The cycle C9 does not admit uniform mixing

2026/07/30 by Alison Gray, Pransu Patel, Isaiah Young
Mathematics · Physics and Astronomy · #math.CO #quant-ph #msc:13P10 #msc:14J81 #msc:97K30

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arxiv created 2026/07/30 · arxiv updated 2026/07/31

Abstract

We study continuous-time quantum walks (CTQWs) on cycles. In particular, we prove that the cycle C₉ does not admit uniform mixing at any time via algebraic geometry and Gröbner basis techniques to rule out all cyclic 9-roots.

Citations

• Uniform Mixing on Cayley Graphs
• Uniform Mixing and Association Schemes
• Mixing in Continuous Quantum Walks on Graphs
• Quantum Walks on the Hypercube

Related

• Mixing in Continuous Quantum Walks on Graphs
• Uniform mixing in continuous-time quantum walks on oriented, nonabelian Cayley graphs
• Uniform Mixing and Association Schemes
• A note on graphs resistant to quantum uniform mixing
• Selected Open Problems in Continuous-Time Quantum Walks