  We show that the Hadamard and Unitary gates could be implemented by a unitary
evolution together with a measurement for any unknown state chosen from a set
$A = {{| {\Psi_i} > ,| {\bar {\Psi}_i} >}}({i = 1,2})$ if and only if $|
{\Psi_1} > ,| {\Psi_2} > ,| {\bar {\Psi}_1} > ,| {\bar {\Psi}_2} >$ are
linearly independent. We also derive the best transformation efficiencies.
