Continuous-time Quantum Walks on a Cycle
Dmitry Solenov, Leonid Evgenevich Fedichkin · arXiv (Cornell University) · 2005
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 to mixing time is obtained. It is found to be linear in the graph size.