Perfect state transfer, integral circulants and join of graphs

Details Perfect state transfer, integral circulants and join of graphs Perfect state transfer, integral circulants and join of graphs

2009-07-13

arxiv.org/abs/0907.2148v4

Quantum Information and Computation 10(3&4):325-342, 2010.

Physics

Quantum Physics

17 pages, 4 figures; added text and one missing citation; attempted to patch TeX->PDF problems

Scientific paper

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 Ba\v{s}i\'{c} et al \cite{bps09,bp09} and construct new integral circulants and regular graphs with perfect state transfer. More specifically, we show that the integral circulant $\textsc{ICG}_{n}(\{2,n/2^{b}\} \cup Q)$ has perfect state transfer, where $b \in \{1,2\}$, $n$ 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 \cite{godsil08}.

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