The quantization of the PageRank algorithm is a promising tool for a future quantum internet. Here we present a modification of the quantum PageRank introducing arbitrary phase rotations (APR) in the underlying Szegedy's quantum walk. We define three different APR schemes with only one phase as a degree of freedom. We have analyzed the behavior of the new algorithms in a small generic graph, observing that a decrease of the phase reduces the standard deviation of the instantaneous PageRank, so the nodes of the network can be distinguished better. However, the algorithm takes more time to converge, so the phase can not be decreased arbitrarily. With these results we choose a concrete value for the phase to later apply the algorithm to complex scale-free graphs. In these networks, the original quantum PageRank is able to break the degeneracy of the residual nodes and detect secondary hubs that the classical algorithm suppresses. Nevertheless, not all of the detected secondary hubs are real according to the PageRank's definition. Some APR schemes can overcome this problem, restoring the degeneration of the residual nodes and highlighting the truly secondary hubs of the networks. Finally, we have studied the stability of the new algorithms. The original quantum algorithm was known to be more stable than the classical. We have found that one of our new algorithms whose PageRank distribution resembles the classical one, has a stability similar to the original quantum algorithm.
翻译:PageRank 算法的量化是未来量子互联网的一个很有希望的工具。 我们在这里展示了对量子 PageRank 的量子转换( APR) 的修改。 我们定义了三种不同的 PRA 方法, 只有一个阶段是自由程度。 我们用一个小的通用图形分析了新算法的行为, 观察到这个阶段的减少会降低瞬时PageRank 的标准偏差, 从而网络的节点可以更明显地区分。 但是, 算法需要更多的时间才能集中起来, 所以这个阶段不能任意减少。 由于这些结果, 我们选择了一个具体值, 使这个阶段以后将算法应用到复杂的无比例图中。 在这些网络中, 原始的量子 PageR 能够打破剩余节点的退化性, 并检测出经典算法抑制的第二中心。 然而, 所检测到的第二中心并不是按照 PageRank 的定义是真实的。 一些 RA 计划可以克服这个问题, 恢复剩余节点的脱位, 并且强调真正二级的算法中心点 。 最后, 我们找到了一个我们所知道的原定的原型算法的稳定性, 我们找到了一个新的级算法。 我们找到了一个新的变数的稳定性。