Spatial search in a honeycomb network

Details Spatial search in a honeycomb network Spatial search in a honeycomb network

2010-01-07

arxiv.org/abs/1001.1139v3

Physics

Quantum Physics

10 pages, 2 figures; Minor typos corrected, one Reference added. accepted in Math. Structures in Computer Science, special vol

Scientific paper

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. In this paper, a quantum algorithm for the spatial search problem on a honeycomb lattice with $N$ sites and torus-like boundary conditions. The search algorithm is based on a modified quantum walk on a hexagonal lattice and the general framework proposed by Ambainis, Kempe and Rivosh is used to show that the time complexity of this quantum search algorithm is $O(\sqrt{N \log N})$.

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