Propagating Quantum Walks: the origin of interference structures
arXiv:quant-ph/0312133 · doi:10.1080/09500340408232489
Abstract
We analyze the solution of the coined quantum walk on a line. First, we derive the full solution, for arbitrary unitary transformations, by using a new approach based on the four "walk fields" which we show determine the dynamics. The particular way of deriving the solution allows a rigorous derivation of a long wavelength approximation. This long wavelength approximation is useful as it provides an approximate analytical expression that captures the basics of the quantum walk and allows us to gain insight into the physics of the process.
17 pages, 3 figures. Submitted to Journal of Modern Optics
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- Classical Simulation of Quantum Adiabatic Algorithms using Mathematica on GPUs