Measurement-Based Quantum Computation on Symmetry Breaking Thermal   States
  We consider measurement-based quantum computation (MBQC) on thermal states of the interacting cluster Hamiltonian containing interactions between the cluster stabilizers that undergoes thermal phase transitions. We show that the long-range order of the symmetry breaking thermal states below a critical temperature drastically enhance the robustness of MBQC against thermal excitations. Specifically, we show the enhancement in two-dimensional cases and prove that MBQC is topologically protected below the critical temperature in three-dimensional cases. The interacting cluster Hamiltonian allows us to perform MBQC even at a temperature an order of magnitude higher than that of the free cluster Hamiltonian. 
Keisuke Fujii, Yoshifumi Nakata, Masayuki Ohzeki, Mio Murao
quant-ph cond-mat.dis-nn cond-mat.stat-mech