We study the interplay between quantum annealing parameters in embedded problems, providing both deeper insights into the physics of these devices and pragmatic recommendations to improve performance on optimization problems. We choose as our test case the class of bounded-degree minimum-spanning-tree problems. Through runs on a D-Wave quantum annealer, we demonstrate that pausing in a specific time window in the anneal provides improvement in the probability of success and in the time to solution for these problems. The time window is consistent across problem instances and its location is within the region suggested by prior theory and seen in previous results on native problems. An approach to enable gauge transformations for problems with the qubit coupling strength $J$ in an asymmetric range is presented and shown to significantly improve performance. We also confirm that the optimal pause location exhibits a shift with the magnitude of the ferromagnetic coupling, $|J_F|$, between physical qubits representing the same logical one. We extend the theoretical picture for pausing and thermalization in quantum annealing to the embedded case. This picture, along with perturbation-theory analysis and exact numerical results on small problems, confirms that the effective pause region moves earlier in the anneal as $|J_F|$ increases. It also suggests why pausing, while still providing significant benefit, has a less pronounced effect on embedded problems.

中文翻译：

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铁磁地改变暂停的力量

我们研究了嵌入问题中的量子退火参数之间的相互作用，不仅提供了对这些设备的物理学的更深刻见解，而且还提供了一些实用的建议，以提高优化问题的性能。我们选择有界度最小生成树问题作为测试用例。通过在D-Wave量子退火炉上运行，我们证明了在退火过程中的特定时间窗口内暂停可以提高成功率和解决这些问题的时间。时间窗在问题实例之间是一致的，并且其位置在先有理论所建议的范围内，并且在先前有关本机问题的结果中也可以看到。一种用于对量子位耦合强度问题进行量规转换的方法$Ĵ$提出并显示了在非对称范围内的性能可以显着提高性能。我们还确认，最佳暂停位置会随铁磁耦合的大小而发生偏移，$|{Ĵ}_F|$，表示相同逻辑位的物理量子位之间。我们将量子退火中暂停和热化的理论图景扩展到嵌入式案例。这张图片，加上微扰理论分析和关于小问题的精确数值结果，证实了有效暂停区域在退火过程中随着时间的推移而提前移动。$|{Ĵ}_F|$增加。这也说明了为什么暂停虽然仍然可以带来很大的好处，但对嵌入的问题却没有那么明显的影响。