论文标题
通过连续时量子搜索在重新归一化的互联网网络上进行空间搜索
Spatial search by continuous-time quantum walks on renormalized Internet networks
论文作者
论文摘要
我们在现实世界中的复杂网络上使用连续的时间量子步行研究空间搜索。我们使用较小的Internet网络复制品，该互联网通过García-Pérez等人Nat引入的最新几何重新规范化方法获得。物理。 14，583（2018）。这使我们能够在现实世界中复杂网络上首次推断出量子空间搜索算法的行为。通过数字模拟动力学并优化耦合参数，我们研究算法的最佳性及其与网络大小的比例，表明它平均比经典的缩放$ \ Mathcal {O} {O}（O}（o}（n）$），但它没有达到理想的Quadratic Quapup $ $ \ Mathcal $ he}（sqr}（sqr}（\ sqr}）实现了，例如在完整的图中。但是，搜索算法的性能在很大程度上取决于节点的程度，实际上，当我们考虑根据该程度下订购的$ 99 $ th the百分点的节点时，发现比例非常接近最佳。
We study spatial search with continuous-time quantum walks on real-world complex networks. We use smaller replicas of the Internet network obtained with a recent geometric renormalization method introduced by García-Pérez et al., Nat. Phys. 14, 583 (2018). This allows us to infer for the first time the behavior of a quantum spatial search algorithm on a real-world complex network. By simulating numerically the dynamics and optimizing the coupling parameter, we study the optimality of the algorithm and its scaling with the size of the network, showing that on average it is considerably better than the classical scaling $\mathcal{O}(N)$, but it does not reach the ideal quadratic speedup $\mathcal{O}(\sqrt{N})$ that can be achieved, e.g. in complete graphs. However, the performance of the search algorithm strongly depends on the degree of the nodes and, in fact, the scaling is found to be very close to optimal when we consider the nodes below the $99$th percentile ordered according to the degree.
