par Cerf, Nicolas 
;Grover, Lov L.K.;Williams, Colin C.P.
Référence Physical review. A, Atomic, Molecular, and Optical Physics, 61, 3, 032303
Publication Publié, 2000
;Grover, Lov L.K.;Williams, Colin C.P.Référence Physical review. A, Atomic, Molecular, and Optical Physics, 61, 3, 032303
Publication Publié, 2000
Article révisé par les pairs
| Résumé : | A quantum algorithm is known that solves an unstructured search problem in a number of iterations of order [Formula Presented] where d is the dimension of the search space, whereas any classical algorithm necessarily scales as [Formula Presented] It is shown here that an improved quantum search algorithm can be devised that exploits the structure of a tree search problem by nesting one quantum search within another. The average number of iterations required to find the solution of a typical hard instance of a constraint satisfaction problem is found to scale as [Formula Presented] with the constant [Formula Presented] depending on the nesting depth and the type of problem considered. This corresponds to a square-root speedup over a classical nested search algorithm, of which our algorithm is the quantum counterpart. When applying a single nesting level to a problem with constraints of size 2 such as the graph coloring problem, [Formula Presented] is estimated to be around 0.62. © 2000 The American Physical Society. |
