  We propose a logical qubit based on the Blume-Capel model: a higher spin
generalization of the Ising chain and which allows for an on-site anisotropy
preserving rotational invariance around the Ising axis. We show that such a
spin-3/2 Blume-Capel model can also support localized Majorana bound states at
the ends of the chain. Inspired by known braiding protocols of these Majorana
bound states, upon appropriate manipulation of the system parameters, we
demonstrate a set of universal gate operations which act on qubits encoded in
the doubly degenerate ground states of the chain.
