  A continuous-time quantum walk is modelled using a graph. In this short
paper, we provide lower bounds on the size of a graph that would allow for some
quantum phenomena to occur. Among other things, we show that, in the adjacency
matrix quantum walk model, the number of edges is bounded below by a cubic
function on the eccentricity of a periodic vertex. This gives some idea on the
shape of a graph that would admit periodicity or perfect state transfer. We
also raise some extremal type of questions in the end that could lead to future
research.
