This article utilizes the inspiration to apply the Wyel operators for producing the Kraus operators, which are crucial in the discrete-time open quantum walk. It assists us in extending the idea of discrete-time open quantum walk on arbitrary directed and undirected graphs. We make the new model of quantum walk useful to build up a quantum PageRank algorithm. In classical computation, Google's PageRank is a significant algorithm for arranging web pages on the World Wide Web. In general, it is also a fundamental measure for quantifying the importance of vertices in a network. Similarly, the new quantum PageRank also represents the importance of the vertices of a network. We can compute the new quantum PageRank algorithm in polynomial time using a classical computer. We compare the classical PageRank and the newly defined quantum PageRank for different types of complex networks, such as the scale-free network, Erdos-Renyi random network, Watts-Strogatz network, spatial network, Zachary Karate club network, random-k-out graph, binary tree graph, GNC network, Barabasi and Albert network, etc.

翻译：本文受Wyel算子启发，将其应用于生成Kraus算子，该算子在离散时间开放量子游走中至关重要。这有助于我们将离散时间开放量子游走的思想推广到任意有向图和无向图上。我们利用这一新型量子游走模型构建量子PageRank算法。在经典计算中，Google的PageRank是万维网上网页排序的重要算法，通常也是衡量网络中顶点重要性的基本指标。类似地，新提出的量子PageRank同样可表征网络顶点的重要性。通过经典计算机，我们能够在多项式时间内计算出该量子PageRank算法。针对不同类型的复杂网络（如无标度网络、Erdos-Renyi随机网络、Watts-Strogatz网络、空间网络、Zachary空手道俱乐部网络、随机k出图、二叉树图、GNC网络、Barabasi-Albert网络等），我们对比了经典PageRank与新定义的量子PageRank的性能。