A note on graphs resistant to quantum uniform mixing

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dc.creatorAdamczak, William
dc.creatorAndrew, Kevin
dc.creatorHernberg, Peter
dc.creatorTamon, Christino
dc.date2003-08-13
dc.date.accessioned2026-07-07T06:07:36Z
dc.date.available2026-07-07T06:07:36Z
dc.descriptionContinuous-time quantum walks on graphs is a generalization of continuous-time Markov chains on discrete structures. Moore and Russell proved that the continuous-time quantum walk on the $n$-cube is instantaneous exactly uniform mixing but has no average mixing property. On complete (circulant) graphs $K_{n}$, the continuous-time quantum walk is neither instantaneous (except for $n=2,3,4$) nor average uniform mixing (except for $n=2$). We explore two natural {\em group-theoretic} generalizations of the $n$-cube as a $G$-circulant and as a bunkbed $G \rtimes \Int_{2}$, where $G$ is a finite group. Analyses of these classes suggest that the $n$-cube might be special in having instantaneous uniform mixing and that non-uniform average mixing is pervasive, i.e., no memoryless property for the average limiting distribution; an implication of these graphs having zero spectral gap. But on the bunkbeds, we note a memoryless property with respect to the two partitions. We also analyze average mixing on complete paths, where the spectral gaps are nonzero.
dc.description9 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/quant-ph/0308073
dc.identifierhttp://arxiv.org/abs/quant-ph/0308073
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/91349
dc.subjectQuantum Physics
dc.titleA note on graphs resistant to quantum uniform mixing
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