Coined Walks on Infinite Lattices
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The coined quantum walk on the line was introduced in Sect. 3 on p. 25 in order to highlight features that are strikingly different from the classical random walk. In this Chapter, we present in detail the analytic calculation of the state of the quantum walk on the line after an arbitrary number of steps. The calculation is a model for the study of quantum walks on many graphs, and the Fourier transform is the key to the success of this calculation.