title: Measurement-based quantum computation on symmetry breaking thermal States.
abstract: 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 enhances 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 1 order of magnitude higher than that of the free cluster Hamiltonian.
authors.affiliation: Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan.
authors.forename: Keisuke
authors.initials: K
authors.lastname: Fujii
authors.affiliation: Department of Physics, Graduate School of Science, University of Tokyo, Tokyo 113-0033, Japan.
authors.forename: Yoshifumi
authors.initials: Y
authors.lastname: Nakata
authors.affiliation: Department of Systems Science, Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan.
authors.forename: Masayuki
authors.initials: M
authors.lastname: Ohzeki
authors.affiliation: Department of Physics, Graduate School of Science, University of Tokyo, Tokyo 113-0033, Japan and Institute for Nano Quantum Information Electronics, University of Tokyo, Tokyo 153-8505, Japan.
authors.forename: Mio
authors.initials: M
authors.lastname: Murao