Adiabatic Deutsch–Jozsa Problem Solved by Modifying the Initial Hamiltonian

We present an alternate adiabatic evolution for the Deutsch–Jozsa problem. The biggest difference of our adiabatic evolution constructed here with those appearing before is that an alternate initial Hamiltonian is used for the adiabatic evolution, with which the evolution task can be finished in O(1) time complexity. Our construction mostly resembles the one discussed by Das et al. Phys. Rev. A 65 (2002) 062310, except for the initial system Hamiltonian of the adiabatic algorithm.