14. 2022Numerical evidence against advantage with quantum fidelity kernels on classical datacited by 11
  15. 2024Investigating and Mitigating Barren Plateaus in Variational Quantum Circuits: A Surveycited by 10
  16. 2024Reinforcement Learning for Variational Quantum Circuits Designcited by 9
  17. 2024Natural gradient and parameter estimation for quantum Boltzmann machinescited by 9
  18. 2023Expressibility-induced Concentration of Quantum Neural Tangent Kernelscited by 7
  19. 2024Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuitscited by 7
  20. 2025Quantum-enhanced Computer Vision: Going Beyond Classical Algorithmscited by 5
  21. 2021F-Divergences and Cost Function Locality in Generative Modelling with Quantum Circuitscited by 3
  22. 2022Quantum Capsule Networkscited by 3
  23. 2022LAWS: Look Around and Warm-Start Natural Gradient Descent for Quantum Neural Networkscited by 3
  24. 2022Provably efficient variational generative modeling of quantum many-body systems via quantum-probabilistic information geometrycited by 3
  25. 2025On the similarity of bandwidth-tuned quantum kernels and classical kernelscited by 3
  26. 2025Adversarial Robustness in Distributed Quantum Machine Learningcited by 2
  27. 2025TITAN: A Trajectory-Informed Technique for Adaptive Parameter Freezing in Large-Scale VQEcited by 2
  28. 2025Meta-Learning for Quantum Optimization via Quantum Sequence Modelcited by 2
  29. 2021Mode connectivity in the loss landscape of parameterized quantum circuitscited by 1
  30. 2022Fundamental limitations on optimization in variational quantum algorithmscited by 1
  31. 2025Inductive Graph Representation Learning with Quantum Graph Neural Networkscited by 1
  32. 2025Taming Barren Plateaus in Arbitrary Parameterized Quantum Circuits without Sacrificing Expressibilitycited by 1
  33. 2025Escaping Barren Plateaus in Variational Quantum Algorithms Using Negative Learning Rate in Quantum Internet of Thingscited by 1
  34. 2024Exploring Channel Distinguishability in Local Neighborhoods of the Model Space in Quantum Neural Networkscited by 0
  35. 2025Connecting phases of matter to the flatness of the loss landscape in analog variational quantum algorithmscited by 0
  36. 2025On the Design of Expressive and Trainable Pulse-based Quantum Machine Learning Modelscited by 0
  37. 2026Ravines in quantum cost landscapes: opportunities for improved VQA predictionscited by 0
  38. 2026Entanglement geometry separates circuit cutting, classical hardness, and trainabilitycited by 0

50 most cited of 53 All 53 (JSON)