The cycle C9 does not admit uniform mixing
arXiv:2607.28345
summary
The paper proves that the 9-vertex cycle graph does not exhibit uniform mixing in continuous-time quantum walks, using algebraic geometry and Gröbner basis methods to eliminate all possible 9th roots of unity.
Abstract
We study continuous-time quantum walks (CTQWs) on cycles. In particular, we prove that the cycle does not admit uniform mixing at any time via algebraic geometry and Gröbner basis techniques to rule out all cyclic 9-roots.
Topics & keywords
#continuous-time quantum walks#uniform mixing#cycle graphs#algebraic geometry#groebner basesC9uniform mixingCTQWcyclic 9-rootsgroebner basis