  We propose a scheme to implement the one-dimensional coined quantum walk with
electrons transported through a two-dimensional network of spintronic
semiconductor quantum rings. The coin degree of freedom is represented by the
spin of the electron, while the discrete position of the walker corresponds to
the label of the rings in one of the spatial directions in the network. We
assume that Rashba-type spin-orbit interaction is present in the rings, the
strength of which can be tuned by an external electric field. The geometry of
the device, together with the appropriate spin-orbit interaction strengths,
ensure the realization of the coin-toss (i.e. spin-flip) and the step operator.
