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 partial_t s = κg^q(s), where g(s) is the instantaneous gap and (κ, 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.