Perfect chiral quantum routing

Routing classical and quantum information is a fundamental task for quantum information technologies and processes. Here, we consider information encoded in the position of a quantum walker on a graph, and we design an optimal structure to achieve perfect quantum routing, exploiting chirality and weighting of the edges. The topology, termed the lily graph, enables perfect (i.e., with fidelity one) and robust routing of classical (localized) or quantum (superposition) states of the walker to $n$ different, orthogonal, spatial regions of the graph, corresponding to the $n$ possible outputs of the device. The routing time is independent of the input signal and the number of outputs, making our scheme a robust and scalable solution for all quantum networks.