mlsanityData to 13 Oct 2026

Group-Invariant Quantum Machine Learning

arXiv 2205.02261 ↗First posted 4 May 2022quant-ph cs.LG stat.MLcited by 56

Not on the map. Why?

Abstract (arXiv)

Quantum Machine Learning (QML) models are aimed at learning from data encoded in quantum states. Recently, it has been shown that models with little to no inductive biases (i.e., with no assumptions about the problem embedded in the model) are likely to have trainability and generalization issues, especially for large problem sizes. As such, it is fundamental to develop schemes that encode as much information as available about the problem at hand. In this work we present a simple, yet powerful, framework where the underlying invariances in the data are used to build QML models that, by construction, respect those symmetries. These so-called group-invariant models produce outputs that remain invariant under the action of any element of the symmetry group mathfrakG associated to the dataset. We present theoretical results underpinning the design of mathfrakG-invariant models, and exemplify their application through several paradigmatic QML classification tasks including cases when mathfrakG is a continuous Lie group and also when it is a discrete symmetry group. Notably, our framework allows us to recover, in an elegant way, several well known algorithms for the literature, as well as to discover new ones. Taken together, we expect that our results will help pave the way towards a more geometric and group-theoretic approach to QML model design.

Key facts. Cited by 56 papers in the map (data through 13 Oct 2026). Builds on 28 of its 108 references that are in the map. First posted on arXiv 4 May 2022.

Builds on

28 of 108 references.

References · 28

  1. 2018Relational inductive biases, deep learning, and graph networkscited by 1,353
  2. 2016Group Equivariant Convolutional Networkscited by 1,157
  3. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,147
  4. 2020Variational Quantum Algorithmscited by 689
  5. 2018Barren plateaus in quantum neural network training landscapescited by 627
  6. 2016Quantum Machine Learningcited by 326
  7. 2018On the Generalization of Equivariance and Convolution in Neural Networks to the Action of Compact Groupscited by 297
  8. 2021Generalization in quantum machine learning from few training datacited by 214
  9. 2021Quantum advantage in learning from experimentscited by 187
  10. 2021Connecting ansatz expressibility to gradient magnitudes and barren plateauscited by 180
  11. 2020Absence of Barren Plateaus in Quantum Convolutional Neural Networkscited by 125
  12. 2021Theory of overparametrization in quantum neural networkscited by 100
16 more
  1. 2018Roto-Translation Covariant Convolutional Networks for Medical Image Analysiscited by 91
  2. 2021Provably efficient machine learning for quantum many-body problemscited by 91
  3. 2019Quantum Graph Neural Networkscited by 66
  4. 2020Trainability of Dissipative Perceptron-Based Quantum Neural Networkscited by 56
  5. 2021Equivalence of quantum barren plateaus to cost concentration and narrow gorgescited by 53
  6. 2021Exponential separations between learning with and without quantum memorycited by 52
  7. 2021Subtleties in the trainability of quantum machine learning modelscited by 33
  8. 2021Speeding up Learning Quantum States through Group Equivariant Convolutional Quantum Ans"atzecited by 29
  9. 2019Quantum Hamiltonian-Based Models and the Variational Quantum Thermalizer Algorithmcited by 27
  10. 2020Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuitscited by 26
  11. 2021Entangled Datasets for Quantum Machine Learningcited by 26
  12. 2022Symmetry Group Equivariant Architectures for Physicscited by 23
  13. 2015Graph Isomorphism in Quasipolynomial Timecited by 19
  14. 2021Revisiting dequantization and quantum advantage in learning taskscited by 11
  15. 2013Graph isomorphism and adiabatic quantum computingcited by 7
  16. 2021Quantum algorithms for group convolution, cross-correlation, and equivariant transformationscited by 5

Built on by

Cited by year (2026 to 13 Oct)

Citing papers per year: 2022: 13; 2023: 18; 2024: 16; 2025: 5; 2026: 4.

56 papers.

Sort:

By area:

  1. 2023Challenges and Opportunities in Quantum Machine Learningcited by 203
  2. 2024Barren Plateaus in Variational Quantum Computingcited by 130
  3. 2022Exponential concentration in quantum kernel methodscited by 90
  4. 2024Better than classical? The subtle art of benchmarking quantum machine learning modelscited by 85
  5. 2023Does provable absence of barren plateaus imply classical simulability?cited by 79
  6. 2022Theory for Equivariant Quantum Neural Networkscited by 61
  7. 2022Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networkscited by 52
  8. 2023Understanding quantum machine learning also requires rethinking generalizationcited by 49
  9. 2022Equivariant quantum circuits for learning on weighted graphscited by 41
  10. 2022Representation Theory for Geometric Quantum Machine Learningcited by 40
  11. 2022Recent Advances for Quantum Neural Networks in Generative Learningcited by 39
  12. 2023Trainability barriers and opportunities in quantum generative modelingcited by 35
38 more
  1. 2024Quantum Convolutional Neural Networks are Effectively Classically Simulablecited by 35
  2. 2023Quantum Deep Hedgingcited by 22
  3. 2023Potential and limitations of random Fourier features for dequantizing quantum machine learningcited by 22
  4. 2022Symmetric Pruning in Quantum Neural Networkscited by 21
  5. 2022Problem-Dependent Power of Quantum Neural Networks on Multi-Class Classificationcited by 20
  6. 2023Thermodynamic AI and the fluctuation frontiercited by 15
  7. 2023Quantum neural networks form Gaussian processescited by 12
  8. 2023Generalization of Quantum Machine Learning Models Using Quantum Fisher Information Metriccited by 10
  9. 2023Splitting and Parallelizing of Quantum Convolutional Neural Networks for Learning Translationally Symmetric Datacited by 10
  10. 2023Approximately Equivariant Quantum Neural Network for p4m Group Symmetries in Imagescited by 10
  11. 2025A Primer on Quantum Machine Learningcited by 9
  12. 2022Mitigating barren plateaus of variational quantum eigensolverscited by 8
  13. 2023Symmetry-invariant quantum machine learning force fieldscited by 8
  14. 2024Reinforcement learning-based architecture search for quantum machine learningcited by 8
  15. 2024Trade-off between Gradient Measurement Efficiency and Expressivity in Deep Quantum Neural Networkscited by 8
  16. 2023On the universality of Sn-equivariant k-body gatescited by 7
  17. 2023All you need is spin: SU(2) equivariant variational quantum circuits based on spin networkscited by 7
  18. 2025TensorRL-QAS: Reinforcement learning with tensor networks for improved quantum architecture searchcited by 6
  19. 2023Time-Warping Invariant Quantum Recurrent Neural Networks via Quantum-Classical Adaptive Gatingcited by 5
  20. 2024Arbitrary Polynomial Separations in Trainable Quantum Machine Learningcited by 5
  21. 2024Learning with SASQuaTCh: a Novel Variational Quantum Transformer Architecture with Kernel-Based Self-Attentioncited by 5
  22. 2022Toward Super-polynomial Quantum Speedup of Equivariant Quantum Algorithms with SU(d) Symmetrycited by 4
  23. 2023Coreset selection can accelerate quantum machine learning models with provable generalizationcited by 4
  24. 2023The role of data embedding in equivariant quantum convolutional neural networkscited by 4
  25. 2024Graph Neural Networks on Quantum Computerscited by 4
  26. 2024Resource-efficient equivariant quantum convolutional neural networkscited by 4
  27. 2022Provably efficient variational generative modeling of quantum many-body systems via quantum-probabilistic information geometrycited by 3
  28. 2024Barren plateaus are amplified by the dimension of quditscited by 2
  29. 2022Learning quantum symmetries with interactive quantum-classical variational algorithmscited by 1
  30. 2022Harmonic (Quantum) Neural Networkscited by 1
  31. 2024Probing many-body Bell correlation depth with superconducting qubitscited by 1
  32. 2024Quantum enhanced stratification of Breast Cancer: exploring quantum expressivity for real omics datacited by 1
  33. 2025Inductive Graph Representation Learning with Quantum Graph Neural Networkscited by 1
  34. 2023A quantum tug of war between randomness and symmetries on homogeneous spacescited by 0
  35. 2024Permutation-equivariant quantum convolutional neural networkscited by 0
  36. 2024Hybrid Classical-Quantum architecture for vectorised image classification of hand-written sketchescited by 0
  37. 2024Reverse Map Projections as Equivariant Quantum Embeddingscited by 0
  38. 2024Exploring Channel Distinguishability in Local Neighborhoods of the Model Space in Quantum Neural Networkscited by 0

50 most cited of 56 All 56 (JSON)