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