Transpilation and optimization of QAOA for maximum weighted independent set

Abstract

In recent years, quantum computing has shown promise in solving certain problems more efficiently than classical methods. The Quantum Approximate Optimization Algorithm (QAOA) has emerged as a leading candidate for achieving quantum advantage on noisy intermediate-scale quantum (NISQ) devices. This study explores the application of QAOA to the Maximum Weighted Independent Set (MWIS) problem, with particular focus on circuit transpilation strategies and parameter optimization methods. Using IBM Qiskit, we systematically examine factors affecting QAOA performance, including different transpilation optimization levels and classical optimizer selection. Our results demonstrate that optimization level 3 reduced circuit depth by 32% compared to level 0 for p=3 circuits, while maintaining solution quality. Among classical optimizers, COBYLA achieved an 81.24% approximation ratio with only 54.8 function evaluations at p=2, outperforming both grid search and SPSA methods. Execution on IBM’s real quantum hardware resulted in performance degradation ranging from 16% at p=1 to 34% at p=3 compared to ideal simulations, highlighting the compounding impact of noise and gate errors as circuit depth increases.These findings provide practical guidance for quantum algorithm implementation on NISQ devices, demonstrating that appropriate selection of transpilation techniques and optimization methods can substantially improve quantum resource efficiency while maintaining solution quality.