  We propose a physical implementation of the step operator of the discrete
quantum walk for an electron in a one-dimensional chain of quantum dots. The
operating principle of the step operator is based on locally enhanced Zeeman
splitting and the role of the quantum coin is played by the spin of the
electron. We calculate the probability of successful transfer of the electron
in the presence of decoherence due to quantum charge fluctuations, modeled as a
bosonic bath. We then analyze two mechanisms for creating locally enhanced
Zeeman splitting based on, respectively, locally applied electric and magnetic
fields and slanting magnetic fields. Our results imply that a success
probability of > 90% is feasible under realistic experimental conditions.
