On the hitting times of quantum versus random walks
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
One-dimensional discrete-time quantum walks on random environments
Quantum Information Processing
Quantum walk based search algorithms
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Quantum walks: a comprehensive review
Quantum Information Processing
| Hi-index | 0.00 |
We consider a d-dimensional random quantum walk with site-dependent random coin operators. The corresponding transition coefficients are characterized by deterministic amplitudes times independent identically distributed site-dependent random phases. When the deterministic transition amplitudes are close enough to those of a quantum walk which forbids propagation, we prove that dynamical localization holds for almost all random phases. This instance of Anderson localization implies that all quantum mechanical moments of the position operator are uniformly bounded in time and that spectral localization holds, almost surely.