Quantum-Enhanced Riemannian-Conditioned Graph Representation Learning for ALS-EEG Decoding

Cross-patient electroencephalography (EEG) decoding for amyotrophic lateral sclerosis (ALS) requires learning from small clinical cohorts while capturing both local EEG evidence and trial-specific inter-component relations. Compact deep encoders capture local temporal–spatial patterns, whereas Riemannian and graph methods explicitly represent relational structure, but these two information sources are typically compressed or aggregated without preserving their component-wise correspondence. We introduce QRG-EEG, a quantum-enhanced Riemannian-conditioned graph model that preserves component identity across deep, graph, and quantum representations. Local evidence from component $i$ controls a single-qubit operation on qubit $i$, while its Riemannian relation $(i,j)$ directly conditions the interaction between qubits $(i,j)$. We analytically show how this edge conditioning becomes observable and induces a joint node–node–edge response. We evaluate QRG-EEG on four public ALS-EEG datasets comprising 30 patient-level LOSO folds, using strict source-only selection, matched classical and quantum controls, and targeted edge interventions. Extensive experiments demonstrate that QRG-EEG achieves the strongest dataset-level Macro-F1, together with secondary metrics (AUROC for P300, balanced accuracy for MI), among the representative competing methods, while removing or misaligning trial-specific edges consistently degrades performance. These results support component-aligned node–edge conditioning as a structured inductive bias for scarce-data cross-patient EEG decoding.