  We study the routing of quantum information in parallel on multi-dimensional
networks of tunable qubits and oscillators. These theoretical models are
inspired by recent experiments in superconducting circuits using Josephson
junctions and resonators. We show that perfect parallel state transfer is
possible for certain networks of harmonic oscillator modes. We further extend
this to the distribution of entanglement between every pair of nodes in the
network, finding that the routing efficiency of hypercube networks is both
optimal and robust in the presence of dissipation and finite bandwidth.
