Geodesic
Uniform mixing on Cayley graphs
The electronic journal of combinatorics, Tome 24 (2017) no. 3
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We provide new examples of Cayley graphs on which the quantum walks reach uniform mixing. Our first result is a complete characterization of all $2(d+2)$-regular Cayley graphs over $\mathbb{Z}_3^d$ that admit uniform mixing at time $2\pi/9$. Our second result shows that for every integer $k\ge 3$, we can construct Cayley graphs over $\mathbb{Z}_q^d$ that admit uniform mixing at time $2\pi/q^k$, where $q=3, 4$.We also find the first family of irregular graphs, the Cartesian powers of the star $K_{1,3}$, that admit uniform mixing.
DOI : 10.37236/6855
Classification : 05C25, 05E30, 81P40
Mots-clés : quantum walk, uniform mixing, Cayley graph 
@article{10_37236_6855,
     author = {Chris Godsil and Hanmeng Zhan},
     title = {Uniform mixing on {Cayley} graphs},
     journal = {The electronic journal of combinatorics},
     year = {2017},
     volume = {24},
     number = {3},
     doi = {10.37236/6855},
     zbl = {1369.05104},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/6855/}
}
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Chris Godsil; Hanmeng Zhan. Uniform mixing on Cayley graphs. The electronic journal of combinatorics, Tome 24 (2017) no. 3. doi: 10.37236/6855

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