mlsanityData to 14 Oct 2026

Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networks

arXiv 2210.09974 ↗First posted 18 Oct 2022quant-ph cs.LG stat.MLcited by 52

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Abstract (arXiv)

Despite the great promise of quantum machine learning models, there are several challenges one must overcome before unlocking their full potential. For instance, models based on quantum neural networks (QNNs) can suffer from excessive local minima and barren plateaus in their training landscapes. Recently, the nascent field of geometric quantum machine learning (GQML) has emerged as a potential solution to some of those issues. The key insight of GQML is that one should design architectures, such as equivariant QNNs, encoding the symmetries of the problem at hand. Here, we focus on problems with permutation symmetry (i.e., the group of symmetry Sn), and show how to build Sn-equivariant QNNs. We provide an analytical study of their performance, proving that they do not suffer from barren plateaus, quickly reach overparametrization, and generalize well from small amounts of data. To verify our results, we perform numerical simulations for a graph state classification task. Our work provides the first theoretical guarantees for equivariant QNNs, thus indicating the extreme power and potential of GQML.

Key facts. Cited by 52 papers in the map (data through 14 Oct 2026). Builds on 67 of its 173 references that are in the map. First posted on arXiv 18 Oct 2022.

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67 of 173 references.

References · 67

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  2. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,167
  3. 2016Group Equivariant Convolutional Networkscited by 1,165
  4. 2018A Convergence Theory for Deep Learning via Over-Parameterizationcited by 787
  5. 2018Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point cloudscited by 746
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38 more
  1. 2018Invariant and Equivariant Graph Networkscited by 346
  2. 2018Learning and Generalization in Overparameterized Neural Networks, Going Beyond Two Layerscited by 340
  3. 2020Power of data in quantum machine learningcited by 338
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  7. 2020Equivariant Flows: Exact Likelihood Generative Learning for Symmetric Densitiescited by 250
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  9. 2021Generalization in quantum machine learning from few training datacited by 216
  10. 2020Noise-Induced Barren Plateaus in Variational Quantum Algorithmscited by 193
  11. 2019Universal Invariant and Equivariant Graph Neural Networkscited by 183
  12. 2021Connecting ansatz expressibility to gradient magnitudes and barren plateauscited by 180
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  16. 2020Absence of Barren Plateaus in Quantum Convolutional Neural Networkscited by 125
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  18. 2020Entanglement Induced Barren Plateauscited by 101
  19. 2021Theory of overparametrization in quantum neural networkscited by 100
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  21. 2018Roto-Translation Covariant Convolutional Networks for Medical Image Analysiscited by 92
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  26. 2017SGD Learns Over-parameterized Networks that Provably Generalize on Linearly Separable Datacited by 79
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  29. 2019Quantum Graph Neural Networkscited by 66
  30. 2022Theory for Equivariant Quantum Neural Networkscited by 62
  31. 2020Trainability of Dissipative Perceptron-Based Quantum Neural Networkscited by 56
  32. 2022Group-Invariant Quantum Machine Learningcited by 56
  33. 2018q-means: A quantum algorithm for unsupervised machine learningcited by 55
  34. 2021Equivalence of quantum barren plateaus to cost concentration and narrow gorgescited by 53
  35. 2022Out-of-distribution generalization for learning quantum dynamicscited by 49
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  37. 2021Representation Learning via Quantum Neural Tangent Kernelscited by 40
  38. 2022Representation Theory for Geometric Quantum Machine Learningcited by 40

50 most cited of 67 All 67 (JSON)

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Citing papers per year: 2022: 2; 2023: 16; 2024: 18; 2025: 9; 2026: 7.

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  1. 2024Barren Plateaus in Variational Quantum Computingcited by 133
  2. 2023Does provable absence of barren plateaus imply classical simulability?cited by 80
  3. 2023Understanding quantum machine learning also requires rethinking generalizationcited by 49
  4. 2024Quantum Convolutional Neural Networks are Effectively Classically Simulablecited by 37
  5. 2023Trainability barriers and opportunities in quantum generative modelingcited by 36
  6. 2024On the relation between trainability and dequantization of variational quantum learning modelscited by 25
  7. 2022Problem-Dependent Power of Quantum Neural Networks on Multi-Class Classificationcited by 20
  8. 2024On the hardness of learning under symmetriescited by 13
  9. 2023The power and limitations of learning quantum dynamics incoherentlycited by 12
  10. 2024VQC-Based Reinforcement Learning with Data Re-uploading: Performance and Trainabilitycited by 12
  11. 2025A Primer on Quantum Machine Learningcited by 12
  12. 2023Generalization of Quantum Machine Learning Models Using Quantum Fisher Information Metriccited by 10
38 more
  1. 2023Splitting and Parallelizing of Quantum Convolutional Neural Networks for Learning Translationally Symmetric Datacited by 10
  2. 2023Approximately Equivariant Quantum Neural Network for p4m Group Symmetries in Imagescited by 10
  3. 2023Effects of noise on the overparametrization of quantum neural networkscited by 9
  4. 2024Adversarial Robustness Guarantees for Quantum Classifierscited by 9
  5. 2024Reinforcement learning-based architecture search for quantum machine learningcited by 9
  6. 2023Symmetry-invariant quantum machine learning force fieldscited by 8
  7. 2024Trade-off between Gradient Measurement Efficiency and Expressivity in Deep Quantum Neural Networkscited by 8
  8. 2024Unitary convolutions for learning on graphs and groupscited by 8
  9. 2022SnCQA: A hardware-efficient equivariant quantum convolutional circuit architecturecited by 7
  10. 2023On the universality of Sn-equivariant k-body gatescited by 7
  11. 2023All you need is spin: SU(2) equivariant variational quantum circuits based on spin networkscited by 7
  12. 2023A Comparison Between Invariant and Equivariant Classical and Quantum Graph Neural Networkscited by 6
  13. 2023Time-Warping Invariant Quantum Recurrent Neural Networks via Quantum-Classical Adaptive Gatingcited by 5
  14. 20233D-QAE: Fully Quantum Auto-Encoding of 3D Point Cloudscited by 5
  15. 2024Symmetry breaking in geometric quantum machine learning in the presence of noisecited by 5
  16. 2023The role of data embedding in equivariant quantum convolutional neural networkscited by 4
  17. 2024MG-Net: Learn to Customize QAOA with Circuit Depth Awarenesscited by 4
  18. 2024Resource-efficient equivariant quantum convolutional neural networkscited by 4
  19. 2025Dynamic Estimation Loss Control in Variational Quantum Sensing via Online Conformal Inferencecited by 4
  20. 2024Image Classification with Rotation-Invariant Variational Quantum Circuitscited by 3
  21. 2025Enhancing variational quantum algorithms by balancing training on classical and quantum hardwarecited by 3
  22. 2024Hamiltonian-based Quantum Reinforcement Learning for Neural Combinatorial Optimizationcited by 2
  23. 2025TabularQGAN: A quantum generative model for tabular data synthesiscited by 2
  24. 2025Expressive and Scalable Quantum Fusion for Multimodal Learningcited by 2
  25. 2026A PAC-Bayesian approach to generalization for quantum modelscited by 2
  26. 2024Architectures and random properties of symplectic quantum circuitscited by 1
  27. 2024Data Efficient Prediction of excited-state properties using Quantum Neural Networkscited by 1
  28. 2026Scalable Message-Passing Quantum Graph Neural Networks in the Weisfeiler-Leman Hierarchycited by 1
  29. 2026Beyond the Expressivity-Trainability Paradox: A Dynamical Lie Algebra Perspective on Navigating Barren Plateaus in Quantum Machine Learningcited by 1
  30. 2023A quantum tug of war between randomness and symmetries on homogeneous spacescited by 0
  31. 2024Permutation-equivariant quantum convolutional neural networkscited by 0
  32. 2024Reverse Map Projections as Equivariant Quantum Embeddingscited by 0
  33. 2025Connecting phases of matter to the flatness of the loss landscape in analog variational quantum algorithmscited by 0
  34. 2025Twirlator: A Pipeline for Analyzing Subgroup Symmetry Effects in Quantum Machine Learning Ansatzescited by 0
  35. 2025Understanding the Nature of Depth-1 Equivariant Quantum Circuitcited by 0
  36. 2025Fragmentation is Efficiently Learnable by Quantum Neural Networkscited by 0
  37. 2026Quantum Generator Kernelscited by 0
  38. 2026Analog Quantum Asynchronous Event-Based Graph Neural Networkcited by 0

50 most cited of 52 All 52 (JSON)