Continuous-time Quantum Walks on a Cycle Graph
  We present analytical treatment of quantum walks on a cycle graph. The investigation is based on a realistic physical model of the graph in which decoherence is induced by continuous monitoring of each graph vertex with nearby quantum point contact. We derive the analytical expression of the probability distribution along the cycle. Upper bound estimate to mixing time is shown. 
Dmitry Solenov and Leonid Fedichkin