The Quantum Approximate Optimization Algorithm (QAOA) is a hybrid quantum-classical algorithm to solve binary-variable optimization problems. Due to its expected robustness to systematic errors and the short circuit depth, it is one of the promising candidates likely to run on near-term quantum devices. We project the performance of QAOA applied to the Max-Cut problem and compare it with some of the best classical alternatives, both for exact or approximate solution. When comparing approximate solvers, their performance is characterized by the computational time taken to achieve a given quality of solution. Since QAOA is based on sampling, we introduce performance metrics based on the probability of observing a sample above a certain quality. In addition, we show that the QAOA performance varies significantly with the graph type. By selecting a suitable optimizer for the variational parameters and reducing the number of function evaluations, QAOA performance improves by up to 2 orders of magnitude compared to previous estimates. Especially for 3-regular random graphs, this setting decreases the performance gap with classical alternatives.

中文翻译：

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基于单样本逼近率的量子逼近优化算法评价

量子近似优化算法 (QAOA) 是一种混合量子经典算法，用于解决二元变量优化问题。由于其对系统误差和短路深度的预期鲁棒性，它是可能在近期量子设备上运行的有希望的候选者之一。我们预测 QAOA 应用于 Max-Cut 问题的性能，并将其与一些最佳经典替代方案进行比较，无论是精确解还是近似解。在比较近似求解器时，它们的性能以实现给定解的质量所需的计算时间为特征。由于 QAOA 是基于抽样的，我们引入了基于观察到某个质量以上样本的概率的性能指标。此外，我们表明 QAOA 性能随图类型而显着变化。通过为变分参数选择合适的优化器并减少函数评估的数量，与之前的估计相比，QAOA 性能提高了 2 个数量级。特别是对于 3-regular 随机图，此设置减少了与经典替代方案的性能差距。