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Quantum walks on Sierpinski gasket and Sierpinski tetrahedron

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Abstract

We investigate discrete-time coined quantum walks on the Sierpinski gasket and the Sierpinski tetrahedron which have non-integer dimensions, by concentrating on the probability distribution, return probability and standard deviation. We compare the calculating results with classical random walks on the two fractal structures and quantum walks on the corresponding regular triangle grids. For the quantum walks, we adopt DFT coin and Grover coin, respectively, which exhibit great differences on the above quantities.

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Authors and Affiliations

  1. College of Physics, Jilin University, Changchun, 130012, China

    Hui-Hui Xie & Guo-Mo Zeng

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  1. Hui-Hui Xie
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Correspondence to Guo-Mo Zeng.

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Xie, HH., Zeng, GM. Quantum walks on Sierpinski gasket and Sierpinski tetrahedron. Quantum Inf Process 20, 240 (2021). https://doi.org/10.1007/s11128-021-03171-4

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