Hyperfine-induced decoherence in triangular spin-cluster qubits

We theoretically investigate hyperfine-induced decoherence in a triangular spin cluster for different qubit encodings. Electrically controllable eigenstates of spin chirality (Cz) show no appreciable decoherence up to 102 ?s, while a complete decoherence is estimated for the eigenstates of the total-spin projection (Sz) and of the partial spin sum (S12) after 10 ?s. The robustness of chirality is due to its decoupling from both the total- and individual-spin components in the cluster. This results in a suppression of the effective interaction between Cz and the nuclear-spin bath. We finally estimate the reduction of the decoherence time scale for Cz, resulting from possible hyperfine contact terms or from the misalignment of the magnetic field.