Abstract
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.
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Note that we use the order coin-position in \({\left| {j, x}\right\rangle }\), which is called the coin-position notation. There is an alternate order which is position-coin written as \({\left| {x, j}\right\rangle }\), which is called the position-coin notation. The notation’s choice is a matter of taste.
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Portugal, R. (2018). Coined Walks on Infinite Lattices. In: Quantum Walks and Search Algorithms. Quantum Science and Technology. Springer, Cham. https://doi.org/10.1007/978-3-319-97813-0_5
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DOI: https://doi.org/10.1007/978-3-319-97813-0_5
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-97812-3
Online ISBN: 978-3-319-97813-0
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