在网络上对量子步行进行集群诱导的本地化
Lucas Böttcher1,2, Mason A Porter3,4,5
1Frankfurt School of Finance and Management, Department of Computational Science and Philosophy, 60322 Frankfurt am Main, Germany.
Physical review. E
|January 21, 2026
概括
网络上的量子步行表现出局部化,这是一个受网络结构影响的现象. 这项研究表明,网络中的局部集群可以诱导这种本地化,影响量子信息处理.
科学领域:
- 量子信息理论 量子信息理论
- 网络科学 网络科学
- 凝聚物质物理学 凝聚物质物理学
背景情况:
- 量子步行是量子信息理论中必不可少的模型,在搜索和分析中具有应用.
- 与古典步行不同,量子步行是单一进化的,不会达到静止分布.
- 了解量子行走的长期行为和网络影响对于应用至关重要.
研究的目的:
- 为了研究网络上的连续时间量子步行中的局部化现象.
- 导出长期逆参与率的分析表达式.
- 探索网络结构,特别是局部聚类和量子步行本地化之间的关系.
主要方法:
- 对长期逆参与率的分析表达式的推导.
- 在专门构建的高度集群网络 (递归连接的三角形) 上分析量子步行.
- 在已建立的网络模型上检查量子步行:克莱因伯格可导航的小世界和Holme-Kim权力规律集群网络.
主要成果:
- 导出了长时间逆参与比的分析表达式,它取决于量子步行哈密尔顿式的自向量.
- 在构建的高度集群网络中观察到本地化.
- 在Kleinberg可导航小世界和Holme-Kim权力法集群网络中也展示了本地化,证实了本地集群的作用.
结论:
- 局部聚类是一种关键的网络特征,可以诱导连续时间量子步行的本地化.
- 这些发现为量子步行的长期动态及其对网络拓学的依赖提供了洞察力.
- 这项研究有助于理解量子步行行为,用于量子信息处理和网络分析的潜在应用.
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