Complex Hadamard Matrices, Instantaneous Uniform Mixing and Cubes

Ada Chan

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arXiv · 1305.5811

Complex Hadamard Matrices, Instantaneous Uniform Mixing and Cubes

Ada Chan

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Abstract

We study the continuous-time quantum walks on graphs in the adjacency algebra of the $n$-cube and its related distance regular graphs. For $k\geq 2$, 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.

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Ada Chan. 2013-05-24. Complex Hadamard Matrices, Instantaneous Uniform Mixing and Cubes. https://arxiv.org/abs/1305.5811

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