Perfect state transfer on distance-regular graphs and association   schemes
  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. 
Gabriel Coutinho, Chris Godsil, Krystal Guo, and Fr\'ed\'eric Vanhove
math.CO quant-ph