Faster algorithms for combinatorial optimization could prove transformative for diverse areas such as logistics, finance and machine learning. Accordingly, the possibility of quantum enhanced optimization has driven much interest in quantum technologies. Here we demonstrate the application of the Google Sycamore superconducting qubit quantum processor to combinatorial optimization problems with the quantum approximate optimization algorithm (QAOA). Like past QAOA experiments, we study performance for problems defined on the planar connectivity graph native to our hardware; however, we also apply the QAOA to the Sherrington–Kirkpatrick model and MaxCut, non-native problems that require extensive compilation to implement. For hardware-native problems, which are classically efficient to solve on average, we obtain an approximation ratio that is independent of problem size and observe that performance increases with circuit depth. For problems requiring compilation, performance decreases with problem size. Circuits involving several thousand gates still present an advantage over random guessing but not over some efficient classical algorithms. Our results suggest that it will be challenging to scale near-term implementations of the QAOA for problems on non-native graphs. As these graphs are closer to real-world instances, we suggest more emphasis should be placed on such problems when using the QAOA to benchmark quantum processors.

更快的组合优化算法可以证明对物流、金融和机器学习等不同领域的变革。因此，量子增强优化的可能性引起了人们对量子技术的极大兴趣。在这里，我们展示了 Google Sycamore 超导量子比特量子处理器在量子近似优化算法 (QAOA) 组合优化问题中的应用。像过去的 QAOA 实验一样，我们研究在我们的硬件原生的平面连接图上定义的问题的性能；然而，我们也将 QAOA 应用于 Sherrington-Kirkpatrick 模型和 MaxCut，需要大量编译才能实现的非原生问题。对于硬件原生问题，这些问题通常可以平均解决，我们获得了一个与问题大小无关的近似比率，并观察到性能随着电路深度的增加而增加。对于需要编译的问题，性能会随着问题的大小而降低。涉及数千个门的电路仍然比随机猜测具有优势，但与一些有效的经典算法相比却没有。我们的结果表明，针对非本地图上的问题扩展 QAOA 的近期实施将是一项挑战。由于这些图表更接近真实世界的实例，我们建议在使用 QAOA 对量子处理器进行基准测试时应该更加重视这些问题。涉及数千个门的电路仍然比随机猜测具有优势，但与一些有效的经典算法相比却没有。我们的结果表明，针对非本地图上的问题扩展 QAOA 的近期实施将是一项挑战。由于这些图表更接近真实世界的实例，我们建议在使用 QAOA 对量子处理器进行基准测试时应该更加重视这些问题。涉及数千个门的电路仍然比随机猜测具有优势，但与一些有效的经典算法相比却没有。我们的结果表明，针对非本地图上的问题扩展 QAOA 的近期实施将是一项挑战。由于这些图表更接近真实世界的实例，我们建议在使用 QAOA 对量子处理器进行基准测试时应该更加重视这些问题。