Explore the application of Quantum Approximate Optimization Algorithm (QAOA) to local variants of classical NP-hard problems in this 28-minute conference talk by Alexandra Kolla from the University of California, Santa Cruz. Delve into the study of QAOA on local problems, focusing on LocalMaxCut as a potential area where quantum algorithms might outperform classical ones. Examine preliminary results suggesting that quantum supremacy may be achievable on complex graphs, while local algorithms still outperform QAOA on simple graph instances. Gain insights into the motivation behind this research, the methodology used, and future directions in the field of quantum numerical linear algebra.