  We investigate the impact of decoherence and static disorder on the dynamics
of quantum particles moving in a periodic lattice. Our experiment relies on the
photonic implementation of a one-dimensional quantum walk. The pure quantum
evolution is characterized by a ballistic spread of a photon's wave packet
along 28 steps. By applying controlled time-dependent operations we simulate
three different environmental influences on the system, resulting in a fast
ballistic spread, a diffusive classical walk and the first Anderson
localization in a discrete quantum walk architecture.
