Spatial search via non-linear quantum walk
Date
2013-02-04
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Abstract
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 most conceivable physical applications, however, one would rather expect to have multiple interacting particles. In bosonic systems at zero temperature, the dynamics would be well-described by a discrete non-linear Schrodinger equation. In this thesis we investigate the role of non-linearity in determining the efficiency of the spatial search algorithm within the quantum walk model, for the complete graph. Our analytical results indicate that the search time for this non-linear quantum search scales with size of the database N like square root of N, equivalent to linear spatial search time. The analytical results will be compared with numerical calculations of multiple interacting quantum walkers.
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Condensed Matter
Citation
Ebrahimi Kahou, M. (2013). Spatial search via non-linear quantum walk (Master's thesis, University of Calgary, Calgary, Canada). Retrieved from https://prism.ucalgary.ca. doi:10.11575/PRISM/27845