6533b81ffe1ef96bd12773b3
RESEARCH PRODUCT
Quantum walks on two-dimensional grids with multiple marked locations
Alexander RivoshNikolajs Nahimovssubject
Discrete mathematicsQuantum PhysicsComputer scienceStructure (category theory)FOS: Physical sciences0102 computer and information sciencesSpace (mathematics)01 natural sciencesRunning time010201 computation theory & mathematicsSearch algorithm0103 physical sciencesComputer Science (miscellaneous)Graph (abstract data type)Quantum walk010306 general physicsQuantum Physics (quant-ph)description
The running time of a quantum walk search algorithm depends on both the structure of the search space (graph) and the configuration (the placement and the number) of marked locations. While the first dependence has been studied in a number of papers, the second dependence remains mostly unstudied.We study search by quantum walks on the two-dimensional grid using the algorithm of Ambainis, Kempe and Rivosh [3]. The original paper analyses one and two marked locations only. We move beyond two marked locations and study the behaviour of the algorithm for several configurations of multiple marked locations.In this paper, we prove two results showing the importance of how the marked locations are arranged. First, we present two placements of [Formula: see text] marked locations for which the number of steps of the algorithm differs by a factor of [Formula: see text]. Second, we present two configurations of [Formula: see text] and [Formula: see text] marked locations having the same number of steps and probability of finding a marked location.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-07-14 |