A Cyclic Layerwise QAOA Training

Abstract

The quantum approximate optimization algorithm (QAOA) is a hybrid quantum-classical algorithm for solving combinatorial optimization problems. Multi-angle QAOA (MA-QAOA), which assigns independent parameters to each Hamiltonian operator term, achieves superior approximation performance even with fewer layers than standard QAOA. Unfortunately, this increased expressibility can raise the classical computational cost due to a greater number of parameters. The recently proposed Layerwise MA-QAOA (LMA-QAOA) reduces this overhead by training one layer at a time, but it may suffer from obtaining the precise solution due to the previously fixed parameters. This work addresses two questions for efficient MA-QAOA training: (i) What is the optimal granularity for parameter updates per epoch, and (ii) How can we get precise final cost function results while only partially updating the parameters per epoch? Despite the benefit of reducing the parameters that update per epoch can reduce the classical computation overhead, too fine or coarse a granularity of Hamiltonian update can degrade the MA-QAOA training efficiency. We find that optimizing one complete layer per epoch is an efficient granularity. Moreover, selectively retraining each layer by tracking gradient variations can achieve a final cost function equivalent to the standard MA-QAOA while lowering the parameter update overhead. Based on these insights, we propose Orbit-QAOA, which cyclically revisits layers and selectively freezes stabilized parameters. Across diverse graph benchmarks, Orbit-QAOA reduces training steps by up to 81.8%, reduces approximation ratio error by up to 72x compared to the unified stop condition-applied enhanced LMA-QAOA, and achieves equivalent approximation performance compared to the standard MA-QAOA.