A modified quantum adiabatic evolution for the Deutsch-Jozsa problem
  Deutsch-Jozsa algorithm has been implemented via a quantum adiabatic evolution by S. Das et al. [Phys. Rev. A 65, 062310 (2002)]. This adiabatic algorithm gives rise to a quadratic speed up over classical algorithms. We show that a modified version of the adiabatic evolution in that paper can improve the performance to constant time. 
Zhaohui Wei and Mingsheng Ying