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

Diatom assemblages in Portuguese temporary rivers

During a survey of benthic diatoms in watercourses from Portugal in spring and summer 2006 and 2007, 76 sites in temporary streams (according to the National Water Institute classification) have been studied. These streams belong to the Ribeiras do Algarve (10 sites), Guadiana (19 sites), Mira (7 sites), Sado (16 sites), Tejo (20 sites), and Douro (4 sites) watersheds. Among these 76 sites, the National Water Institute classified only 48 as reference sites, and only these were therefore considered in the statistical analysis performed. A total of 276 diatom taxa have been identified in the 48 reference sites, from which 112 were present in abundance above 2% in at least one inventory. The most frequent taxa, present in more than 50% of the studied sites, were Achnanthidium minutissimum (Kützing) Czarnecki, Amphora pediculus (Kützing) Grunow, Cocconeis euglypta Ehrenberg, Eolimna minima (Grunow) Lange-Bertalot, Gomphonema parvulum Kützing, G. rosenstockianum Lange-Bertalot & E. Reichardt, Navicula gregaria Donkin, N. veneta Kützing, Nitzschia inconspicua Grunow and Planothidium frequentissimum (Lange-Bertalot) Lange-Bertalot. These are neutrophilous to alcaliphilous, mesosaprobous to -meso-saprobous, eutraphentic to indifferent taxa. Furthermore, a multivariate analysis relating diatom assemblages with environmental parameters is presented and the ecological preferences of not yet well known taxa, such as G. rosenstockianum, are provided

Self-similar solutions to the mean curvature flow in R3\mathbb{R}^{3}

In this paper we make an analysis of self-similar solutions for the mean curvature flow (MCF) by surfaces of revolution and ruled surfaces in $\mathbb{R}^{3}$. We prove that self-similar solutions of the MCF by non-cylindrival surfaces and conical surfaces in $\mathbb{R}^{3}$ are trivial. Moreover, we characterize the self-similar solutions of the MCF by surfaces of revolutions under a homothetic helicoidal motion in $\mathbb{R}^{3}$ in terms of the curvature of the generating curve. Finally, we characterize the self-similar solutions for the MCF by cylindrical surfaces under a homothetic helicoidal motion in $\mathbb{R}^3$. Explicit families of exact solutions for the MCF by cylindrical surfaces in $\mathbb{R}^{3}$ are also given

Avaliação do impacto da marcha com canadianas no dispêndio energético: análise comparativa entre jovens e idosos

Introdução: As canadianas são utilizadas em múltiplos quadros clínicos em que existe compromisso da marcha. No entanto, é fulcral considerar as diferentes exigências metabólicas associadas a cada auxiliar e tipo de marcha. Objetivo: Avaliar o dispêndio energético (DE) na marcha normal (MN), com uma canadiana e com duas canadianas a 3 pontos e a 3 pontos modificada em jovens e idosos. Metodologia: Estudo analítico transversal, composto por 21 indivíduos. As variáveis analisadas foram o volume de oxigénio inspirado (VO2), volume de dióxido de carbono expirado (VCO2) e quociente respiratório (QR), obtidas através do sistema portátil (Cosmed K4b2, Cosmed, Roma, Itália). Resultados: Os participantes tinham idades entre 18 e 75 anos (11 jovens e 10 idosos). Os idosos apresentaram valores significativamente mais elevados que os jovens no DE na marcha com uma canadiana a 3 pontos (p=0,009) e com duas canadianas a 3 pontos (p=0,008), enquanto nas restantes marchas não houve diferenças estatisticamente significativas (p>0,05). A MN e a marcha com duas canadianas a 3 pontos foram os tipos de marcha com maior DE nos jovens, e nos idosos. Nos jovens, a MN apresentou 19% a 45% maior DE do que as restantes marchas, enquanto nos idosos verificou-se que todas as marchas (à exceção de uma canadiana a 3 pontos modificada) apresentaram um maior DE (entre 7 e 16%) comparativamente à MN. Conclusão: Os idosos apresentaram valores significativamente mais elevados de DE que os jovens nas marchas uma e duas canadianas a 3 pontos. Na MN e na marcha uma canadiana a 3 pontos modificada existe uma tendência para os jovens apresentarem valores de DE superior aos idosos. A medição do DE fornece uma indicação precisa da eficiência da marcha, sendo útil como suporte para a decisão clínica e para uma adequada reabilitação.Background: Crutches are used in multiple clinical conditions in which there is a commitment of walking. However, it is crucial to consider the different metabolic requirements associated with each auxiliary device and type of walking. Objective: Evaluate the energy expenditure (EE) during normal walking (NW), with one crutch, with two crutches to 3 points and to 3 points modified in young and elderly. Methods: A broad-range analytical study, composed of 21 individuals. The variables analyzed were the volume of inspired oxygen (VO2), volume of expired carbon dioxide (VCO2) and respiratory exchange ratio (RER), obtained through the portable system (Cosmed K4b2, Cosmed, Rome, Italy). Results: Participants were aged between 18 and 75 years (11 young and 10 elderly). The elderly had significantly higher values than the young at EE walking with one 3 points crutch (p = 0,009) and with two 3 points crutches (p = 0,008), while, in the other types of walking, no statistically significant differences (p> 0,05) were observed. The NW and walking with two 3 points crutches were the types of walking with higher EE in young and elderly. In young people, the NW showed 19% to 45% higher EE than other walking, while in the elderly it was found that all walking (except for a 3 points modified crutch) showed a higher EE (between 7 and 16% ) compared to NW

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

Os primeiros arroubos de exaltação patriótica e liberal do académico Garrett

Quando estamos perante um génio da Literatura como Almeida Gar rett, mesmo os vestígios mais remotos da sua produção literária, por mais insignificantes e pueris que possam parecer perante o cânone dos títulos publicados, acabam por revelar facetas recônditas que ajudarão a definir ou acentuar as linhas de uma personalidade e de um talento em pr ogresso. É o caso das suas primícias teatrais, enquanto estudante de Coimbra. Entre os fragmentos autógrafos desses textos, encontra-se um elogio dramático com o título O Amor da Pátria, escrito em 1819, para festejar o nascimento da futura rainha D. Maria II. Publicada uma primeira versão muito incompleta, nas Obras Póstumas, em 1914, damos agora a conhecer a versão final desse texto, posta em confronto com todas as variantes textuais anteriores, permitindo ao leitor acompanhar o pulsar da inspiração e o fluir da escrita, reprimida em certos momentos pelo rigor da expressão.peerreviewe