An infinite family of circulant graphs with perfect state transfer in discrete quantum walks

Abstract

We study perfect state transfer in Kendon’s model of discrete quantum walks. In particular, we give a characterization of perfect state transfer purely in terms of the graph spectra, and construct an infinite family of 4-regular circulant graphs that admit perfect state transfer. Prior to our work, the only known infinite families of examples were variants of cycles and diamond chains.

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Acknowledgements

The author would like to thank Ada Chan, Gabriel Coutinho, Chris Godsil, Krystal Guo, and Christino Tamon for their helpful discussion and generous comments. The author appreciates the time and effort taken by the referees to review this manuscript.

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Correspondence to Hanmeng Zhan.

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Zhan, H. An infinite family of circulant graphs with perfect state transfer in discrete quantum walks. Quantum Inf Process 18, 369 (2019). https://doi.org/10.1007/s11128-019-2483-3

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