  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.
