The cycle C9 does not admit uniform mixing

Alison Gray; Pransu Patel; Isaiah Young

The cycle C9 does not admit uniform mixing

Combinatorics 2026-07-30 v1 Quantum Physics

Authors: Alison Gray , Pransu Patel , Isaiah Young

Abstract

We study continuous-time quantum walks (CTQWs) on cycles. In particular, we prove that the cycle $C_9$ does not admit uniform mixing at any time via algebraic geometry and Gr\"obner basis techniques to rule out all cyclic 9-roots.

Cite

@article{arxiv.2607.28345,
  title  = {The cycle C9 does not admit uniform mixing},
  author = {Alison Gray and Pransu Patel and Isaiah Young},
  journal= {arXiv preprint arXiv:2607.28345},
  year   = {2026}
}