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 speedup 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.

• Received 21 June 2012

DOI:https://doi.org/10.1103/PhysRevA.86.022335