Quantum alternating operator ansatz (QAOA) has a strong connection to the adiabatic algorithm, which it can approximate with sufficient depth. However, it is unclear to what extent the lessons from the adiabatic regime apply to QAOA as executed in practice with small to moderate depth. In this paper, we demonstrate that the intuition from the adiabatic algorithm applies to the task of choosing the QAOA initial state. Specifically, we observe that the best performance is obtained when the initial state of QAOA is set to be the ground state of the mixing Hamiltonian, as required by the adiabatic algorithm. We provide numerical evidence using the examples of constrained portfolio optimization problems with both low (p ≤ 3) and high (p = 100) QAOA depth. Additionally, we successfully apply QAOA with XY mixer to portfolio optimization on a trapped-ion quantum processor using 32 qubits and discuss our findings in near-term experiments.

量子交替算子 ansatz (QAOA) 与绝热算法有很强的联系，它可以以足够的深度进行近似。然而，目前尚不清楚绝热机制的经验教训在多大程度上适用于在小到中等深度的实践中执行的 QAOA。在本文中，我们证明了绝热算法的直觉适用于选择 QAOA 初始状态的任务。具体来说，我们观察到，当按照绝热算法的要求将 QAOA 的初始状态设置为混合哈密顿量的基态时，可以获得最佳性能。我们使用具有低 ( p  ≤ 3) 和高 ( p  = 100) QAOA 深度的约束投资组合优化问题的示例提供数值证据。此外，我们成功地将 QAOA 与 XY 混合器应用于使用 32 量子位的俘获离子量子处理器上的组合优化，并讨论了我们在近期实验中的发现。