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arXiv · 1401.1745

Perfect state transfer on distance-regular graphs and association schemes

Gabriel Coutinho·Chris Godsil·Krystal Guo·Frédéric Vanhove
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Abstract

We consider the representation of a continuous-time quantum walk in a graph $X$ by the matrix $\exp(itA(X))$. We provide necessary and sufficient criteria for distance-regular graphs and, more generally, for graphs in association schemes to have perfect state transfer. Using these conditions, we provide several new examples of perfect state transfer in simple graphs.

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Gabriel Coutinho, Chris Godsil, Krystal Guo, Frédéric Vanhove. 2014-01-08. Perfect state transfer on distance-regular graphs and association schemes. https://doi.org/10.1016/j.laa.2015.03.024

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