Temporal Encoding and Optimization in Variational Quantum Forecasting for Quantum-Network Links

Forecasting elementary-link success can inform quantum-network allocation, but telemetry collection consumes service capacity in the charged-probe setting studied here. We study temporal encoding and optimizer choice in variational quantum circuits (VQCs), and evaluate their effects on multi-request service. A Brier-risk decomposition quantifies history-compression loss as the expected conditional variance of the full-history Bayes forecast; a hidden-Markov example illustrates why event order matters. Across 20 independent seeds, temporal re-uploading reduces Brier score relative to a parameter-matched repeated-PCA VQC by 0.0026, 0.0041, and 0.0066 on stable, bursty, and withheld-shift traces, respectively, while histogram gradient-boosted trees remain more accurate. A separate 16-seed study favors validation-selected Adam over the tested momentum-SGD grid under shift. We also derive finite-sample certification and a service-risk bound under explicit joint-law coverage and robust-risk assumptions. Separately, charged-probe scheduling on chain and diamond networks does not resolve an aggregate service improvement from noncommuting over same-axis encoding. The synthetic, exact-statevector experiments establish neither hardware feasibility nor quantum advantage.