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\title{Enable Quantum Graph Neural Networks on a Single Qubit via Quantum Walk}



\author[1]{Yijie Zhu }%
\author[2]{Richard Jiang }%
\affil[1]{Affiliation not available}%
\affil[2]{Lancaster University}%


\vspace{-1em}



  
  \date{May 08, 2026}


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\begin{abstract}
In the NISQ era, implementing practical quantum ma002 chine learning
faces challenges due to limited resources. A recent advancement involves
a novel single-qubit methodology, allowing for the execution of numerous
operations on a single qubit. However, its applicability to complex
neural network architectures remains uncertain. This study focuses on
graph data, known for its intricate structure and inherent challenges
for machine learning. Utilizing the quantum walk, we introduce a graph
embedding approach to reduce network parameters, resulting in the design
of a novel architecture called the single-qubit Quantum Graph Neural
Network (sQGNN). Experimental assessments, including simulations,
demonstrate the adaptability of sQGNNs to graphs of varying dimensions
and compositions. The resource-efficient nature of sQGNNs is showcased
through practical executions on quantum computers, using only one qubit.
This capability highlights the efficient utilization of limited qubit
resources, paving the way for expansive quantum graph neural networks on
resource-constrained Variational Quantum Circuits (VQCs). This
breakthrough opens up new possibilities for practical applications
within the current NISQ regime.%
\end{abstract}%



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