Quantum search by partial adiabatic evolution

A quantum search algorithm based on the partial adiabatic evolution\cite{Tulsi2009} is provided. We calculate its time complexity by studying the Hamiltonian in a two-dimensional Hilbert space. It is found that the algorithm improves the time complexity, which is $O(\sqrt{N\mathrm{/}M})$, of the local adiabatic search algorithm\cite{Roland2002}, to $O(\sqrt{N}\mathrm{/}M)$.