Optimisation of electrically-driven multi-donor quantum dot qubits

Multi-donor quantum dots have been at the forefront of recent progress in Si-based quantum computation. Among them, $2P:1P$ qubits have a built-in dipole moment, enabling all-electrical spin operation via hyperfine mediated electron dipole spin resonance (EDSR). The development of all-electrical multi-donor dot qubits requires a full understanding of their EDSR and coherence properties, incorporating multi-valley nature of their ground state. Here, by introducing a variational effective mass wave-function, we examine the impact of qubit geometry and nearby charge defects on the electrical operation and coherence of $2P:1P$ qubits. We report four outcomes: (i) The difference in the hyperfine interaction between the $2P$ and $1P$ sites enables fast EDSR, with $T_\pi \sim 10-50$ ns and a Rabi ratio $ (T_1/T_\pi) \sim 10^6$. We analyse qubits with the $2P:1P$ axis aligned along the [100], [110] and [111] crystal axes, finding that the fastest EDSR time $T_\pi$ occurs when the $2P:1P$ axis is $\parallel$[111], while the best Rabi ratio occurs when it is $\parallel$ [100]. This difference is attributed to the difference in the wave function overlap between $2P$ and $1P$ for different geometries. In contrast, the choice of $2P$ axis has no visible impact on qubit operation. (ii) Sensitivity to random telegraph noise due to nearby charge defects depends strongly on the location of the nearby defects with respect to the qubit. For certain orientations of defects random telegraph noise has an appreciable effect both on detuning and $2P-1P$ tunneling, with the latter inducing gate errors. (iii) The qubit is robust against $1/f$ noise provided it is operated away from the charge anticrossing. (iv) Entanglement via exchange is several orders of magnitude faster than dipole-dipole coupling. These findings pave the way towards fast, low-power, coherent and scalable donor dot-based quantum computing.