Quantum random walks in one dimension via generating functions
Andrew Bressler, Robin Pemantle · Discrete Mathematics & Theoretical Computer Science · 2007
We analyze nearest neighbor one-dimensional quantum random walks with 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.