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

TL;DR

This paper introduces a spectral-gap-informed schedule transfer method for QAOA that reduces parameter complexity and enhances scalability by leveraging small-scale problem insights to larger systems.

Contribution

It proposes a novel schedule-learning framework that transfers adiabatic control strategies from small to large problems, significantly reducing optimization parameters.

Findings

Transferred schedules perform well on larger instances.

Parameter reduction from 2p to 2 simplifies optimization.

Achieves competitive approximation ratios on benchmark problems.

Abstract

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 \(\partial_t s = \kappa g^q(s)\), 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.