The tessellation problem of quantum walks [article]

A. Abreu, L. Cunha, T. Fernandes, C. de Figueiredo, L. Kowada, F. Marquezino, D. Posner, R. Portugal
2017 arXiv   pre-print
Quantum walks have received a great deal of attention recently because they can be used to develop new quantum algorithms and to simulate interesting quantum systems. In this work, we focus on a model called staggered quantum walk, which employs advanced ideas of graph theory and has the advantage of including the most important instances of other discrete-time models. The evolution operator of the staggered model is obtained from a tessellation cover, which is defined in terms of a set of
more » ... tions of the graph into cliques. It is important to establish the minimum number of tessellations required in a tessellation cover, and what classes of graphs admit a small number of tessellations. We describe two main results: (1) infinite classes of graphs where we relate the chromatic number of the clique graph to the minimum number of tessellations required in a tessellation cover, and (2) the problem of deciding whether a graph is k-tessellable for k> 3 is NP-complete.
arXiv:1705.09014v1 fatcat:xc2wbsnm2jghrhacxzax3qgn4a