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.混合量子寄存器（hybrid quantum registers）——以电子-核自旋体系为典型代表——已成为可扩展系统中实现量子信息与量子计算协议的极具潜力的硬件方案。然而，此类体系的相干调控仍面临诸多挑战。具体而言，核自旋较低的旋磁比使其对调控场的响应速率较慢，导致量子门时长普遍长于电子的相干时间。本研究提出一种间接调控方案以解决该问题：仅对电子施加少量短脉冲，使全系统在脉冲间隔内借助超精细耦合（hyperfine coupling）发生自由演化。基于该方案，我们在电子-核自旋体系中实现了鲁棒量子门，包括针对核自旋的哈达玛门（Hadamard gate）以及以核自旋为目标量子比特的受控非门（controlled-NOT gate）。此类量子门的时长均短于电子的相干时间，因此无需额外操作来延长系统的相干时间。本实验演示成果可作为电子-核自旋体系（如金刚石中的氮-空位中心（NV centers））高效相干调控的概念验证。即便核自旋与电子仅存在弱耦合，该方案依然适用。