A Spatial‐Based Quantum Graph Convolutional Neural Network and Its Full‐Quantum Circuit Implementation

Abstract

With the rapid advancement of quantum computing, the exploration of quantum graph neural networks is gradually emerging. However, the absence of a circuit framework for quantum implementation and limited physical qubits hinder their realization on real quantum computers. To address these challenges, this paper proposes a spatial‐based quantum graph convolutional neural network and implements it on a superconducting quantum computer. Specifically, this model exclusively consists of quantum circuits, including quantum aggregation circuits in the quantum graph convolutional layer and quantum classification circuits in the quantum dense layer. To meet the requirements of Noisy Intermediate‐Scale Quantum computing, a first‐order extraction method to reduce circuit size is employed. Experimental results in node classification tasks demonstrate that this model achieves comparable or even superior performance compared to classical graph neural networks while utilizing fewer parameters. Therefore, this model can inspire further advancements in quantum graph neural networks and facilitate their implementation on physical quantum devices.

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RESEARCH ARTICLE
www.advquantumtech.com
A Spatial-Based Quantum Graph Convolutional Neural
Network and Its Full-Quantum Circuit Implementation
Yi Zeng, Jin He, Qijun Huang, Hao Wang,* and Sheng Chang*
With the rapid advancement of quantum computing, the exploration of
quantum graph neural networks is gradually emerging. However, the absence
of a circuit framework for quantum implementation and limited physical
qubits hinder their realization on real quantum computers. To address these
challenges, this paper proposes a spatial-based quantum graph convolutional
neural network and implements it on a superconducting quantum computer.
Specifically, this model exclusively consists of quantum circuits, including
quantum aggregation circuits in the quantum graph convolutional layer and
quantum classification circuits in the quantum dense layer. To meet the
requirements of Noisy Intermediate-Scale Quantum computing, a first-order
extraction method to reduce circuit size is employed. Experimental results in
node classification tasks demonstrate that this model achieves comparable or
even superior performance compared to classical graph neural networks while
utilizing fewer parameters. Therefore, this model can inspire further
advancements in quantum graph neural networks and facilitate their
implementation on physical quantum devices.
1. Introduction
Quantum computing, leveraging the unique properties of
quantum superposition and quantum entanglement, offers ex-
ponential acceleration[1–3]in solving specific problems com-
pared to classical computing. As an interdisciplinary field that
blends quantum computing with machine learning, Quan-
tum Machine Learning (QML) [4–7]has been capturing the
interest of researchers worldwide. Over the past few years,
Y. Zeng, J. He, Q. Huang, H. Wang, S. Chang
School of Physics and Technology
Wuhan University
Wuhan, Hubei 430072, China
E-mail: wanghao@whu.edu.cn;changsheng@whu.edu.cn
Y. Z e n g
National Key Laboratory of Integrated Circuits and Microsystems
Chongqing 401332, China
Y. Z e n g
The 24th Research Institute of China Electronics Technology Group Corp
Chongqing 400060, China
S. Chang
School of Microelectronics
Wuhan University
Wuhan, Hubei 430072, China
The ORCID identification number(s) for the author(s) of this article
can be found under https://doi.org/10.1002/qute.202400395
DOI: 10.1002/qute.202400395
a plethora of groundbreaking algorithms
has emerged, including the Quantum Vari-
ational Eigensolver,[8]Quantum Approxi-
mate Optimization Algorithm,[9]Hybrid
Quantum-Classical Neural Networks,[10–12]
Quantum Support Vector Machines,[13–15]
Quantum Nearest-Neighbor Algorit-
hms,[16,17]Quantum Convolutional Neural
Networks,[18,19]Quantum Recurrent Neural
Networks,[20,21]and Quantum Generative
Adversarial Networks.[22,23]These innova-
tionsarepavingthewayforanewerain
computational power and efficiency. While
these studies predominantly address the
processing of Euclidean data, the quantum
domain’s exploration for non-Euclidean
data remains an underexplored frontier.
In recent years, only a limited num-
ber of studies have been conducted to
explore the application of QML in pro-
cessing graph-structured data. S. Dern-
bach et al.[24]proposed a quantum walk
neural network for operating on graph-structured data. This net-
work learns a diffusion operation though the graph’s geometry,
the nodes’ features, and the learning tasks. At about the same
time,G.Verdonetal.
[25]conducted pioneering research on quan-
tum graph neural network, which is specifically tailored to repre-
sent graph-structured quantum processes.
In addition, P. Mernyei et al.[26]carried out an investigation on
quantum circuits for graph representation learning and proposed
the equivariant quantum graph circuits, which represent a class
of parameterized quantum circuits with a robust relational induc-
tive bias for learning on graph-structured data. In the same year,
Z. Hu et al.[27]proposed a quantum graph convolutional neu-
ral network, which utilizes givens rotations for message passing
with neighboring nodes and employs variational quantum cir-
cuits to introduce learnable parameters. Besides, J. Ryu et al.[28]
proposed a quantum graph neural network model for predicting
the chemical and physical properties of molecules and materi-
als. Moreover, N. Innan et al.[29]presented an approach for de-
tecting financial fraud by employing quantum graph neural net-
works, which utilize variational quantum circuits to enhance the
model’s performance. Meanwhile, B. Collis et al.[30]proposed two
quantum graph neural networks, which are implemented using
quantum-classical hybrid learning models and applied to sim-
ulate particle interactions. Furthermore, N. Singh et. al [31]pro-
posed a link prediction model based on parameterized quantum
circuit. This model employs quantum circuits to project features
into the quantum space and perform training and optimization
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