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

Recently, Li et al. [Phys. Rev. Lett. 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.

Figure 1

The error probabilities $q_1$ (red) and $q_2=q_3$ (green) are plotted as functions of the temperature $T/\Delta$.

Figure 2

(a) The unit cell of the model by Li et al. [23]. (b) The unit cell of the present model with only spin-3/2 particles. (c) In the present model, each center particle connected with four bond particles in the Li et al.'s model [23] is replaced by two center particles, each of which is connected with three bond particles. (d) One of two center particles and the bond particle between them are measured locally to obtain the five-qubit GHZ state. (e) An $m$-connected cluster state is created from a thermal state of spin-3/2 particles on the lattice of a tree structure by single-particle measurements. The center particles with dotted circles form the $m$-connected cluster state.