Scaling QAOA: transferring optimal adiabatic schedules from small-scale to large-scale variational circuits

The Quantum Approximate Optimization Algorithm (QAOA) is a leading approach for combinatorial optimization on near-term quantum devices, yet its scalability is limited by the difficulty of optimizing $2p$ variational parameters for a large number $p$ of layers. Recent empirical studies indicate that optimal QAOA angles exhibit concentration and transferability across problem sizes. Leveraging this observation, we propose a schedule-learning framework that transfers spectral-gap-informed adiabatic control strategies from small-scale instances to larger systems. Our method extracts the spectral gap profile of small problems and constructs a continuous schedule governed by ${\mathrm{\partial }}_{t}s=\kappa g^q(s)$, where $g(s)$ is the instantaneous gap and $(\kappa ,q)$ are global hyperparameters. Discretizing this schedule yields closed-form expressions for all QAOA angles, reducing the classical optimization task from $2p$ parameters to only $2$, independent of circuit depth. This drastic parameter compression mitigates classical optimization overhead and reduces sensitivity to barren plateau phenomena. Numerical simulations on random QUBO and 3-regular MaxCut instances demonstrate that the learnt schedules transfer effectively to larger systems while achieving competitive approximation ratios. Our results suggest that gap-informed schedule transfers provide a scalable and parameter-efficient strategy for QAOA.