Single electron spins bound to multi-phosphorus nuclear spin registers in silicon have demonstrated fast (0.8 ns) two-qubit \(\sqrt{\mathrm{SWAP}}\) gates and long spin relaxation times (~30 s). In these spin registers, when the donors are ionized, the nuclear spins remain weakly coupled to their environment, allowing exceptionally long coherence times. When the electron is present, the hyperfine interaction allows coupling of the spin and charge degrees of freedom for fast qubit operation and control. Here we demonstrate the use of the hyperfine interaction to enact electric dipole spin resonance to realize high-fidelity (\(F=10{0}_{-6}^{+0}\)%) initialization of all the nuclear spins within a four-qubit nuclear spin register. By controllably initializing the nuclear spins to \(\left\vert \Downarrow \Downarrow \Downarrow \right\rangle\), we achieve single-electron qubit gate fidelities of F = 99.78 ± 0.07% (Clifford gate fidelities of 99.58 ± 0.14%), above the fault-tolerant threshold for the surface code with a coherence time of \({T}_{2}^{\,* }=12\,\upmu {{{\rm{s}}}}\).

与硅中多磷核自旋寄存器结合的单电子自旋已证明具有快速（0.8 ns）双量子位\(\sqrt{\mathrm{SWAP}}\)门和长自旋弛豫时间（~30 s）。在这些自旋寄存器中，当供体被电离时，核自旋与其环境保持弱耦合，从而允许非常长的相干时间。当电子存在时，超精细相互作用允许自旋和电荷自由度耦合，以实现快速量子位操作和控制。在这里，我们演示了使用超精细相互作用来产生电偶极子自旋共振，以实现内部所有核自旋的高保真度（ \(F=10{0}_{-6}^{+0}\) %）初始化四量子位核自旋寄存器。通过可控地将核自旋初始化为\(\left\vert \Downarrow \Downarrow \Downarrow \right\rangle\) ，我们实现了F = 99.78 ± 0.07%的单电子量子位门保真度 （Clifford 门保真度为 99.58 ± 0.14% ），高于表面代码的容错阈值，相干时间为\({T}_{2}^{\,* }=12\,\upmu {{{\rm{s}}}}\ ）。