ALGEBRAIC COMBINATORICS

no. 3

Complex Hadamard matrices, instantaneous uniform mixing and cubes
Algebraic Combinatorics, Volume 3 (2020) no. 3, pp. 757-774.

We study the continuous-time quantum walks on graphs in the adjacency algebra of the n-cube and its related distance regular graphs.

For k≥2, we find graphs in the adjacency algebra of (2 k+2 -8)-cube that admit instantaneous uniform mixing at time π/2 k and graphs that have perfect state transfer at time π/2 k .

We characterize the folded n-cubes, the halved n-cubes and the folded halved n-cubes whose adjacency algebra contains a complex Hadamard matrix. We obtain the same conditions for the characterization of these graphs admitting instantaneous uniform mixing.

Received: 2019-06-22
Revised: 2020-02-09
Accepted: 2020-02-09
Published online: 2020-06-02
DOI: https://doi.org/10.5802/alco.112
Classification: 05E03
Keywords: Association schemes, Hamming schemes, complex Hadamard matrix, continuous-time quantum walks, instantaneous uniform mixing, perfect state transfer. 
@article{ALCO_2020__3_3_757_0,
     author = {Chan, Ada},
     title = {Complex Hadamard matrices, instantaneous uniform mixing and cubes},
     journal = {Algebraic Combinatorics},
     pages = {757--774},
     publisher = {MathOA foundation},
     volume = {3},
     number = {3},
     year = {2020},
     doi = {10.5802/alco.112},
     language = {en},
     url = {alco.centre-mersenne.org/item/ALCO_2020__3_3_757_0/}
}
Chan, Ada. Complex Hadamard matrices, instantaneous uniform mixing and cubes. Algebraic Combinatorics, Volume 3 (2020) no. 3, pp. 757-774. doi : 10.5802/alco.112. https://alco.centre-mersenne.org/item/ALCO_2020__3_3_757_0/

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