Efficient quantum gates for individual nuclear spin qubits by indirect control

Hybrid quantum registers, such as electron-nuclear spin systems, have emerged as promising hard-<br> ware for implementing quantum information and computing protocols in scalable systems. Neverthe-<br> less, the coherent control of such systems still faces challenges. Particularly, the lower gyromagnetic<br> ratios of the nuclear spins cause them to respond slowly to control fields, resulting in gate times<br> that are generally longer than the coherence time of the electron. Here, we demonstrate a scheme<br> for circumventing this problem by indirect control: We apply a small number of short pulses only<br> to the electron and let the full system undergo free evolution under the hyperfine coupling between<br> the pulses. Using this scheme, we realize robust quantum gates in an electron-nuclear spin system,<br> including a Hadamard gate on the nuclear spin and a controlled-NOT gate with the nuclear spin<br> as the target qubit. The durations of these gates are shorter than the electron coherence time, and<br> thus additional operations to extend the system coherence time are not needed. Our demonstration<br> serves as a proof of concept for achieving efficient coherent control of electron-nuclear spin systems,<br> such as NV centers in diamond. Our scheme is still applicable when the nuclear spins are only<br> weakly coupled to the electron.