Spatial quantum search in a triangular network
Abstract
The spatial search problem consists in minimizing the number of steps required to find a given site in a network, under the restriction that only oracle queries or translations to neighboring sites are allowed. We propose a quantum algorithm for the spatial search problem on a triangular lattice with N sites and torus-like boundary conditions. The proposed algortithm is a special case of the general framework for abstract search proposed by Ambainis, Kempe and Rivosh [AKR05] (AKR) and Tulsi [Tulsi08], applied to a triangular network. The AKR-Tulsi formalism was employed to show that the time complexity of the quantum search on the triangular lattice is O(sqrt(N logN)).
Keywords
Cite
@article{arxiv.1009.1422,
title = {Spatial quantum search in a triangular network},
author = {G. Abal and R. Donangelo and M. Forets and R. Portugal},
journal= {arXiv preprint arXiv:1009.1422},
year = {2014}
}
Comments
10 pages, 4 Postscript figures, uses sbc-template.sty, appeared in Annals of WECIQ 2010, III Workshop of Quantum Computation and Quantum Information