统计景观探索与选择性振荡器伊辛机中的弱场缺陷
Statistical Landscape Exploration and Weak-Field Defects in Selective Oscillator Ising Machines
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中文总结 AI 辅助
本研究提出OIM+选择性振荡器伊辛机方案，结合退火与能量消除重填，探索SK模型低能态，识别弱场缺陷并用Metropolis细化修正，实现集体搜索与局部优化的高效分工。
中文摘要 AI 辅助
振荡器伊辛机（OIMs）为组合优化提供了一种模拟动力学方法，但对其生成的系综的统计结构知之甚少。利用Sherrington-Kirkpatrick（SK）自旋玻璃模型，我们引入了一种选择性振荡器方案OIM+，在该方案中，连续的退火阶段与基于能量的消除和复制品重新填充相结合。我们通过重叠分布、汉明距离、层次聚类和局部场统计来表征所得状态。尽管经过重复选择，OIM+仍能探索结构化的低能区域，同时保留非平凡的构型系综。我们识别出稀疏的弱局部场残余缺陷作为该动力学的一个特征性局限。简短的Metropolis-Hastings细化优先纠正这些缺陷，表明振荡器动力学执行主要的集体探索，而剩余的修正主要是局部的。弱场主要源于竞争性相互作用项之间的抵消，而非均匀的弱耦合。同样的行为在反铁磁偏置的SK系综中持续存在，其中混合方法达到的合并平均能量与显著更长的纯Metropolis退火相当。完整协议在标准G-set Max-Cut基准上也取得了有竞争力的性能。这些结果表明，集体模拟搜索与针对性局部细化之间存在自然的劳动分工。
英文摘要
Oscillator Ising machines (OIMs) provide an analog dynamical approach to combinatorial optimization, but comparatively little is known about the statistical structure of the ensembles they generate. Using the Sherrington-Kirkpatrick (SK) spin-glass model, we introduce a selective oscillator scheme, OIM+, in which successive annealing epochs are combined with energy-based elimination and repopulation of replicas. We characterize the resulting states through overlap distributions, Hamming distances, hierarchical clustering, and local-field statistics. OIM+ explores structured low-energy regions while retaining a nontrivial ensemble of configurations despite repeated selection. We identify sparse weak-local-field residual defects as a characteristic limitation of the dynamics. A short Metropolis-Hastings refinement preferentially corrects these defects, indicating that the oscillator dynamics performs the dominant collective exploration while the remaining corrections are predominantly local. The weak fields arise mainly from cancellation among competing interaction terms rather than uniformly weak couplings. The same behavior persists for an antiferromagnetically biased SK ensemble, where the hybrid method reaches a pooled mean energy comparable to a substantially longer pure Metropolis anneal. The complete protocol also achieves competitive performance on standard G-set Max-Cut benchmarks. These results suggest a natural division of labor between collective analog search and targeted local refinement.
发表机构
- Bilkent University（比尔肯特大学）
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