This work presents a quantum graph neural network architecture in which each edge of the input graph carries a $d$-level quantum system and the model acts on the associated line graph. The set of circuits generated by the model is dense in the unitary group of the total Hilbert space, subject to an irrationality condition on the angular parameters. The model constructively separates pairs of 1-WL-indistinguishable graphs whose line graphs are $k$-WL-distinguishable, making it a quantum model that lies beyond the 1-WL ceiling. The function class realizable at dimension $d$ admits a strictly positive residual loss floor, which yields a criterion for adaptive expansion of the local dimension. Numerical validation confirms the impossibility of separation by node-based architectures for $\mathrm{SRG}(16,6,2,2)$, establishes the 3-WL distinguishability of its line graphs, and demonstrates direct separation by the edge-qudit architecture between the Petersen graph and the pentagonal prism. Taken together, these results establish the structural expressivity of edge qudits as an advantage over existing node-based architectures.

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• Quantum circuits
• Qudits
• Artificial neural networks
• Graph theory