A relation between fidelity and quantum adiabatic evolution
  Recently, some quantum algorithms have been implemented by quantum adiabatic evolutions. In this paper, we discuss the accurate relation between the running time and the distance of the initial state and the final state of a kind of quantum adiabatic evolutions. We show that this relation can be generalized to the case of mixed states. 
Zhaohui Wei and Mingsheng Ying