  We propose a proof-of-principle experiment to encode one logical qubit in
noise protected subspace of three identical spins in a methyl group. The
symmetry analysis of the wavefunction shows that this fermionic system exhibits
a symmetry correlation between the spatial degree of freedom and the spin
degree of freedom. We show that one can use this correlation to populate the
noiseless subsystem by relying on the interaction between the electric dipole
moment of the methyl group with a circularly polarized microwave field. Logical
gates are implemented by controlling both the intensity and phase of the
applied field.
