On the Cayley digraphs that are patterns of unitary matrices

Details On the Cayley digraphs that are patterns of unitary matrices On the Cayley digraphs that are patterns of unitary matrices

2002-07-09

arxiv.org/abs/math/0207079v1

Mathematics

Combinatorics

Scientific paper

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.

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