Local electrical control of a single-atom spin qubit in a continuous microwave field*

An ideal physical system to encode quantum information should be well isolated from its environment, but locally addressable and readable. Kane's proposal for a silicon spin-based quantum computer suggested tuning the qubit in/out of resonance with a global oscillating magnetic field by applying a local electric field and exploiting the Stark shift of the electron-nuclear hyperfine interaction (``$A$-gate''). We demonstrate universal single-qubit logic gates on both the electron and $^{31}$P nuclear spin of a single phosphorus atom in silicon, subject to an always-on microwave field, and operated via an $A$-gate controlled by nanometre-scale electrodes. The experiment is facilitated by the exceptionally sharp spin resonance frequencies in the nuclear-spin-free $^{28}$Si host material. Randomized benchmarking yields quantum gate fidelities $\geq 99$ $\%$, and the millisecond-long spin coherence times remain identical to those obtained by pulsed spin resonance. This method provides a natural pathway to address arbitrarily many qubits in large-scale quantum computers.