MPE-Adam: Multi-Population Evolutionary Optimization with Adam Refinement for QAOA

2026-06-25

AI Summary

This work addresses the challenge of optimizing Quantum Approximate Optimization Algorithm (QAOA) parameters in high-dimensional non-convex landscapes, where measurement noise hinders the balance between global exploration and local convergence. To overcome this, the authors propose a phased hybrid optimization framework that first employs a multi-population evolutionary algorithm for broad global search and subsequently refines the solution using the Adam gradient-based optimizer. This approach introduces, for the first time, a multi-stage optimization paradigm to QAOA parameter tuning, decoupling exploration from refinement to significantly enhance both solution quality and software modularity. Evaluated on MaxCut problems over random 3-regular graphs with up to 22 nodes, the method consistently outperforms pure evolutionary strategies and SPSA baselines, achieving superior approximation ratios and improved result stability.

Abstract

Parameter optimization is a central bottleneck in variational quantum algorithms such as the Quantum Approximate Optimization Algorithm (QAOA). The classical optimizer must navigate a high-dimensional, non-convex parameter space under measurement noise. From a quantum software perspective, this process forms a multi-stage workflow: global exploration of the parameter space followed by local refinement within the hybrid quantum-classical loop. Most existing approaches, however, employ single-stage optimizers that do not separate these roles, which limits the use of complementary strategies. We propose MPE-Adam, a hybrid optimization framework that integrates multi-population evolutionary search for global exploration with Adam-based gradient refinement for local convergence. The method is structured as a modular component suitable for quantum software pipelines. We evaluate MPE-Adam on MaxCut instances generated from random 3-regular graphs with up to 22 nodes. The results show that MPE-Adam achieves higher approximation ratios and lower variance than evolutionary-only and SPSA-based baselines, with statistically significant improvements. These findings indicate that structured multi-stage optimization improves both solution quality and software-level flexibility in quantum applications.

Problem

• parameter optimization
• Quantum Approximate Optimization Algorithm
• variational quantum algorithms
• non-convex optimization
• measurement noise

Innovation

• multi-population evolutionary optimization
• Adam refinement
• hybrid quantum-classical optimization
• QAOA parameter optimization
• modular optimization framework