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
ans\"atze. 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. We
provide evidence that this speedup is connected to the concept of shortcuts to
adiabaticity.Comment: 5 pages, 3 figure