We present a study of the effects of decoherence in the operation of a discrete quantum walk on a line, cycle, and hypercube. We find high sensitivity to decoherence, increasing with the number of steps in the walk, as the particle is becoming more delocalized with each step. However, the effect of a small amount of decoherence is to enhance the properties of the quantum walk that are desirable for the development of quantum algorithms. Specifically, we observe a highly uniform distribution on the line, a very fast mixing time on the cycle, and more reliable hitting times across the hypercube.

• Received 11 September 2002

DOI:https://doi.org/10.1103/PhysRevA.67.042315