par Krovi, Hari;Magniez, Frédéric;Ozols, Maris;Roland, Jérémie 
Référence 37th International Colloquium on Automata, Languages and Programming (ICALP'10), Springer, Vol. 6198, page (540-551)
Publication Publié, 2010
Référence 37th International Colloquium on Automata, Languages and Programming (ICALP'10), Springer, Vol. 6198, page (540-551)
Publication Publié, 2010
Publication dans des actes
| Résumé : | We solve an open problem by constructing quantum walks that not only detect but also find marked vertices in a graph. The number of steps of the quantum walk is quadratically smaller than the classical hitting time of any reversible random walk P on the graph. Our approach is new, simpler and more general than previous ones. We introduce a notion of interpolation between the walk P and the absorbing walk Pâ², whose marked states are absorbing. Then our quantum walk is simply the quantum analogue of the interpolation. Contrary to previous approaches, our results remain valid when the random walk P is not state-transitive, and in the presence of multiple marked vertices. As a consequence we make a progress on an open problem related to the spatial search on the 2D-grid. |
