We present a quantum algorithm for ranking the nodes of a network in their order of importance. The algorithm is based on a directed discrete-time quantum walk and works on all directed networks. This algorithm can theoretically be applied to the entire internet and thus can function as a quantum PageRank algorithm. Our analysis shows that the hierarchy of quantum ranks matches well with the hierarchy of classical ranks for directed trees and other acyclic networks. For cyclic networks, however, the hierarchy of quantum ranks does not exactly match the hierarchy of the classical ranks. This highlights the role of quantum interference and fluctuations in networks and the importance of using quantum algorithms to rank nodes in quantum networks. Another application this algorithm can envision is to model the dynamics on networks mimicking chemical complexes and rank active centres in the order of reactivities. Since discrete-time quantum walks are implementable on current quantum processing systems, this algorithm will also be of practical relevance in the analysis of quantum architecture.

中文翻译：

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用于对网络上的节点进行排名的离散时间量子行走算法

我们提出一种量子算法，用于按重要性顺序对网络节点进行排名。该算法基于有向离散时间量子游走，并在所有有向网络上运行。该算法理论上可以应用于整个互联网，因此可以用作量子PageRank算法。我们的分析表明，对于有向树和其他非循环网络，量子秩的层次与经典秩的层次非常匹配。但是，对于循环网络，量子秩的层次结构与经典秩的层次结构不完全匹配。这突出了量子干扰和网络波动的作用，以及使用量子算法对量子网络中的节点进行排名的重要性。该算法可以设想的另一个应用是在模拟化学络合物的网络上建立动力学模型，并以反应性的顺序对活性中心进行排名。由于离散时间量子游走可以在当前的量子处理系统上实现，因此该算法在量子体系结构分析中也将具有实际意义。