Quantum Walks on Necklaces and Mixing
Quantum Physics
2012-04-16 v2
Abstract
We analyze continuous-time quantum walks on necklace graphs - cyclical graphs consisting of many copies of a smaller graph (pearl). Using a Bloch-type ansatz for the eigenfunctions, we block-diagonalize the Hamiltonian, reducing the effective size of the problem to the size of a single pearl. We then present a general approach for showing that the mixing time scales (with growing size of the necklace) similarly to that of a simple walk on a cycle. Finally, we present results for mixing on several necklace graphs.
Keywords
Cite
@article{arxiv.1111.4433,
title = {Quantum Walks on Necklaces and Mixing},
author = {Maria Kieferova and Daniel Nagaj},
journal= {arXiv preprint arXiv:1111.4433},
year = {2012}
}
Comments
11 pages, 5 figures, typos corrected, acknowledgements updated