论文标题
大规模网络中的量子pagerank的张量求解器
TensorFlow Solver for Quantum PageRank in Large-Scale Networks
论文作者
论文摘要
Google Pagerank是一种对网络中节点或网站的重要性进行排名的普遍且有用的算法，并且已经提高了Pagerank算法的最新量子对应物，以表明与Google Pagerank相比，对排名的准确性更高。量子pagerank算法本质上是基于量子随机步行，可以使用lindblad主方程表示，但是，该方程需要求解O（n^4）维度的Kronecker产品，并且需要严格的内存，并且需要严格的记忆力，并且需要在此处使用量子量的量子来减少量子的数量。矩阵尺寸为O（n^2），并采用张力流进行GPU并行计算。我们展示了它在解决美国主要航空公司网络的量子pagerank方面的性能，最多922个节点。与以前的量子pagerank求解器相比，我们的求解器将所需的内存和时间分别降低到只有1％和0.2％，这使得在不超过100秒内的4-8 GB的正常计算机中工作是可行的。对于大规模量子pagerank和量子随机步行的这一有效求解器将极大地促进对现实生活应用中量子信息的研究。
Google PageRank is a prevalent and useful algorithm for ranking the significance of nodes or websites in a network, and a recent quantum counterpart for PageRank algorithm has been raised to suggest a higher accuracy of ranking comparing to Google PageRank. The quantum PageRank algorithm is essentially based on quantum stochastic walks and can be expressed using Lindblad master equation, which, however, needs to solve the Kronecker products of an O(N^4) dimension and requires severely large memory and time when the number of nodes N in a network increases above 150. Here, we present an efficient solver for quantum PageRank by using the Runge-Kutta method to reduce the matrix dimension to O(N^2) and employing TensorFlow to conduct GPU parallel computing. We demonstrate its performance in solving quantum PageRank for the USA major airline network with up to 922 nodes. Compared with the previous quantum PageRank solver, our solver dramatically reduces the required memory and time to only 1% and 0.2%, respectively, making it practical to work in a normal computer with a memory of 4-8 GB in no more than 100 seconds. This efficient solver for large-scale quantum PageRank and quantum stochastic walks would greatly facilitate studies of quantum information in real-life applications.
