Hardware-efficient error-correcting codes for large nuclear spins*

Improving the performance of near-term quantum devices involves correcting dominant sources of error. Donor nuclear spins in silicon are attractive qubits as they are compact, robust, and show record coherence time for solid-state systems. Amazingly, these coherence times are still “brief” with respect to the near-infinite relaxation times of the donors’ spins. This observation motivates a hardware-efficient approach to error correction that corrects the dominant dephasing errors. Here we present a protocol consisting of experimentally feasible operations that leverages the extended Hilbert space of a large nuclear spin to correct dephasing errors. Simulations, using state-of-the-art manipulation fidelities, predict significant improvement in reachable logical fidelity over existing spin quantum-error-correction protocols. These results provide a realizable blueprint for a corrected spin-based qubit using built-in error correction schemes.