The continuous-time quantum walk (CTQW) provides a new approach to problems in graph theory. In this paper, the correlation between the CTQW and cliques in graphs is studied, and an approximate algorithm for the maximum clique problem (MCP) based on the CTQW is given. Via both numerical and theoretical analyses, it is found that the maximum clique is related to the transmission characteristics of the CTQW on some special graphs. For general graphs, the correlation is difficult to describe analytically. Therefore, the transmission characteristics of the CTQW are applied as a vertex selection criterion to a classical MCP algorithm and it is compared with the original algorithm. Numerous simulation on general graphs shows that the new algorithm is more efficient. Furthermore, an approximate MCP algorithm based on the CTQW is introduced, which only requires a very small number of searches with a high approximation ratio.

中文翻译：

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图中连续时间量子游走与团的相关性及其应用

连续时间量子游走 (CTQW) 为图论中的问题提供了一种新方法。本文研究了CTQW与图中团的相关性，给出了一种基于CTQW的最大团问题(MCP)的近似算法。通过数值和理论分析，在一些特殊的图表上发现最大团与CTQW的传输特性有关。对于一般图形，相关性很难分析描述。因此，将CTQW的传输特性作为顶点选择标准应用于经典MCP算法，并与原算法进行比较。对一般图的大量模拟表明，新算法更有效。此外，还介绍了一种基于 CTQW 的近似 MCP 算法，