  We propose fast phase-gates of single nuclear spins interacting with single
electron spins. The gate operation utilizes geometric phase shifts of the
electron spin induced by fast/slow rotating fields; the path difference
depending on nuclear spin states enables nuclear phase shifts. The gate time is
inversely proportional to the frequency of the slow rotating field. As an
example, we use nitrogen-vacancy centers in diamond, and show the phase-gate
time orders of magnitude shorter than previously reported. We also show the
robustness of the gate against decoherence and systematic errors.
