Abstract
We examine the prospects of discrete quantum walks (QWs) with trapped ions. In particular, we analyze in detail the limitations of the protocol of Travaglione and Milburn (2002 Phys. Rev. A 65 032310) that has been implemented by several experimental groups in recent years. Based on the first realization in our group (Schmitz et al 2009 Phys. Rev. Lett.103 090504), we investigate the consequences of leaving the scope of the approximations originally made, such as the Lamb–Dicke approximation. We explain the consequential deviations from the idealized QW for different experimental realizations and an increasing number of steps by taking into account higher-order terms of the quantum evolution. It turns out that these already become significant after a few steps, which is confirmed by experimental results and is currently limiting the scalability of this approach. Finally, we propose a new scheme using short laser pulses, derived from a protocol from the field of quantum computation. We show that this scheme is not subject to the above-mentioned restrictions and analytically and numerically evaluate its limitations, based on a realistic implementation with our specific setup. Implementing the protocol with state-of-the-art techniques should allow for substantially increasing the number of steps to 100 and beyond and should be extendable to higher-dimensional QWs.
Highlights
We examine the prospects of discrete quantum walks (QWs) with trapped ions
QWs can be interpreted as the one-particle sector of a quantum cellular automaton, which is a fundamental model of a quantum computer [6]
It has been shown that QWs themselves are suitable for universal quantum computation [7] and different aspects of quantum information processing [8,9,10]
Summary
We give a theoretical description of the discrete QW on a line as it is realized in our proof-of-principle experiment for the first three steps. Only if the step size | α| is large enough such that the overlap between different position states remains negligible, the above probability is given by the coefficients cLH and cTL only. In our experiment we set the step size to | α| ≈ 1 In this case, the overlaps between the position states amount to |. The probabilities of finding the walker in the coin state |H or |T after three steps are given by PH (ψ3) = ψ3|(|H H | ⊗ 1)|ψ3 and PT (ψ3) = ψ3|(|T T | ⊗ 1)|ψ3.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have