Hardware-efficient error-correcting codes for large nuclear spins

Universal quantum computers require a large network of qubits robust against errors. Recent theoretical and experimental studies on donor nuclear spins in silicon, engineered on semiconductor platforms compatible with industrial fabrication, show their coherent behavior and potential for scalability. Here we present a hardware-efficient quantum protocol that corrects phase flips of a nuclear spin using explicit experimentally feasible operations. We introduce moment angular system encoding that uses the large Hilbert space provided by the nuclear spin of the donor to encode the information and employ the electron spin of the donor as an ancilla for error correction. Simulations using present-day experimental manipulation fidelities predict significant improvement in logical qubit fidelity over existing spin quantumerror-correction protocols. These results provide a realizable blueprint for a corrected spin-based qubit.