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 (C-z) show no appreciable decoherence up to 10(2) mu s, while a complete decoherence is estimated for the eigenstates of the total-spin projection (S-z) and of the partial spin sum (S-12) after 10 mu 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 C-z and the nuclear-spin bath. We finally estimate the reduction of the decoherence time scale for C-z, resulting from possible hyperfine contact terms or from the misalignment of the magnetic field.