  Quantum approximate optimization algorithm (QAOA) is a promising hybrid
quantum-classical algorithm to solve combinatorial optimization problems in the
era of noisy intermediate-scale quantum computers. Recently warm-start
approaches have been proposed to improve the performance of QAOA, where
approximate solutions are obtained by classical algorithms in advance and
incorporated into the initial state and/or unitary ansatz. In this work, we
study in detail how the accuracy of approximate solutions affect the
performance of the warm-start QAOA (WS-QAOA). We numerically find that in
typical MAX-CUT problems, WS-QAOA tends to outperform QAOA as approximate
solutions become closer to the exact solutions in terms of the Hamming
distance. We reveal that this could be quantitatively attributed to the initial
state of the ansatz. We also solve MAX-CUT problems by WS-QAOA with approximate
solutions obtained via QAOA, having a better result than QAOA especially when
the circuit is relatively shallow. We believe that our study may deepen
understanding of the performance of WS-QAOA and also provide a guide as to the
necessary quality of approximate solutions.
