Quantum Walks on Necklaces and Mixing

Details Quantum Walks on Necklaces and Mixing Quantum Walks on Necklaces and Mixing

2011-11-18

arxiv.org/abs/1111.4433v2

International Journal of Quantum Information, Vol.10, Issue 2, 1250025 (2012)

Physics

Quantum Physics

11 pages, 5 figures, typos corrected, acknowledgements updated

Scientific paper

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.

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