Distributed Quantum-Assisted Robust AoII Minimization in Satellite-Ground Integrated Edge Networks

Mission-critical edge applications in 6G-and-beyond networks, such as autonomous systems, disaster response, and infrastructure monitoring, require that the edge decision-maker's estimate of a monitored process remain correct, not merely up to date. Satellite-ground integrated networks (SAGIN) often provide the only connectivity in infrastructure-limited or disaster-affected regions, yet satellite handover and shadowing interrupt links, during which the process may change state several times, leaving the edge node's estimate substantially wrong. Age of information (AoI) tracks only elapsed time and cannot distinguish a harmless delay from a dangerous error. We instead adopt the age of incorrect information (AoII), which penalizes both the duration and magnitude of estimation error, and formulate, to our knowledge, the first network-level, multi-node AoII minimization problem over SAGIN under stochastic handover and shadowing. We propose SENTINEL, a distributed hybrid quantum-classical framework that jointly schedules update rates, satellite-to-base-station associations, and bandwidth allocation to minimize the worst-case time-average AoII. Because AoII is history dependent, it resists per-slot optimization; a renewal-interval decomposition that separates source dynamics from channel disruption yields a closed-form AoII cost per inter-delivery interval. The resulting robust scheduling problem, VANGUARD, is formulated as a QUBO, mapped to an Ising Hamiltonian, and solved via distributed QAOA with ADMM-based coordination across satellite and ground domains. Every returned schedule carries a certified worst-case AoII over all disruption scenarios. Simulations show that SENTINEL outperforms learning-based and random baselines, matches a state-aware threshold policy in small networks while additionally providing a worst-case guarantee, and remains close to an exact minimax reference.