Superdiffusivity of quantum walks: A Feynman sum-over-paths description
Fabiano M. Andrade, M. G. E. da Luz · Physical Review A · 2012
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 84, 042343 (2011)], we describe here---in a rather general way---the problem dynamics in terms of a true Feynman sum-over-paths history. This allows one to explicitly 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.