  We give new observations on the mixing dynamics of a continuous-time quantum
walk on circulants and their bunkbed extensions. These bunkbeds are defined
through two standard graph operators: the join G + H and the Cartesian product
of graphs G and H.Our results include the following:
  1. The quantum walk is average uniform mixing on circulants with bounded
eigenvalue multiplicity. This extends a known fact about the cycles. 2.
Explicit analysis of the probability distribution of the quantum walk on the
join of circulants. This explains why complete partite graphs are not average
uniform mixing, using the fact the complete n-vertex graph is the join of a
1-vertex graph and the (n-1)-vertex complete graph, and that the complete
m-partite graph, where each partition has size n, is the m-fold join of the
empty n-vertex graph. 3. The quantum walk on the Cartesian product of a
m-vertex path P and a circulant G, is average uniform mixing if G is. This
highlights a difference between circulants and the hypercubes. Our proofs
employ purely elementary arguments based on the spectra of the graphs.
