Quantum random walk on the integer lattice: examples and phenomena (2009)
Bressler, Andrew, Greenwood, Torin, Pemantle, Robin, Petkovsek, Marko
We apply results from Baryshnikov, Brady, Bressler and Pemantle (2008) to compute limiting probability profiles for various quantum random walks in one and two dimensions. Using analytic machinery we...
Two-dimensional quantum random walk (2008)
Baryshnikov, Yuliy, Brady, Wil, Bressler, Andrew, Pemantle, Robin
We analyze several families of two-dimensional quantum random walks. The feasible region (the region where probabilities do not decay exponentially with time) grows linearly with time, as is the case...
Quantum random walks in one dimension via generating functions (2007)
Andrew Bressler, Robin Pemantle
We analyze nearest neighbor one-dimensional quantum random walks with arbitary unitary coin-flip matrices. Using a multivariate generating function analysis we give a simplified proof of a known...