SafeER: Safety-First Learning-Augmented Entanglement Routing under Fidelity Uncertainty

Entanglement routing is a fundamental network-control problem in quantum networks, where end-to-end entangled pairs are established through probabilistic generation, purification, memory storage, and entanglement swapping. A delivered pair is useful only if its realized fidelity meets the application-specific threshold, yet routing decisions must rely on fidelity estimates before the final outcome is known. This uncertainty creates a safety--efficiency tradeoff between admitting more requests and avoiding low-fidelity deliveries. We propose \emph{SafeER}, a safety-first learning-augmented framework for online fidelity-constrained entanglement routing under uncertain realized fidelity. SafeER considers routing and purification decisions under finite quantum memory, request-specific fidelity and latency constraints, and uncertain fidelity estimates. Its key design separates conservative fidelity screening from resource-aware candidate selection. An analytic--learned fidelity estimate combined with a safety margin determines candidate eligibility, while a learned surrogate ranks only candidates passing the screen. We establish computational hardness of a restricted fidelity-constrained routing problem, deterministic and probabilistic safety guarantees under explicit one-sided fidelity-overestimation conditions, candidate-set ranking bounds, and online complexity bounds. Extensive routing-layer simulations across traffic loads, network sizes, and fidelity uncertainty models show that SafeER achieves zero observed violations under calibrated bounded uncertainty and substantially suppresses violations under misspecified errors. SafeER improves weighted qualified goodput by approximately $3.0\times$ over greedy fidelity-aware routing while achieving competitive performance against safe non-learning methods. Controlled ablations further show that the measurable incremental benefit of learning arises primarily from fidelity screening rather than utility ranking. These results support conservative, learning-assisted admission as an approach to fidelity-constrained quantum-network routing.