An adaptive quantum approximate optimization algorithm for solving combinatorial problems on a quantum computer.

The quantum approximate optimization algorithm (QAOA) is a hybrid variational quantum-classical algorithm that solves combinatorial optimization problems. While there is evidence suggesting that the fixed form of the original QAOA ansatz is not optimal, there is no systematic approach for finding better ansatze. We address this problem by developing an iterative version of QAOA that is problem-tailored, and which can also be adapted to specific hardware constraints. We simulate the algorithm on a class of Max-Cut graph problems and show that it converges much faster than the original QAOA, while simultaneously reducing the required number of CNOT gates and optimization parameters.