复杂网络中的量子导航与排序
Quantum Navigation and Ranking in Complex Networks
摘要：
复杂网络是一种形式化的框架，它捕捉了大型系统和数据库元素之间的相互依赖关系。这种形式主义允许使用网络导航方法来排列每个组成部分对系统的全局组织的重要性。一个关键的例子是网页排名导航，它是万维网最常用的搜索引擎的核心。在这个经典算法的启发下，我们定义了一个量子导航方法，提供了一个独特的网络元素的排名。我们分析了量子导航收敛到网络的稳定秩，并表明量子性减少了收敛前的导航步骤的数量。此外，我们表明，量子导航允许解决经典秩中发现的简并。通过在真实网络中实现量子算法，我们证实了这些改进，并表明量子相干性揭示了复杂系统的全球组织的新的层次特征。
英文摘要：
Complex networks are formal frameworks capturing the interdependencies between the elements of large systems and databases. This formalism allows to use network navigation methods to rank the importance that each constituent has on the global organization of the system. A key example is Pagerank navigation which is at the core of the most used search engine of the World Wide Web. Inspired in this classical algorithm, we define a quantum navigation method providing a unique ranking of the elements of a network. We analyze the convergence of quantum navigation to the stationary rank of networks and show that quantumness decreases the number of navigation steps before convergence. In addition, we show that quantum navigation allows to solve degeneracies found in classical ranks. By implementing the quantum algorithm in real networks, we confirm these improvements and show that quantum coherence unveils new hierarchical features about the global organization of complex systems.
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