## Abstract

We propose new families of graphs which exhibit quantum perfect state transfer. Our constructions are based on the join operator on graphs, its circulant generalizations, and the Cartesian product of graphs. We build upon the results of Bašić and Petković (Applied Mathematics Letters 22(10):1609-1615, 2009) and construct new integral circulants and regular graphs with perfect state transfer. More specifically, we show that the integral circulant ICGn({2, n/2b} ∪ Q) has perfect state transfer, where b ∈ {1, 2}, n is a multiple of 16 and Q is a subset of the odd divisors of n. Using the standard join of graphs, we also show a family of double-cone graphs which are non-periodic but exhibit perfect state transfer. This class of graphs is constructed by simply taking the join of the empty two-vertex graph with a specific class of regular graphs. This answers a question posed by Godsil (arxiv. org math/08062074).

Original language | English (US) |
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Pages (from-to) | 325-342 |

Number of pages | 18 |

Journal | Quantum Information and Computation |

Volume | 10 |

Issue number | 3-4 |

State | Published - Mar 1 2010 |

## Keywords

- Integral circulants
- Join of graphs
- Perfect state transfer
- Quantum walks

## ASJC Scopus subject areas

- Theoretical Computer Science
- Statistical and Nonlinear Physics
- Nuclear and High Energy Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Computational Theory and Mathematics