Counterintuitive role of geometry in transport by quantum walks

Quantum walks are accepted as a generic model for quantum transport. The character of the transport crucially depends on the properties of the walk like its geometry and the driving coin. We demonstrate that increasing transport distance between source and target or adding redundant branches to the actual graph may surprisingly result in a significant enhancement of transport efficiency. We explain analytically the observed nonclassical effects using the concept of trapped states for several intriguing geometries, including the ladder graph, the Cayley tree, and its modifications.