Aperiodic quantum random walks.
We generalize the quantum random walk protocol for a particle in a one-dimensional chain, by using several types of biased quantum coins, arranged in aperiodic sequences, in a manner that leads to a rich variety of possible wave-function evolutions. Quasiperiodic sequences, following the Fibonacci prescription, are of particular interest, leading to a sub-ballistic wave-function spreading. In contrast, random sequences lead to diffusive spreading, similar to the classical random walk behavior. We also describe how to experimentally implement these aperiodic sequences.
Ribeiro
P
P
Groupe de Physique des Solides, Universités Paris 6 et 7, campus Boucicaut, 140 rue de Lourmel, 75015 Paris France. pedro.ribeiro@polytechnique.fr
Milman
P
P
Mosseri
R
R