  The quantum approximate optimization algorithm (QAOA) is a prospective
near-term quantum algorithm due to its modest circuit depth and promising
benchmarks. However, an external parameter optimization required in QAOA could
become a performance bottleneck. This motivates studies of the optimization
landscape and search for heuristic ways of parameter initialization. In this
work we visualize the optimization landscape of the QAOA applied to the MaxCut
problem on random graphs, demonstrating that random initialization of the QAOA
is prone to converging to local minima with sub-optimal performance. We
introduce the initialization of QAOA parameters based on the Trotterized
quantum annealing (TQA) protocol, parameterized by the Trotter time step. We
find that the TQA initialization allows to circumvent the issue of false minima
for a broad range of time steps, yielding the same performance as the best
result out of an exponentially scaling number of random initializations.
Moreover, we demonstrate that the optimal value of the time step coincides with
the point of proliferation of Trotter errors in quantum annealing. Our results
suggest practical ways of initializing QAOA protocols on near-term quantum
devices and reveals new connections between QAOA and quantum annealing.
