Equivariant Quantum Graph Circuits

Peter Mernyei, Konstantinos Meichanetzidis, Ismail Ilkan Ceylan
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:15401-15420, 2022.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-mernyei22a, title = {Equivariant Quantum Graph Circuits}, author = {Mernyei, Peter and Meichanetzidis, Konstantinos and Ceylan, Ismail Ilkan}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {15401--15420}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/mernyei22a/mernyei22a.pdf}, url = {https://proceedings.mlr.press/v162/mernyei22a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Equivariant Quantum Graph Circuits %A Peter Mernyei %A Konstantinos Meichanetzidis %A Ismail Ilkan Ceylan %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-mernyei22a %I PMLR %P 15401--15420 %U https://proceedings.mlr.press/v162/mernyei22a.html %V 162 %X 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.
APA
Mernyei, P., Meichanetzidis, K. & Ceylan, I.I.. (2022). Equivariant Quantum Graph Circuits. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:15401-15420 Available from https://proceedings.mlr.press/v162/mernyei22a.html.

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