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Recently, Li {\it et al.} [Phys. Rev. Lett. {\bf 107}, 060501 (2011)] havedemonstrated that topologically protected measurement-based quantum computationcan be implemented on the thermal state of a nearest-neighbor two-bodyHamiltonian with spin-2 and spin-3/2 particles provided that the temperature issmaller than a critical value, namely, threshold temperature. Here we show thatthe thermal state of a nearest-neighbor two-body Hamiltonian, which consists ofonly spin-3/2 particles, allows us to perform topologically protectedmeasurement-based quantum computation. The threshold temperature is calculatedand 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 beefficiently generated from the thermal state of the spin-3/2 system withoutsevere thermal noise accumulation.

physical review. a, atomic, molecular, and optical physics/physical review, a, atomic, molecular, and optical physics

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