Fidelity of the surface code in the presence of a bosonic bath

We study the resilience of the surface code to decoherence caused by the presence of a bosonic bath. This approach allows us to go beyond the standard stochastic error model commonly used to quantify decoherence and error threshold probabilities in this system. The full quantum mechanical system-bath dynamics is computed exactly over one quantum error correction cycle. Since all physical qubits interact with the bath, space-time correlations between errors are taken into account. We compute the fidelity of the surface code as a function of the quantum error correction time. The calculation allows us to map the problem onto an Ising-like statistical spin model with two-body interactions and a fictitious temperature which is related to the inverse bath coupling constant. The model departs from the usual Ising model in the sense that interactions can be long ranged and can involve complex exchange couplings; in addition, the number of allowed configurations is restricted by the syndrome extraction. Using analytical estimates and numerical calculations, we argue that, in the limit of an infinite number of physical qubits, the spin model sustain a phase transition which can be associated to the existence of an error threshold in the surface code. An estimate of the transition point is given for the case of nearest-neighbor interactions.Comment: 15 pages, 5 figure

Surface code fidelity at finite temperatures

We study the dependence of the fidelity of the surface code in the presence of a single finite-temperature massless bosonic environment after a quantum error correction cycle. The three standard types of environment are considered: super-Ohmic, Ohmic, and sub-Ohmic. Our results show that, for regimes relevant to current experiments, quantum error correction works well even in the presence of environment-induced, long-range inter-qubit interactions. A threshold always exists at finite temperatures, although its temperature dependence is very sensitive to the type of environment. For the super-Ohmic case, the critical coupling constant separating high- from low-fidelity decreases with increasing temperature. For both Ohmic and super-Ohmic cases, the dependence of the critical coupling on temperature is weak. In all cases, the critical coupling is determined by microscopic parameters of the environment. For the sub-Ohmic case, it also depends strongly on the duration of the QEC cycle.Comment: 13 pages, 6 figure

Surface Code Threshold in the Presence of Correlated Errors

We study the fidelity of the surface code in the presence of correlated errors induced by the coupling of physical qubits to a bosonic environment. By mapping the time evolution of the system after one quantum error correction cycle onto a statistical spin model, we show that the existence of an error threshold is related to the appearance of an order-disorder phase transition in the statistical model in the thermodynamic limit. This allows us to relate the error threshold to bath parameters and to the spatial range of the correlated errors.Comment: 5 pages, 2 figure

Comparison of low and high pressure infiltration regimes on the density and highly porous microstructure of ceria ecoceramics made from sustainable cork templates

Cork templates were used to produce lightweight bulk biomimetic ecoceramic (environmentally conscious ceramic) monoliths. Bulk/monolithic ceramics are vital for many applications, i.e. energy materials and fuel cells. Using simple and flexible, aqueous green-chemistry procedures, for the first time the influence of infiltration regime, number of infiltration cycles and sintering temperature on ecoceramic density and microstructure was studied. This lightweight three-dimensionally ordered macroporous (3DOM) CeO2 preserved the hexagonal cellular structure of cork, but unlike the wood, the rear cell walls were open, greatly increasing open porosity. Higher sintering temperatures (1600 instead of 1000 °C) were required to produce cm size monolithic ecoceramics mechanically strong enough to be handled. The infiltration regime and number of infiltration cycles affected density and porosity. Lower infiltration pressure led to higher porosity ecoceramics (3.3–5.7%), which may favour catalytic performance, showing the possibility of tailoring porosity and specific surface area by modifying the number of infiltration cycles

O desafio de introduzir o modelo de ensino por pesquisa nas escolas públicas de pernambuco

Essa pesquisa avaliou se um programa de formação continuada fundamentado numa visão sistêmica e na Didática das Ciências favoreceu a introdução de mudanças didático-pedagógica nas escolas. Estratégias foram planejadas para facilitar aos cursistas a superação de suas dificuldades. Duzentos professores de Ciências e Matemática foram capazes de elaborar e desenvolver projetos de intervenção pedagógica em suas salas de aula, assumindo o modelo de Ensino por Pesquisa. Os resultados foram alcançados na medida em que os professores foram apoiados para introduzirem as mudanças tendo seus saberes práticos respeitados