On the Cayley digraphs that are patterns of unitary matrices

Severini Simone

Research output: Working paperWorking paper and Preprints

Abstract

This is a short note on some properties of a family of Cayley digraphs. 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, I prove that if a Cayley digraph is a line digraph then it is the pattern of a unitary matrix. I 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. Investigating this subject might be useful in the perspective of design quantum algorithms for groups (e.g. for hidden subgroup problems, et simil.).
Translated title of the contributionOn the Cayley digraphs that are patterns of unitary matrices
Original languageEnglish
PublisherUniversity of Bristol
Publication statusPublished - 2003

Bibliographical note

Other page information: -4
Other identifier: 1000699

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