  The quantum approximate optimization algorithm (QAOA) is known for its
capability and universality in solving combinatorial optimization problems on
near-term quantum devices. The results yielded by QAOA depend strongly on its
initial variational parameters. Hence, parameters selection for QAOA becomes an
active area of research as bad initialization might deteriorate the quality of
the results, especially at great circuit depths. We first discuss on the
patterns of optimal parameters in QAOA in two directions: the angle index and
the circuit depth. Then, we discuss on the symmetries and periodicity of the
expectation that is used to determine the bounds of the search space. Based on
the patterns in optimal parameters and the bounds restriction, we propose a
strategy which predicts the new initial parameters by taking the difference
between previous optimal parameters. Unlike most other strategies, the strategy
we propose does not require multiple trials to ensure success. It only requires
one prediction when progressing to the next depth. We compare this strategy
with our previously proposed strategy and the layerwise strategy on solving the
Max-cut problem, in terms of the approximation ratio and the optimization cost.
We also address the non-optimality in previous parameters, which is seldom
discussed in other works, despite its importance in explaining the behavior of
variational quantum algorithms.
