Combinatorial optimization problems are ubiquitous and computationally hard
to solve in general. Quantum computing is envisioned as a powerful tool
offering potential computational advantages for solving some of these problems.
Quantum approximate optimization algorithm (QAOA), one of the most
representative quantum-classical hybrid algorithms, is designed to solve
certain combinatorial optimization problems by transforming a discrete
optimization problem into a classical optimization problem over a continuous
circuit parameter domain. QAOA objective landscape over the parameter variables
is notorious for pervasive local minima and barren plateaus, and its viability
in training significantly relies on the efficacy of the classical optimization
algorithm. To enhance the performance of QAOA, we design double adaptive-region
Bayesian optimization (DARBO), an adaptive classical optimizer for QAOA. Our
experimental results demonstrate that the algorithm greatly outperforms
conventional gradient-based and gradient-free optimizers in terms of speed,
accuracy, and stability. We also address the issues of measurement efficiency
and the suppression of quantum noise by successfully conducting the full
optimization loop on the superconducting quantum processor. This work helps to
unlock the full power of QAOA and paves the way toward achieving quantum
advantage in practical classical tasks.Comment: Main text: 11 pages, 4 figures, SI: 5 pages, 5 figure