Topological color codes on Union Jack lattices: A stable implementation of the whole Clifford group

We study the error threshold of topological color codes on Union Jack lattices that allow for the full implementation of the whole Clifford group of quantum gates. After mapping the error-correction process onto a statistical mechanical random 3-body Ising model on a Union Jack lattice, we compute its phase diagram in the temperature-disorder plane using Monte Carlo simulations. Surprisingly, topological color codes on Union Jack lattices have similar error stability than color codes on triangular lattices, as well as the Kitaev toric code. The enhanced computational capabilities of the topological color codes on Union Jack lattices with respect to triangular lattices and the toric code demonstrate the inherent robustness of this implementation.Comment: 8 pages, 4 figures, 1 tabl

Tricolored Lattice Gauge Theory with Randomness: Fault-Tolerance in Topological Color Codes

We compute the error threshold of color codes, a class of topological quantum codes that allow a direct implementation of quantum Clifford gates, when both qubit and measurement errors are present. By mapping the problem onto a statistical-mechanical three-dimensional disordered Ising lattice gauge theory, we estimate via large-scale Monte Carlo simulations that color codes are stable against 4.5(2)% errors. Furthermore, by evaluating the skewness of the Wilson loop distributions, we introduce a very sensitive probe to locate first-order phase transitions in lattice gauge theories.Comment: 12 pages, 5 figures, 1 tabl

オオサカダイガク カンゴガク ザッシ 13カン 1ゴウ タイショク キネン トクシュウ

退職記念特

Generalized Toric Codes Coupled to Thermal Baths

We have studied the dynamics of a generalized toric code based on qudits at finite temperature by finding the master equation coupling the code's degrees of freedom to a thermal bath. As a consequence, we find that for qutrits new types of anyons and thermal processes appear that are forbidden for qubits. These include creation, annihilation and diffusion throughout the system code. It is possible to solve the master equation in a short-time regime and find expressions for the decay rates as a function of the dimension $d$ of the qudits. Although we provide an explicit proof that the system relax to the Gibbs state for arbitrary qudits, we also prove that above a certain crossing temperature, qutrits initial decay rate is smaller than the original case for qubits. Surprisingly this behavior only happens with qutrits and not with other qudits with $d>3$.Comment: Revtex4 file, color figures. New Journal of Physics' versio

Epidemiologic survey in Swiss group-housed breeding rabbits: extent of lesions and potential risk factors

In Switzerland, group-housing for breeding rabbit does is not explicitly required by law, but label programmes, as well as the general public and animal welfare groups, are advocating it. Although group-housing is of great benefit to the gregariously living rabbits, the establishment of a social hierarchy within the group might lead to stress and lesions. In the present epidemiological study, lesions were scored twice on 30% of the breeding does on all 28 commercial Swiss farms with group-housed breeding does. Additionally, a detailed questionnaire was filled out with all producers to determine risk factors potentially associated with lesions. Data were analysed using hierarchical proportional odds models. About 33% of the does examined had lesions, including wounds that were almost healed and small scratches. Severe lesions were counted on 9% of the animals. Differences between seasons in lesions score were identified, with the extent of lesions being higher in summer than in spring. Fewer lesions occurred on farms on which mastitis was more common. More lesions were found on farms where the does were isolated between littering and artificial insemination than on farms without isolation. According to the producers, most of the aggression occurred directly after the isolation phase when the does were regrouped again. We conclude that lesions in group-housed breeding does might be reduced by appropriate reproductive management