  A duality between the properties of many spinor bosons on a regular lattice
and those of a single particle on a weighted graph reveals that a quantum
particle can traverse an infinite hierarchy of networks with perfect
probability in polynomial time, even as the number of nodes increases
exponentially. The one-dimensional `quantum wire' and the hypercube are special
cases in this construction, where the number of spin degrees of freedom is
equal to one and the number of particles, respectively. An implementation of
near-perfect quantum state transfer across a weighted parallelepiped with
ultracold atoms in optical lattices is discussed.
