Spectral Implementation for creating a labeled pseudo-pure state and the Bernstein-Vaziranis algorithm in a four-qubit nuclear magnetic resonance quantum processor

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.