Perfect quantum state transfer with spinor bosons on weighted graphs

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.