Discrete-Time Quantum Walks on Oriented Graphs

Bruno Chagas
(Universidade Federal de Minas Gerais)
Renato Portugal
(National Laboratory of Scientific Computing - LNCC)

The interest in quantum walks has been steadily increasing during the last two decades. It is still worth to present new forms of quantum walks that might find practical applications and new physical behaviors. In this work, we define discrete-time quantum walks on arbitrary oriented graphs by partitioning a graph into tessellations, which is a collection of disjoint cliques that cover the vertex set. By using the adjacency matrices associated with the tessellations, we define local unitary operators, whose product is the evolution operator of our quantum walk model. We introduce a parameter, called alpha, that quantifies the amount of orientation. We show that the parameter alpha can be tuned in order to increase the amount of quantum walk-based transport on oriented graphs.

In Giuseppe Di Molfetta, Vivien Kendon and Yutaka Shikano: Proceedings 9th International Conference on Quantum Simulation and Quantum Walks (QSQW 2020), Marseille, France, 20-24/01/2020, Electronic Proceedings in Theoretical Computer Science 315, pp. 26–37.
Published: 3rd April 2020.

ArXived at: http://dx.doi.org/10.4204/EPTCS.315.3 bibtex PDF
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