Optimizing quantum-repeater placement in a 2D plane

When designing a quantum-repeater network that services a set of end nodes, it needs to be decided how many repeaters are installed and at which locations they are placed. While often the locations where quantum hardware could be installed may be limited by existing infrastructure, we here consider an unconstrained scenario where repeaters can be placed anywhere in a two-dimensional plane, as may be appropriate for, e.g., free-space quantum communication and quantum-sensor networks. Additionally, understanding network design in the unconstrained case can provide a point of reference for network design in the constrained case. We study the optimal placement of repeaters and the dependence of network performance on the number of repeaters in the network. In particular, we investigate how the optimal repeater locations depend on what type of network metric is optimized, the protocols executed by the repeaters, and how good the quantum hardware is. We use the obtained insights to formulate heuristics for the design of quantum networks.