Friday, March 15, 2013

1303.3537 (Mahdi Ebrahimi Kahou et al.)

Quantum search with interacting Bose-Einstein condensates    [PDF]

Mahdi Ebrahimi Kahou, David L. Feder
One approach to the development of quantum search algorithms is the quantum walk. A spatial search can be effected by the continuous-time evolution of a single quantum particle on a lattice or graph containing a marked site. In many physical implementations, however, one might expect to have multiple particles. In interacting bosonic systems at zero temperature, the dynamics is well-described by a discrete nonlinear Schr\"odinger equation. We investigate the role of nonlinearity in determining the efficiency of the spatial search algorithm within the quantum walk model, for the complete graph. The analytical calculations reveal that the nonlinear search time scales as the square root of the size of the search space, equivalent to the linear quantum spatial search though with a different overall constant. The results indicate that Bose-Einstein condensates in optical lattices could be natural systems for the implementation of the quantum search algorithm.
View original: http://arxiv.org/abs/1303.3537

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