Universally optimal noisy quantum walks on complex networks

Transport properties play a crucial role in several fields of science, for example biology, chemistry, sociology, information science and physics. The behavior of many dynamical processes running over complex networks is known to be closely related to the geometry of the underlying topology, but this connection becomes even harder to understand when quantum effects come into play. Here, we exploit the Kossakowski-Lindblad formalism of quantum stochastic walks to investigate the capability of quickly and robustly transmitting energy (or information) between two distant points in very large complex structures, remarkably assisted by external noise and quantum features such as coherence. An optimal mixing of classical and quantum transport is, very surprisingly, quite universal for a large class of complex networks. This widespread behavior turns out to be also extremely robust with respect to geometry changes. These results might pave the way for designing optimal bio-inspired geometries of efficient transport nanostructures that can be used for solar energy and also quantum information and communication technologies.