The maximum-independent set (MIS) problem of graph theory using the quantum alternating operator ansatz is studied. We perform simulations on the Rigetti Forest simulator for the square ring, [Formula: see text], and [Formula: see text] graphs and analyze the dependence of the algorithm on the depth of the circuit and initial states. The probability distribution of observation of the feasible states representing maximum-independent sets is observed to be asymmetric for the MIS problem, which is unlike the Max-Cut problem where the probability distribution of feasible states is symmetric. For asymmetric graphs, it is shown that the algorithm clearly favors the independent set with the larger number of elements even for finite circuit depth. We also compare the approximation ratios for the algorithm when we choose different initial states for the square ring graph and show that it is dependent on the choice of the initial state.

中文翻译：

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最大独立集和量子交替算子 ansatz

研究了使用量子交替算子ansatz的图论的最大独立集（MIS）问题。我们在 Rigetti Forest 模拟器上对方形环、[公式：见文本] 和 [公式：见文本] 图进行了仿真，并分析了算法对电路深度和初始状态的依赖性。对于 MIS 问题，观察到表示最大独立集的可行状态的概率分布是不对称的，这与可行状态的概率分布是对称的 Max-Cut 问题不同。对于非对称图，即使对于有限的电路深度，该算法也明显有利于具有更多元素的独立集。