Continuous-time quantum-walk spatial search on the Bollobás scale-free network
Continuous-time quantum-walk spatial search on the Bollobás scale-free network
复制标题
Bollobás 无标度网络上的连续时间量子行走空间搜索
作者：
Tomo Osada;B. Coutinho;Y. Omar;K. Sanaka;W. Munro;K. Nemoto
无标度特性出现在各种现实世界的网络中，是表征这种网络的动态或特征的基本特性。在这项工作中，我们研究了这种无标度特性对量子信息处理任务的影响，即在网络中找到一个标记节点，即量子空间搜索。利用Bollob'as网络上的连续时间量子行走分析了量子空间搜索算法，并计算了从无偏初始状态开始在标记节点上定位量子行走的时间$T$。我们的主要发现是，$T$是由被标记节点周围的全局结构决定的，而被标记节点的一些局部信息，如度，并不能识别$T$。我们通过检查$T$和网络的一些中心性度量之间的相关性来讨论这个问题，并且我们表明标记节点的密切中心性与$T$高度相关。我们还通过标记网络中的不同节点来表征$T$的分布，它显示了多模对数正态分布。特别是在Bollob'as网络上，根据标记节点是否与最大度轮毂节点相邻，$T$要短几个数量级。然而，由于$T$依赖于被标记节点的属性，为了确定测量量子步行者的最佳时间并实现快速搜索，人们需要对被标记节点的这种属性有一定的先验知识。这些结果表明，无标度网络中枢纽节点的存在对量子空间搜索起着至关重要的作用。
The scale-free property emerges in various real-world networks and is an essential property that characterizes the dynamics or features of such networks. In this work, we investigate the effect of this scale-free property on a quantum information processing task of finding a marked node in the network, known as the quantum spatial search. We analyze the quantum spatial search algorithm using a continuous-time quantum walk on the Bollob'as network, and we evaluate the time $T$ to localize the quantum walker on the marked node starting from an unbiased initial state. Our main finding is that $T$ is determined by the global structure around the marked node, while some local information of the marked node, such as the degree, does not identify $T$. We discuss this by examining the correlation between $T$ and some centrality measures of the network, and we show that the closeness centrality of the marked node is highly correlated with $T$. We also characterize the distribution of $T$ by marking different nodes in the network, which displays a multimode log-normal distribution. Especially on the Bollob'as network, $T$ is a few orders of magnitude shorter depending on whether the marked node is adjacent to the largest degree hub node. However, as $T$ depends on the property of the marked node, one requires some amount of prior knowledge about such a property of the marked node in order to identify the optimal time to measure the quantum walker and achieve a fast search. These results indicate that the existence of the hub node in the scale-free network plays a crucial role in the quantum spatial search.
影响因子：
7.6
作者：
M. Pant;H. Krovi;D. Towsley;L. Tassiulas;Liang Jiang;P. Basu;D. Englund;S. Guha
通讯作者：
M. Pant;H. Krovi;D. Towsley;L. Tassiulas;Liang Jiang;P. Basu;D. Englund;S. Guha
影响因子：
13.6
作者：
Schlipf L;Oeckinghaus T;Xu K;Dasari DBR;Zappe A;de Oliveira FF;Kern B;Azarkh M;Drescher M;Ternes M;Kern K;Wrachtrup J;Finkler A
通讯作者：
Finkler A