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