ALGEBRAIC COMBINATORICS

no. 3
Complex Hadamard matrices, instantaneous uniform mixing and cubes
Chan, Ada1
1 York University Dept. of Mathematics and Statistics 4700 Keele Street Toronto Ontario M3J 1P3, Canada
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:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.112
Classification: 05E03
Keywords: Association schemes, Hamming schemes, complex Hadamard matrix, continuous-time quantum walks, instantaneous uniform mixing, perfect state transfer.
Chan, Ada 1

1 York University Dept. of Mathematics and Statistics 4700 Keele Street Toronto Ontario M3J 1P3, Canada
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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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/articles/10.5802/alco.112/

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