Mathematical Beauty as Computational Advantage: Exceptional Lie Groups in Quantum Reservoir Computing

We demonstrate that exceptional Lie groups (E6, E7, E8, F4, G2) provide genuine computational advantages over classical Lie groups (A, B, C, D series) in quantum reservoir computing. Through systematic experiments on the qBraid IonQ simulator, we show that E6 achieves 58.0% higher information entropy than classical structures (Cohen’s d = 1.884), with participation ratio strongly correlating with performance (r = 0.963, p < 0.01). The exceptional advantage stems from superior quantum state utilization: E6 shows 115.9% higher participation ratio than classical average. These results provide empirical evidence that mathematical elegance translates directly to computational power, suggesting that nature’s most beautiful mathematical structures may be optimal substrates for quantum information processing.