Green function approach for scattering quantum walks
arXiv:1112.2614 · doi:10.1103/PhysRevA.84.042343
Abstract
In this work a Green function approach for scattering quantum walks is developed. The exact formula has the form of a sum over paths and always can be cast into a closed analytic expression for arbitrary topologies and position dependent quantum amplitudes. By introducing the step and path operators, it is shown how to extract any information about the system from the Green function. The method relevant features are demonstrated by discussing in details an example, a general diamond-shaped graph.
13 pages, 6 figures, this article was selected by APS for Virtual Journal of Quantum Information, Vol 11, Iss 11 (2011)
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- Unitary equivalence between the Green's function and Schrödinger approaches for quantum graphs
- Unveiling and exemplifying the unitary equivalence of discrete time quantum walk models
- Superdiffusivity of quantum walks: A Feynman sum-over-paths description