mlsanityData to 14 Oct 2026

Equivariant Quantum Graph Circuits

arXiv 2112.05261 ↗First posted 10 Dec 2021cs.LG quant-phcited by 2

Not on the map. Why?

Abstract (arXiv)

We investigate quantum circuits for graph representation learning, and propose equivariant quantum graph circuits (EQGCs), as a class of parameterized quantum circuits with strong relational inductive bias for learning over graph-structured data. Conceptually, EQGCs serve as a unifying framework for quantum graph representation learning, allowing us to define several interesting subclasses which subsume existing proposals. In terms of the representation power, we prove that the studied subclasses of EQGCs are universal approximators for functions over the bounded graph domain. This theoretical perspective on quantum graph machine learning methods opens many directions for further work, and could lead to models with capabilities beyond those of classical approaches. We empirically verify the expressive power of EQGCs through a dedicated experiment on synthetic data, and additionally observe that the performance of EQGCs scales well with the depth of the model and does not suffer from barren plateu issues.

Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 28 of its 57 references that are in the map. First posted on arXiv 10 Dec 2021.

Builds on

28 of 57 references.

References · 28

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,361
  2. 2017Graph Attention Networkscited by 8,923
  3. 2018How Powerful are Graph Neural Networks?cited by 4,393
  4. 2017Neural Message Passing for Quantum Chemistrycited by 3,487
  5. 2017Deep Setscited by 1,421
  6. 2018Relational inductive biases, deep learning, and graph networkscited by 1,360
  7. 2018Deeper Insights into Graph Convolutional Networks for Semi-Supervised Learningcited by 1,102
  8. 2017MoleculeNet: A Benchmark for Molecular Machine Learningcited by 1,051
  9. 2018Weisfeiler and Leman Go Neural: Higher-order Graph Neural Networkscited by 881
  10. 2018Link Prediction Based on Graph Neural Networkscited by 832
  11. 2015Gated Graph Sequence Neural Networkscited by 796
  12. 2018Barren plateaus in quantum neural network training landscapescited by 630
16 more
  1. 2019Provably Powerful Graph Networkscited by 389
  2. 2018Invariant and Equivariant Graph Networkscited by 346
  3. 2020The effect of data encoding on the expressive power of variational quantum machine learning modelscited by 333
  4. 2019Parameterized quantum circuits as machine learning modelscited by 332
  5. 2020A rigorous and robust quantum speed-up in supervised machine learningcited by 271
  6. 2019What graph neural networks cannot learn: depth vs widthcited by 201
  7. 2020The Surprising Power of Graph Neural Networks with Random Node Initializationcited by 198
  8. 2020Random Features Strengthen Graph Neural Networkscited by 186
  9. 2017Quantum machine learning: a classical perspectivecited by 95
  10. 2021The Inductive Bias of Quantum Kernelscited by 91
  11. 2019Quantum Graph Neural Networkscited by 66
  12. 2019Coloring graph neural networks for node disambiguationcited by 52
  13. 2020Universal Approximation Property of Quantum Machine Learning Models in Quantum-Enhanced Feature Spacescited by 44
  14. 2021Hybrid Quantum-Classical Graph Convolutional Networkcited by 21
  15. 2021Quantum Graph Convolutional Neural Networkscited by 18
  16. 2021Learnability of the output distributions of local quantum circuitscited by 7

Built on by

Cited by year

Citing papers per year: 2024: 2.

2 papers.

  1. 2024From Graphs to Qubits: A Critical Review of Quantum Graph Neural Networkscited by 6
  2. 2024Hamiltonian-based Quantum Reinforcement Learning for Neural Combinatorial Optimizationcited by 2