  A quantum circuit is introducted to describe the preparation of a labeled
pseudo-pure state by mutiplet-component excitation scheme which has been
experimentally implemented on a 4-qubit nuclear magnetic resonance quantum
processor. Meanwhile, we theoretically analyze and numerically inverstigate the
low-power selective single-pulse implementation of a controlled-rotation gate,
which manifests its validity in our experiment. Based on the labeled
pseudo-pure state prepared, a 3-qubit Bernstein-Vazirani algorithm has been
experimentally demonstrated by spectral implementation. The "answers" of the
computations are indentified from the split speak positions in the spectra of
the observer spin, which are equivalent to projective measurements required by
the algorithms.
