Instituto de Ciencia de Materiales de Aragón (ICMA), CSIC-Universidad de Zaragoza, E-50012 Zaragoza, Spain.
Sci Rep. 2012;2:605. doi: 10.1038/srep00605. Epub 2012 Aug 28.
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.
复杂网络是一种形式化框架，用于捕捉大型系统和数据库中元素之间的相互依存关系。这种形式主义允许使用网络导航方法来对每个组成部分对系统全局组织的重要性进行排名。一个关键的例子是网页排名导航，它是世界上使用最广泛的搜索引擎的核心。受此经典算法的启发，我们定义了一种量子导航方法，为网络中的元素提供了独特的排序。我们分析了量子导航到网络固定排名的收敛性，并表明量子性减少了收敛前的导航步骤数。此外，我们还表明，量子导航可以解决经典排名中出现的简并性问题。通过在实际网络中实现量子算法，我们证实了这些改进，并表明量子相干揭示了复杂系统全局组织的新层次特征。
