  A continuous-time quantum random walk describes the motion of a quantum
mechanical particle on an underlying graph. The graph itself is associated with
a Hilbert space of dimension equal to the number of vertices. The dynamics of
the walk is governed by the unitary operator $\mathcal{U}(t) = e^{iAt}$, where
$A$ is the adjacency matrix of the graph. An important notion in the quantum
random walk is the transfer of a quantum state from one vertex to another. If
the fidelity of the transfer is unity, we call it a perfect state transfer.
Many graph families have been shown to admit PST or periodicity, including
cubelike graphs. These graphs are unweighted. In this paper, we generalize the
PST or periodicity of cubelike graphs to that of weighted cubelike graphs. We
characterize the weights for which they admit PST or show periodicity, both at
time $t=\frac{\pi}{2}$.
