发表机构
The Institute of Mathematical Sciences, A CI of Homi Bhabha National Institute（马蒂亚科学研究所，霍米·巴巴国家研究所的附属机构）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对稀疏约束保持型量子退火，推导了归一化最小间隙的交换分辨敏感性，发现改进瓶颈可触发“修复并暴露”机制，提出绑定最小值的最大-最小更新方法，建立了局部间隙敏感性与瓶颈迁移的关联。
AI 中文摘要
约束保持型交换驱动程序允许许多保留相同可行扇区的耦合图，但在退火路径上表现出不同的最小间隙。我们针对共享Dicke基态的固定基数拉普拉斯驱动程序，推导了归一化最小间隙的交换分辨敏感性，并将其应用于识别驱动程序的局部有利修改。数值实验表明，该敏感性可可靠预测有益的无穷小变化，但当同一方向扩展到有限边替换时，其可靠性会降低。间隙景观追踪揭示了这种可靠性损失的一种机制：改进活动瓶颈可暴露一个竞争的最小值，伴随低能子空间更广泛的重组，我们将此称为“修复并暴露”机制，并在稠密二次和稀疏受挫目标族中均观察到该现象。这促使在竞争最小值变为共同活动时重新线性化响应。在测试的 oracle 设置中，绑定最小值的最大-最小更新比继续原始方向或仅优化输入最小值的可靠性高得多。支持有限大小搜索和选择器的测试表明，该局部信息在超出无穷小极限后仍可保持有用，但其实际提取取决于驱动程序几何结构和相关低能竞争者的识别。这些结果将局部交换分辨间隙敏感性与瓶颈迁移及条件驱动重定向联系起来。
英文摘要
Constraint-preserving exchange drivers allow many coupling graphs that preserve the same feasible sector, but exhibit different minimum gaps along an annealing path. We derive an exchange-resolved sensitivity of the normalised minimum gap for fixed-cardinality Laplacian drivers sharing a Dicke ground state, and apply it to identify locally favourable modifications of the driver. Numerical experiments indicate this sensitivity reliably predicts beneficial infinitesimal changes, but its reliability decreases when the same direction is extended to a finite edge replacement. The gap landscape tracking reveals one mechanism of this loss of reliability. Improving the active bottleneck can expose a competing minimum, with a more extensive reorganisation of the low-energy subspace. We call this the "repair-and-expose" mechanism and observe it in both dense quadratic and sparse frustrated objective families. This motivates relinearizing the response when competing minima become co-active. In the tested oracle setting, a tied-minimum max-min update is substantially more reliable than continuing the original direction or optimizing only the incoming minimum. Supporting finite-size search and selector tests show that this local information can remain useful beyond the infinitesimal limit, while its practical extraction depends on the driver geometry and identification of the relevant low-energy competitors. These results connect local exchange-resolved gap sensitivity to bottleneck migration and conditional driver redirection.
