  In the era of Internet of Things (IoT), multi-access edge computing
(MEC)-enabled satellite-aerial-terrestrial integrated network (SATIN) has
emerged as a promising technology to provide massive IoT devices with seamless
and reliable communication and computation services. This paper investigates
the cooperation of low Earth orbit (LEO) satellites, high altitude platforms
(HAPs), and terrestrial base stations (BSs) to provide relaying and computation
services for vastly distributed IoT devices. Considering the uncertainty in
dynamic SATIN systems, we formulate a stochastic optimization problem to
minimize the time-average expected service delay by jointly optimizing resource
allocation and task offloading while satisfying the energy constraints. To
solve the formulated problem, we first develop a Lyapunov-based online control
algorithm to decompose it into multiple one-slot problems. Since each one-slot
problem is a large-scale mixed-integer nonlinear program (MINLP) that is
intractable for classical computers, we further propose novel hybrid
quantum-classical generalized Benders' decomposition (HQCGBD) algorithms to
solve the problem efficiently by leveraging quantum advantages in parallel
computing. Numerical results validate the effectiveness of the proposed
MEC-enabled SATIN schemes.
