COMMUNICATION IN XYZ ALL-TO-ALL QUANTUM NETWORKS WITH A MISSING LINK

We explicitate the relation between Hamiltonians for networks of interacting qubits in the XYZ model and graph Laplacians. We then study evolution in networks in which all sites can communicate with each other. These are modeled by the complete graph K-n and called all-to-all networks. It turns out that K-n does not exhibit perfect state transfer (PST). However, we prove that deleting an edge in K-n allows PST between the two non-adjacent sites, when n is a multiple of four. An application is routing a qubit over n different sites, by switching off the link between the sites that we wish to put in communication. Additionally, we observe that, in certain cases, the unitary inducing evolution in K-n is equivalent to the Grover operator.