mlsanityData to 14 Oct 2026

Quantum Natural Gradient

arXiv 1909.02108 ↗First posted 4 Sep 2019quant-ph cs.LG stat.MLcited by 106

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Abstract (arXiv)

A quantum generalization of Natural Gradient Descent is presented as part of a general-purpose optimization framework for variational quantum circuits. The optimization dynamics is interpreted as moving in the steepest descent direction with respect to the Quantum Information Geometry, corresponding to the real part of the Quantum Geometric Tensor (QGT), also known as the Fubini-Study metric tensor. An efficient algorithm is presented for computing a block-diagonal approximation to the Fubini-Study metric tensor for parametrized quantum circuits, which may be of independent interest.

Key facts. Cited by 106 papers in the map (data through 14 Oct 2026). First posted on arXiv 4 Sep 2019.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 24; 2022: 15; 2023: 13; 2024: 19; 2025: 17; 2026: 18.

106 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. 2021The Inductive Bias of Quantum Kernelscited by 91
  5. 2021Noisy intermediate-scale quantum (NISQ) algorithmscited by 79
  6. 2021Equivalence of quantum barren plateaus to cost concentration and narrow gorgescited by 53
  7. 2022Escaping from the Barren Plateau via Gaussian Initializations in Deep Variational Quantum Circuitscited by 43
  8. 2021Recent advances for quantum classifierscited by 35
  9. 2021Capacity and quantum geometry of parametrized quantum circuitscited by 32
  10. 2021Analyzing the barren plateau phenomenon in training quantum neural networks with the ZX-calculuscited by 30
  11. 2022Ab-initio quantum chemistry with neural-network wavefunctionscited by 29
  12. 2021NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systemscited by 28
38 more
  1. 2022QSAN: A Near-term Achievable Quantum Self-Attention Networkcited by 25
  2. 2021Universal Adversarial Examples and Perturbations for Quantum Classifierscited by 23
  3. 2023QKSAN: A Quantum Kernel Self-Attention Networkcited by 23
  4. 2023ASDL: A Unified Interface for Gradient Preconditioning in PyTorchcited by 21
  5. 2021The dilemma of quantum neural networkscited by 20
  6. 2021Optimal training of variational quantum algorithms without barren plateauscited by 16
  7. 2021A semi-agnostic ansatz with variable structure for quantum machine learningcited by 15
  8. 2022Policy Gradients using Variational Quantum Circuitscited by 15
  9. 2021Explicitly antisymmetrized neural network layers for variational Monte Carlo simulationcited by 14
  10. 2022Federated Quantum Natural Gradient Descent for Quantum Federated Learningcited by 14
  11. 2023Optimizing Quantum Federated Learning Based on Federated Quantum Natural Gradient Descentcited by 14
  12. 2023Quantum Machine Learning on Near-Term Quantum Devices: Current State of Supervised and Unsupervised Techniques for Real-World Applicationscited by 14
  13. 2021Learning quantum data with the quantum Earth Mover's distancecited by 13
  14. 2021Graph neural network initialisation of quantum approximate optimisationcited by 13
  15. 2022Quantum Neural Network Classifiers: A Tutorialcited by 13
  16. 2022Near-Term Quantum Computing Techniques: Variational Quantum Algorithms, Error Mitigation, Circuit Compilation, Benchmarking and Classical Simulationcited by 13
  17. 2023Wasserstein Quantum Monte Carlo: A Novel Approach for Solving the Quantum Many-Body Schr"odinger Equationcited by 12
  18. 2023Generalization of Quantum Machine Learning Models Using Quantum Fisher Information Metriccited by 10
  19. 2024Natural gradient and parameter estimation for quantum Boltzmann machinescited by 9
  20. 2025L2M: Mutual Information Scaling Law for Long-Context Language Modelingcited by 9
  21. 2024Qiskit-Torch-Module: Fast Prototyping of Quantum Neural Networkscited by 8
  22. 2021Stochastic Gradient Line Bayesian Optimization for Efficient Noise-Robust Optimization of Parameterized Quantum Circuitscited by 7
  23. 2022Classical versus Quantum: comparing Tensor Network-based Quantum Circuits on LHC datacited by 7
  24. 2022QuACK: Accelerating Gradient-Based Quantum Optimization with Koopman Operator Learningcited by 7
  25. 2023Improving Gradient Methods via Coordinate Transformations: Applications to Quantum Machine Learningcited by 7
  26. 2024Sequential-in-time training of nonlinear parametrizations for solving time-dependent partial differential equationscited by 7
  27. 2025Quantum-Informed Machine Learning for Predicting Spatiotemporal Chaos with Practical Quantum Advantagecited by 7
  28. 2021Rayleigh-Gauss-Newton optimization with enhanced sampling for variational Monte Carlocited by 6
  29. 2021On exploring the potential of quantum auto-encoder for learning quantum systemscited by 6
  30. 2023Quantum Natural Policy Gradients: Towards Sample-Efficient Reinforcement Learningcited by 6
  31. 2024GQHAN: A Grover-inspired Quantum Hard Attention Networkcited by 5
  32. 2024Approximately-symmetric neural networks for quantum spin liquidscited by 5
  33. 2021Variational Quantum Classifiers Through the Lens of the Hessiancited by 4
  34. 2023Coreset selection can accelerate quantum machine learning models with provable generalizationcited by 4
  35. 2024TENG: Time-Evolving Natural Gradient for Solving PDEs With Deep Neural Nets Toward Machine Precisioncited by 4
  36. 2024Guided-SPSA: Simultaneous Perturbation Stochastic Approximation assisted by the Parameter Shift Rulecited by 4
  37. 2025Quantum Machine Unlearning: Foundations, Mechanisms, and Taxonomycited by 4
  38. 2022LAWS: Look Around and Warm-Start Natural Gradient Descent for Quantum Neural Networkscited by 3

50 most cited of 106 All 106 (JSON)