Quantum Positional Encodings for Graph Neural Networks

Slimane Thabet, Mehdi Djellabi, Igor Olegovich Sokolov, Sachin Kasture, Louis-Paul Henry, Loic Henriet
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:47965-47996, 2024.

Abstract

In this work, we propose novel families of positional encodings tailored to graph neural networks obtained with quantum computers. These encodings leverage the long-range correlations inherent in quantum systems that arise from mapping the topology of a graph onto interactions between qubits in a quantum computer. Our inspiration stems from the recent advancements in quantum processing units, which offer computational capabilities beyond the reach of classical hardware. We prove that some of these quantum features are theoretically more expressive for certain graphs than the commonly used relative random walk probabilities. Empirically, we show that the performance of state-of-the-art models can be improved on standard benchmarks and large-scale datasets by computing tractable versions of quantum features. Our findings highlight the potential of leveraging quantum computing capabilities to enhance the performance of transformers in handling graph data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-thabet24a, title = {Quantum Positional Encodings for Graph Neural Networks}, author = {Thabet, Slimane and Djellabi, Mehdi and Sokolov, Igor Olegovich and Kasture, Sachin and Henry, Louis-Paul and Henriet, Loic}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {47965--47996}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/thabet24a/thabet24a.pdf}, url = {https://proceedings.mlr.press/v235/thabet24a.html}, abstract = {In this work, we propose novel families of positional encodings tailored to graph neural networks obtained with quantum computers. These encodings leverage the long-range correlations inherent in quantum systems that arise from mapping the topology of a graph onto interactions between qubits in a quantum computer. Our inspiration stems from the recent advancements in quantum processing units, which offer computational capabilities beyond the reach of classical hardware. We prove that some of these quantum features are theoretically more expressive for certain graphs than the commonly used relative random walk probabilities. Empirically, we show that the performance of state-of-the-art models can be improved on standard benchmarks and large-scale datasets by computing tractable versions of quantum features. Our findings highlight the potential of leveraging quantum computing capabilities to enhance the performance of transformers in handling graph data.} }
Endnote
%0 Conference Paper %T Quantum Positional Encodings for Graph Neural Networks %A Slimane Thabet %A Mehdi Djellabi %A Igor Olegovich Sokolov %A Sachin Kasture %A Louis-Paul Henry %A Loic Henriet %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-thabet24a %I PMLR %P 47965--47996 %U https://proceedings.mlr.press/v235/thabet24a.html %V 235 %X In this work, we propose novel families of positional encodings tailored to graph neural networks obtained with quantum computers. These encodings leverage the long-range correlations inherent in quantum systems that arise from mapping the topology of a graph onto interactions between qubits in a quantum computer. Our inspiration stems from the recent advancements in quantum processing units, which offer computational capabilities beyond the reach of classical hardware. We prove that some of these quantum features are theoretically more expressive for certain graphs than the commonly used relative random walk probabilities. Empirically, we show that the performance of state-of-the-art models can be improved on standard benchmarks and large-scale datasets by computing tractable versions of quantum features. Our findings highlight the potential of leveraging quantum computing capabilities to enhance the performance of transformers in handling graph data.
APA
Thabet, S., Djellabi, M., Sokolov, I.O., Kasture, S., Henry, L. & Henriet, L.. (2024). Quantum Positional Encodings for Graph Neural Networks. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:47965-47996 Available from https://proceedings.mlr.press/v235/thabet24a.html.

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