Topologically protected measurement-based quantum computation on the thermal state of a nearest-neighbor two-body Hamiltonian with spin-3/2 particles

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.