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

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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 (real) linear combinations of permutation matrices of order three. 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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Acknowledgements

Rohit Sarma Sarkar acknowledges support through Prime Minister’s Research Fellowship (PMRF), Government of India.

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  1. Bibhas Adhikari

    Present address: Fujitsu Research of America, Inc., Santa Clara, California, USA

Authors and Affiliations

  1. Department of Mathematics, IIT Kharagpur, Kharagpur, India

    Rohit Sarma Sarkar & Bibhas Adhikari

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  1. Rohit Sarma Sarkar
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RSS and BA have conceptualized the problem, and wrote and reviewed the manuscript.

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Correspondence to Bibhas Adhikari.

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Sarkar, R.S., Adhikari, B. Discrete-time quantum walks on Cayley graphs of Dihedral groups using generalized Grover coins. Quantum Inf Process 23, 172 (2024). https://doi.org/10.1007/s11128-024-04385-y

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