The Virtues of the Quantum Approximate Optimization Algorithm

Explore the potential of the Quantum Approximate Optimization Algorithm (QAOA) in this 52-minute lecture by Edward Farhi from Google, presented at the Simons Institute. Delve into the algorithm's design for solving combinatorial optimization problems through alternating unitary transformations. Examine proven worst-case performance guarantees for MaxCut and other problems, as well as established QAOA performance for the Sherrington Kirkpatrick model with random all-to-all connections. Learn about QAOA's quantum supremacy at its shallowest depth and discuss obstacles to performance, including locality and the Overlap Gap property. Analyze the practical implications of these limitations for large-scale quantum systems and consider the potential for QAOA to improve performance with increased depth. Gain insights into the ongoing research and possibilities for QAOA's computational usefulness in experimentally realizable depths.