Quantum Computation and Information Seminar 

10/09/2004, 15:00 — 16:00 — Room P4.35, Mathematics Building
Pedro Ribeiro, École Polytechnique

Quantum walks with two quantum coins

This work presents quantum walks which are the quantum counterparts of classical random walks. Quantum walks are first defined on general graphs and the possibility of very different behavior between a classical random walk and its quantum analogue is illustrated with a simple graph. A generalization of the quantum walk protocol for a particle in a one-dimensional chain, by using several types of biased quantum coins, is presented. We study the evolution of the system when different types of sequences are applied. Quasiperiodic sequences, following the Fibonacci prescription, are of particular interest, leading to a sub-ballistic wave function spreading. In contrast, random sequences leads to diffusive spreading, similar to the classical random walk behavior. We describe qualitatively how to experimentally implement these processes.