We analyze one-dimensional quantum random walks with both Hadamard and arbitrary unitary coin-flip matrices. Using a multivariate generating function analysis we give a simplified proof of a known phenomenon, namely that the walk has linear speed rather than the diffusive behavior observed in classical random walks. We also obtain exact formulae for the leading asymptotic term of the wave function and the location probabilities.
Probability and Combinatorics
Tuesday, March 13, 2007 - 4:00pm
Andrew Bressler
University of Pennsylvania