Superdiffusivity of quantum walks: A Feynman sum-over-paths description

Abstract

Quantum walks constitute important tools in different applications, especially in quantum algorithms. To a great extent their usefulness is due to unusual diffusive features, allowing much faster spreading than their classical counterparts. Such behavior, although frequently credited to intrinsic quantum interference, usually is not completely characterized. Using a recently developed Green's function approach [Phys. Rev. A {\bf 84}, 042343 (2011)], here it is described -- in a rather general way -- the problem dynamics in terms of a true sum over paths history a la Feynman. It allows one to explicit identify interference effects and also to explain the emergence of superdiffusivity. The present analysis has the potential to help in designing quantum walks with distinct transport properties.