Ab-initio calculations of shallow dopant qubits in silicon from pseudopotential and all-electron mixed approach

Obtaining an accurate first-principle description of the electronic properties of dopant qubits is critical for engineering and optimizing high-performance quantum computing. However, density functional theory (DFT) has had limited success in providing a full quantitative description of these dopants due to their large wavefunction extent. Here, we build on recent advances in DFT to evaluate phosphorus dopants in silicon on a lattice comprised of 4096 atoms with hybrid functionals on a pseudopotential and all-electron mixed approach. Remarkable agreement is achieved with experimental measurements including: the electron-nuclear hyperfine coupling (115.5 MHz) and its electric field response (−2.65 × 10 −3 μm 2 /V 2 ), the binding energy (46.07 meV), excited valley-orbital energies of 1sT 2 (37.22 meV) and 1sE (35.87 meV) states, and super-hyperfine couplings of the proximal shells of the silicon lattice. This quantitative description of spin and orbital properties of phosphorus dopant simultaneously from a single theoretical framework will help as a predictive tool for the design of qubits.