Graph coloring is a computationally difficult problem, and currently the best known classical algorithm for $k$-coloring of graphs on $n$ vertices has runtimes $\Omega(2^n)$ for $k\ge 5$. The list coloring problem asks the following more general question: given a list of available colors for each vertex in a graph, does it admit a proper coloring? We propose a quantum algorithm based on Grover search to quadratically speed up exhaustive search. Our algorithm loses in complexity to classical ones in specific restricted cases, but improves exhaustive search for cases where the lists and graphs considered are arbitrary in nature.

翻译：图表颜色是一个难以计算的问题, 而目前最知名的以 $n 元为顶点的图表以 $k$为颜色的经典算法已经运行时间 $\ omega (2 ⁇ n)$ $k\ ge 5$。 列表颜色问题提出了以下更一般性的问题: 给图表中每个顶点的可用颜色列表, 它是否承认适当的颜色? 我们提议基于 Grover 搜索的量子算法, 以四面形加速彻底搜索 。 我们的算法在特定限制情况下, 将复杂性丢失到经典的, 但会改进对列表和图表被认为具有任意性的案例的详尽搜索 。