We study the continuous-time quantum walks on graphs in the adjacency algebra of the -cube and its related distance regular graphs.
For , we find graphs in the adjacency algebra of -cube that admit instantaneous uniform mixing at time and graphs that have perfect state transfer at time .
We characterize the folded -cubes, the halved -cubes and the folded halved -cubes whose adjacency algebra contains a complex Hadamard matrix. We obtain the same conditions for the characterization of these graphs admitting instantaneous uniform mixing.
Revised: 2020-02-09
Accepted: 2020-02-09
Published online: 2020-06-02
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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