Severini, S; (2002) On the Cayley digraphs that are patterns of unitary matrices.

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## Abstract

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.

Type: | Article |
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Title: | On the Cayley digraphs that are patterns of unitary matrices |

Keywords: | math.CO, math.CO, quant-ph |

UCL classification: | UCL > School of BEAMS > Faculty of Engineering Science > Computer Science |

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