This paper builds on top of a paper we have published very recently, in which we have proposed a novel approach to prime factorization (PF) by quantum annealing, where 8,219,999=32,749x251 was the highest prime product we were able to factorize -- which, to the best of our knowledge is the largest number which was ever factorized by means of a quantum device. The series of annealing experiments which led us to these results, however, did not follow a straight-line path; rather, they involved a convoluted trial-and-error process, full of failed or partially-failed attempts and backtracks, which only in the end drove us to find the successful annealing strategies. In this paper, we delve into the reasoning behind our experimental decisions and provide an account of some of the attempts we have taken before conceiving the final strategies that allowed us to achieve the results. This involves also a bunch of ideas, techniques, and strategies we investigated which, although turned out to be inferior wrt. those we adopted in the end, may instead provide insights to a more-specialized audience of D-Wave users and practitioners. In particular, we show the following insights: ($i$) different initialization techniques affect performances, among which flux biases are effective when targeting locally-structured embeddings; ($ii$) chain strengths have a lower impact in locally-structured embeddings compared to problem relying on global embeddings; ($iii$) there is a trade-off between broken chain and excited CFAs, suggesting an incremental annealing offset remedy approach based on the modules instead of single qubits. Thus, by sharing the details of our experiences, we aim to provide insights into the evolving landscape of quantum annealing, and help people access and effectively use D-Wave quantum annealers.

翻译：本文基于我们近期发表的一篇论文展开，该论文提出了一种通过量子退火实现质因数分解（PF）的新方法，其中8,219,999=32,749×251是我们能够分解的最高质数乘积——据我们所知，这是迄今利用量子设备分解的最大数字。然而，取得这些成果所经历的一系列退火实验并非一帆风顺；相反，它们涉及一个曲折的试错过程，充斥着失败或部分失败的尝试与回溯，最终才引导我们找到了成功的退火策略。本文深入探讨了实验决策背后的逻辑，并详细记录了在构思最终策略之前所尝试的部分方案，这些策略最终使我们取得了前述成果。此外，文中还涵盖了我们研究过的一系列思路、技术与策略——尽管它们被证明不如最终采纳的方案优越，却可能为更专业的D-Wave用户与实践者提供启发。具体而言，我们揭示了以下见解：（i）不同的初始化技术会影响性能，其中通量偏置在针对局部结构化嵌入时效果显著；（ii）与依赖全局嵌入的问题相比，链强度在局部结构化嵌入中的影响较小；（iii）断链与激发态CFA之间存在权衡，这提示了一种基于模块（而非单个量子比特）的增量退火偏移修正方法。因此，通过分享我们的实验经验细节，本文旨在揭示量子退火领域的动态演变，并帮助人们接触及有效使用D-Wave量子退火器。