# ALGEBRAIC COMBINATORICS

Continuous-time Quantum Walks on Cayley Graphs of Extraspecial Groups
Algebraic Combinatorics, Volume 5 (2022) no. 4, pp. 699-714.

We study continuous-time quantum walks on normal Cayley graphs of certain non-abelian groups called extraspecial groups. By applying general results for graphs in association schemes we determine the precise conditions for perfect state transfer and fractional revival. Using partial spreads, we construct Cayley graphs on extraspecial $2$-groups that admit these phenomena. We also show that there is no normal Cayley graph of an extraspecial group that admits instantaneous uniform mixing.

Revised:
Accepted:
Published online:
DOI: 10.5802/alco.237
Classification: 05C25, 81Q35
Keywords: Cayley graph, perfect state transfer, fractional revival, uniform mixing, extraspecial groups
Sin, Peter 1; Sorci, Julien 1

1 Department of Mathematics University of Florida P.O. Box 118105 Gainesville FL 32611, USA
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Sin, Peter; Sorci, Julien. Continuous-time Quantum Walks on Cayley Graphs of Extraspecial Groups. Algebraic Combinatorics, Volume 5 (2022) no. 4, pp. 699-714. doi : 10.5802/alco.237. https://alco.centre-mersenne.org/articles/10.5802/alco.237/

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