  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.
