A digraph D is the pattern of a matrix M when D has an arc ij if and only if
the ij-th entry of M is nonzero. Study the relationship between unitary
matrices and their patterns is motivated by works in quantum chaology and
quantum computation. In this note, we prove that if a Cayley digraph is a line
digraph then it is the pattern of a unitary matrix. We prove that for any
finite group with two generators there exists a set of generators such that the
Cayley digraph with respect to such a set is a line digraph and hence the
pattern of a unitary matrix
