We introduce quantum walks on Cayley graphs of non-Abelian groups. We focus
on the easiest case of virtually Abelian groups, and introduce a technique to
reduce the quantum walk to an equivalent one on an Abelian group with coin
system having larger dimension. We apply the technique in the case of two
quantum walks on virtually Abelian groups with planar Cayley graphs, finding
the exact solution.Comment: 10 pages, 3 figure
