2002/07/09 by Simone Severini, Severini, Simone
Computer Science · Mathematics · Physics and Astronomy · #Cellular Automata and Applications #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Graph theory and applications #Matrix Theory and Algorithms #Quantum Physics (quant-ph) #math.CO #quant-ph
paper · pdf · doi:10.48550/arxiv.math/0207079
arxiv created 2002/07/09 · openalex publication_date 2002/07/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.