  We develop a new class of genetic algorithm that computationally determines
efficient pulse sequences to implement a quantum gate U in a three-qubit
system. The method is shown to be quite general, and the same algorithm can be
used to derive efficient sequences for a variety of target matrices. We
demonstrate this by implementing the inversion-on-equality gate efficiently
when the spin-spin coupling constants $J_{12}=J_{23}=J$ and $J_{13}=0$. We also
propose new pulse sequences to implement the Parity gate and Fanout gate, which
are about 50% more efficient than the previous best efforts. Moreover, these
sequences are shown to require significantly less RF power for their
implementation. The proposed algorithm introduces several new features in the
conventional genetic algorithm framework. We use matrices instead of linear
chains, and the columns of these matrices have a well defined hierarchy. The
algorithm is a genetic algorithm coupled to a fast local optimizer, and is
hence a hybrid GA. It shows fast convergence, and running on a MATLAB platform
takes about 20 minutes on a standard personal computer to derive efficient
pulse sequences for any target 8X8 matrix $U$.
