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Quantum Simulation

Discrete-time quantum walks on Cayley graphs of Dihedral groups using generalized Grover coins

arXiv

Authors: Rohit Sarma Sarkar, Bibhas Adhikari

Year

2023

Paper ID

54411

Status

Preprint

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~2 min

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Abstract

In this paper we study discrete-time quantum walks on Cayley graphs corresponding to Dihedral groups, which are graphs with both directed and undirected edges. We consider the walks with coins that are one-parameter continuous deformation of the Grover matrix and can be written as linear combinations of certain permutation matrices. We show that the walks are periodic only for coins that are permutation or negative of a permutation matrix. Finally, we investigate the localization property of the walks through numerical simulations and observe that the walks localize for a wide range of coins for different sizes of the graphs.

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In this paper we study discrete-time quantum walks on Cayley graphs corresponding to Dihedral groups, which are graphs with both directed and undirected edges.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2309.15194 [2] arXiv https://arxiv.org/abs/2309.15194 [3] Publisher https://arxiv.org/abs/2309.15194

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