  We present two-dimensional nuclear magnetic resonance spectroscopy protocols
based on nitrogen-vacancy (NV) centers in diamond as efficient quantum sensors
of protein structure. Continuous microwave driving fields are used to achieve
Hartmann-Hahn resonances between NV spin sensor and proximate nuclei for
selective control of nuclear spins and measurement of their polarization. Our
protocols take advantage of the strong coupling between the NV sensor and the
nuclei, thus facilitating coherence control of nuclear spins and relax the
requirement of nuclear spin polarization. We dramatically reduce the
experimental effort by employing a singular value thresholding matrix
completion algorithm from signal processing to regain the resolution of protein
structure based on sub-sampled data from NV based single molecule nuclear
magnetic resonance spectroscopy. As an illustration, we demonstrate the power
of this approach by identifying the nitrogen-Hydrogen interaction peak in an
Alanine spectrum based on merely 5% of the sample data.
