The quantum approximate optimization algorithm (QAOA) has become a cornerstone of contemporary quantum applications development. Here we show that the $density$ of problem constraints versus problem variables acts as a performance indicator. Density is found to correlate strongly with approximation inefficiency for fixed depth QAOA applied to random graph minimization problem instances. Further, the required depth for accurate QAOA solution to graph problem instances scales critically with density. Motivated by Google's recent experimental realization of QAOA, we preform a reanalysis of the reported data reproduced in an ideal noiseless setting. We found that the reported capabilities of instances addressed experimentally by Google, approach a rapid fall-off region in approximation quality experienced beyond intermediate-density. Our findings offer new insight into performance analysis of contemporary quantum optimization algorithms and contradict recent speculation regarding low-depth QAOA performance benefits.

中文翻译：

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图问题的量子近似优化中的可达性缺陷

量子近似优化算法（QAOA）已成为当代量子应用开发的基石。在这里，我们展示了问题约束与问题变量的密度作为性能指标。发现密度与应用于随机图最小化问题实例的固定深度 QAOA 的近似低效密切相关。此外，绘制问题实例的精确 QAOA 解决方案所需的深度与密度成正比。受 Google 最近对 QAOA 的实验性实现的启发，我们对在理想无噪声环境中再现的报告数据进行了重新分析。我们发现，谷歌通过实验解决的实例的报告能力，接近中等密度以外的近似质量的快速下降区域。