Quantum walk search on Johnson graphs
Abstract
The Johnson graph J(n,k) is defined by n symbols, where vertices are kelement subsets of the symbols, and vertices are adjacent if they differ in exactly one symbol. In particular, J(n,1) is the complete graph K _{ n }, and J(n,2) is the strongly regular triangular graph T _{ n }, both of which are known to support fast spatial search by continuoustime quantum walk. In this paper, we prove that J(n,3), which is the ntetrahedral graph, also supports fast search. In the process, we show that a change of basis is needed for degenerate perturbation theory to accurately describe the dynamics. This method can also be applied to general Johnson graphs J(n,k) with fixed k.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 May 2016
 DOI:
 10.1088/17518113/49/19/195303
 arXiv:
 arXiv:1601.04212
 Bibcode:
 2016JPhA...49s5303W
 Keywords:

 Quantum Physics
 EPrint:
 17 pages, 9 figures