Two dimensional quantum repeaters
  The endeavour to develop quantum networks gave rise to a rapidly developing field with far reaching applications such as secure communication and the realisation of distributed computing tasks. This ultimately calls for the creation of flexible multi-user structures that allow for quantum communication between arbitrary pairs of parties in the network and facilitate also multi-user applications. To address this challenge, we propose a 2D quantum repeater architecture to establish long-distance entanglement shared between multiple communication partners in the presence of channel noise and imperfect local control operations. The scheme is based on the creation of self-similar multi-qubit entanglement structures at growing scale, where variants of entanglement swapping and multi-party entanglement purification are combined to create high fidelity entangled states. We show how such networks can be implemented using trapped ions in cavities. 
J. Walln\"ofer, M. Zwerger, C. Muschik, N. Sangouard and W. D\"ur
quant-ph