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We examine the prospects of discrete quantum walks (QWs) with trapped ions.In particular, we analyze in detail the limitations of the protocol ofTravaglione and Milburn (PRA 2002) that has been implemented by severalexperimental groups in recent years. Based on the first realization in ourgroup (PRL 2009), we investigate the consequences of leaving the scope of theapproximations originally made, such as the Lamb--Dicke approximation. Weexplain the consequential deviations from the idealized QW for differentexperimental realizations and an increasing number of steps by taking intoaccount higher-order terms of the quantum evolution. It turns out that thesebecome dominant after a few steps already, which is confirmed by experimentalresults and is currently limiting the scalability of this approach. Finally, wepropose a new scheme using short laser pulses, derived from a protocol from thefield of quantum computation. We show that the new scheme is not subject to theabove-mentioned restrictions, and analytically and numerically evaluate itslimitations, based on a realistic implementation with our specific setup.Implementing the protocol with state-of-the-art techniques should allow forsubstantially increasing the number of steps to 100 and beyond and should beextendable to higher-dimensional QWs.

Experimental simulation and limitations of quantum walks with trapped ions