We study the implementation of quantum random walks (QRWs) in a realistic system, an optical lattice of ultracold Rydberg atoms. The power-law nature of the dipolar interaction between Rydberg atoms influences the behaviour of QRWs. We discuss the QRW with a short-range nearest-neighbour interaction for two types of power-law interactions, the dipole–dipole and the van der Waals interaction. A specific scheme to implement a QRW using Rydberg atoms in different sites of an optical lattice is described, in which the sites are prepared using a blockade mechanism to ensure a single Rydberg atom per site.
Ultracold Rydberg-atom arrays are an emerging platform for quantum simulation and computing. However, decoherence in these systems remains incompletely understood. Recent experiments [Guardado-Sanchez et al., Phys. Rev. X 8, 021069 (2018)] observed strong decoherence in the quench and longitudinal-field-sweep dynamics of two-dimensional Ising models realized with
6Li Rydberg atoms in optical lattices. This decoherence was conjectured to arise from the effective spin
21 formed by the ground and Rydberg electronic states coupling to atom motion and therefore inducing an effective interaction noise. Here we show that this spin-motion coupling indeed leads to decoherence in qualitative, and often quantitative, agreement with the experimental data, by treating the difficult spin-motion-coupled problem using the discrete truncated Wigner approximation method. We also show that this decoherence will be an important factor to account for in future experiments with Rydberg atoms in optical lattices and microtrap arrays and discuss methods to mitigate the effect of motion, such as using heavier atoms or deeper traps.