bibkey: ahmadi2003circulant authors: A. Ahmadi; R. Belk; C. Tamon; C. Wendler year: 2003 title: On mixing in continuous-time quantum walks on some circulant graphs doi: 10.26421/qic3.6-4 url: https://arxiv.org/abs/quant-ph/0209106v5 claim: The authors conjecture that no cycle other than C3 and C4 has instantaneous uniform mixing. strata_touched:

• D5/S3/Quantum/Dynamics/CycleUniformMixing/CycleTwentyOneNoUniformMixing license: citation-only triage: anchor

On mixing in continuous-time quantum walks on some circulant graphs

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DOI: 10.26421/qic3.6-4

Source: https://arxiv.org/abs/quant-ph/0209106v5

Page 7, Conjecture 1 in the cycle section; main.tex lines 730–733. The adjacency normalization A/2 only rescales the real time parameter.

Source statement

No complete cycle $C_n$, except for $C_3,C_4$, has the instantaneous uniform mixing property under the continuous-time quantum walk model.

The C21 exclusion is partial progress on the Ahmadi–Belk–Tamon–Wendler conjecture. The conjecture for all cycles of length at least five remains outside this result.