Quantum Walks on Trees with Disorder: Decay, Diffusion, and Localization
  Quantum walks have been shown to have impressive transport properties compared to classical random walks. However, imperfections in the quantum walk algorithm can destroy any quantum mechanical speed-up due to Anderson localization. We numerically study the effect of static disorder on a quantum walk on the glued trees graph. For small disorder, we find that the dominant effect is a type of quantum decay, and not quantum localization. For intermediate disorder, there is a crossover to diffusive transport, while a localization transition is observed at large disorder, in agreement with Anderson localization on the Cayley tree. 
Steven R. Jackson, Teng Jian Khoo, and Frederick W. Strauch
quant-ph