mlsanityData to 14 Oct 2026

Equivariant quantum circuits for learning on weighted graphs

arXiv 2205.06109 ↗First posted 12 May 2022quant-ph cs.LGcited by 41

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Abstract (arXiv)

Variational quantum algorithms are the leading candidate for advantage on near-term quantum hardware. When training a parametrized quantum circuit in this setting to solve a specific problem, the choice of ansatz is one of the most important factors that determines the trainability and performance of the algorithm. In quantum machine learning (QML), however, the literature on ansatzes that are motivated by the training data structure is scarce. In this work, we introduce an ansatz for learning tasks on weighted graphs that respects an important graph symmetry, namely equivariance under node permutations. We evaluate the performance of this ansatz on a complex learning task, namely neural combinatorial optimization, where a machine learning model is used to learn a heuristic for a combinatorial optimization problem. We analytically and numerically study the performance of our model, and our results strengthen the notion that symmetry-preserving ansatzes are a key to success in QML.

Key facts. Cited by 41 papers in the map (data through 14 Oct 2026). Builds on 28 of its 69 references that are in the map. First posted on arXiv 12 May 2022.

Builds on

28 of 69 references.

References · 28

  1. 2021Zero-Shot Text-to-Image Generationcited by 4,288
  2. 2019A Comprehensive Survey on Graph Neural Networkscited by 2,919
  3. 2018Graph Neural Networks: A Review of Methods and Applicationscited by 1,576
  4. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,167
  5. 2015Pointer Networkscited by 895
  6. 2019Graph Neural Networks for Social Recommendationcited by 714
  7. 2020Variational Quantum Algorithmscited by 692
  8. 2018Barren plateaus in quantum neural network training landscapescited by 630
  9. 2018Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizoncited by 623
  10. 2017Learning Combinatorial Optimization Algorithms over Graphscited by 561
  11. 2018Reinforcement Learning for Solving the Vehicle Routing Problemcited by 333
  12. 2019Parameterized quantum circuits as machine learning modelscited by 332
16 more
  1. 2021Combinatorial optimization and reasoning with graph neural networkscited by 268
  2. 2021Generalization in quantum machine learning from few training datacited by 216
  3. 2013Ising formulations of many NP problemscited by 207
  4. 2020Noise-Induced Barren Plateaus in Variational Quantum Algorithmscited by 193
  5. 2019Variational Quantum Circuits for Deep Reinforcement Learningcited by 167
  6. 2020Entanglement Induced Barren Plateauscited by 101
  7. 2019Molecular geometry prediction using a deep generative graph neural networkcited by 91
  8. 2021Learning with invariances in random features and kernel modelscited by 89
  9. 2020Chip Placement with Deep Reinforcement Learningcited by 83
  10. 2020Effect of barren plateaus on gradient-free optimizationcited by 80
  11. 2020Reinforcement Learning with Quantum Variational Circuitscited by 77
  12. 2019Recurrent Neural Networks (RNNs): A gentle Introduction and Overviewcited by 68
  13. 2019Quantum Graph Neural Networkscited by 66
  14. 2022Group-Invariant Quantum Machine Learningcited by 56
  15. 2021Quantum Graph Convolutional Neural Networkscited by 18
  16. 2021Identifying optimal cycles in quantum thermal machines with reinforcement-learningcited by 6

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 6; 2023: 11; 2024: 12; 2025: 10; 2026: 2.

41 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. 2022Exponential concentration in quantum kernel methodscited by 90
  4. 2023Does provable absence of barren plateaus imply classical simulability?cited by 80
  5. 2022Theory for Equivariant Quantum Neural Networkscited by 62
  6. 2022Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networkscited by 52
  7. 2023Understanding quantum machine learning also requires rethinking generalizationcited by 49
  8. 2022Representation Theory for Geometric Quantum Machine Learningcited by 40
  9. 2022Recent Advances for Quantum Neural Networks in Generative Learningcited by 39
  10. 2024Quantum Convolutional Neural Networks are Effectively Classically Simulablecited by 37
  11. 2024VQC-Based Reinforcement Learning with Data Re-uploading: Performance and Trainabilitycited by 12
  12. 2025A Primer on Quantum Machine Learningcited by 12
29 more
  1. 2023Generalization of Quantum Machine Learning Models Using Quantum Fisher Information Metriccited by 10
  2. 2023Splitting and Parallelizing of Quantum Convolutional Neural Networks for Learning Translationally Symmetric Datacited by 10
  3. 2023Symmetry-invariant quantum machine learning force fieldscited by 8
  4. 2024Trade-off between Gradient Measurement Efficiency and Expressivity in Deep Quantum Neural Networkscited by 8
  5. 2024Unitary convolutions for learning on graphs and groupscited by 8
  6. 2022SnCQA: A hardware-efficient equivariant quantum convolutional circuit architecturecited by 7
  7. 2023On the universality of Sn-equivariant k-body gatescited by 7
  8. 2023All you need is spin: SU(2) equivariant variational quantum circuits based on spin networkscited by 7
  9. 2025TensorRL-QAS: Reinforcement learning with tensor networks for improved quantum architecture searchcited by 7
  10. 2023A Comparison Between Invariant and Equivariant Classical and Quantum Graph Neural Networkscited by 6
  11. 2023mathbbZ2× mathbbZ2 Equivariant Quantum Neural Networks: Benchmarking against Classical Neural Networkscited by 4
  12. 2023The role of data embedding in equivariant quantum convolutional neural networkscited by 4
  13. 2024Graph Neural Networks on Quantum Computerscited by 4
  14. 2024Resource-efficient equivariant quantum convolutional neural networkscited by 4
  15. 2024Image Classification with Rotation-Invariant Variational Quantum Circuitscited by 3
  16. 2025Addressing the Current Challenges of Quantum Machine Learning through Multi-Chip Ensemblescited by 3
  17. 2024Hamiltonian-based Quantum Reinforcement Learning for Neural Combinatorial Optimizationcited by 2
  18. 2024Architectures and random properties of symplectic quantum circuitscited by 1
  19. 2025Inductive Graph Representation Learning with Quantum Graph Neural Networkscited by 1
  20. 2025Quantum-Efficient Reinforcement Learning Solutions for Last-Mile On-Demand Deliverycited by 1
  21. 2026Scalable Message-Passing Quantum Graph Neural Networks in the Weisfeiler-Leman Hierarchycited by 1
  22. 2024Automatic re-calibration of quantum devices by reinforcement learningcited by 0
  23. 2024Permutation-equivariant quantum convolutional neural networkscited by 0
  24. 2025Guided Graph Compression for Quantum Graph Neural Networkscited by 0
  25. 2025Enhancement of Quantum Semi-Supervised Learning via Improved Laplacian and Poisson Methodscited by 0
  26. 2025QGraphLIME - Explaining Quantum Graph Neural Networkscited by 0
  27. 2025Understanding the Nature of Depth-1 Equivariant Quantum Circuitcited by 0
  28. 2025PERM EQ x GRAPH EQ: Equivariant Neural Networks for Quantum Molecular Learningcited by 0
  29. 2026Quantum Kernel Machine Learning for Autonomous Materials Sciencecited by 0