We show that a multi-step quantum walk can be realized for a single trapped ion with interpolation between quantum and random walk achieved by randomizing the generalized Hadamard coin flip phase. The signature of the quantum walk is manifested not only in the ion's position but also its phonon number, which makes an ion trap implementation of the quantum walk feasible.
@article{arxiv.0904.1451,
title = {Quantum walk on a line for a trapped ion},
author = {Peng Xue and Barry C. Sanders and Dietrich Leibfried},
journal= {arXiv preprint arXiv:0904.1451},
year = {2009}
}