  Recently, Li {\it et al.} [Phys. Rev. Lett. {\bf 107}, 060501 (2011)] have
demonstrated that topologically protected measurement-based quantum computation
can be implemented on the thermal state of a nearest-neighbor two-body
Hamiltonian with spin-2 and spin-3/2 particles provided that the temperature is
smaller than a critical value, namely, threshold temperature. Here we show that
the thermal state of a nearest-neighbor two-body Hamiltonian, which consists of
only spin-3/2 particles, allows us to perform topologically protected
measurement-based quantum computation. The threshold temperature is calculated
and turns out to be comparable to that with the spin-2 and spin-3/2 system.
Furthermore, we generally show that a cluster state of high connectivity can be
efficiently generated from the thermal state of the spin-3/2 system without
severe thermal noise accumulation.
