  Due to their long coherence times, nuclear spins have gained considerable
attention as physical qubits. Two-qubit gates between nuclear spins of distinct
resonance frequencies can be mediated by electron spins, usually employing a
sequence of electron-nuclear gates. Here we present a different approach
inspired by, but not limited to, NV centers in diamond and discuss possible
applications. To this end we generalize external electron spin control
sequences for nuclear spin initialization and hyperpolarization to achieve the
simultaneous control of distinct nuclear spins via an electron spin. This
approach results in efficient entangling gates that, compared to standard
techniques, reduce the gate time by more than 50% when the gate time is limited
by off-resonant coupling to other spins, and by up to 22% when the gate time is
limited by small electron-nuclear coupling.
