A Noise-resilient Quantum Error Correction Technique for Nuclear Spin Qubits in Silicon

Nuclear spin qubits in silicon (e.g., donors such as ³¹P, ⁷⁵As, ¹²³Sb or isoelectronic species such as ²⁹Si, ⁷³Ge, or ¹¹⁹Sn) are well-isolated from their environment. Consequently, they have very long lifetimes and low sensitivity to noise, but this also suggests that control and measurement is challenging. We introduce electron pair interferometry (EPI), a protocol to overcome this challenge and maintain robustness to noise. By using electrostatic controls to prepare a pair of electrons into a singlet ground state, split them apart, and shuttle them to dots containing nuclear spin qubits, we show it is possible to coherently transfer the parity of the nuclei onto the measurable state of singlet/triplet-encoded electrons. Global nuclear magnetic resonance (NMR) can be used to change bases and implement dynamical coupling (DD). Combined with selective hyperfine-induced Z_π rotations, our gate set is complete for universal quantum computation, tailored to CSS-style quantum error correction, and robust to noise. We predict very low sensitivity to charge noise and study the sensitivity to both DC and AC magnetic field inhomogeneity which depends strongly on their relative strengths and is mitigated by DD.