Quantum error correction with biased noise

Quantum computing offers powerful new techniques for speeding up the calculation of many classically intractable problems. Quantum algorithms can allow for the efficient simulation of physical systems, with applications to basic research, chemical modeling, and drug discovery; other algorithms have important implications for cryptography and internet security.

At the same time, building a quantum computer is a daunting task, requiring the coherent manipulation of systems with many quantum degrees of freedom while preventing environmental noise from interacting too strongly with the system. Fortunately, we know that, under reasonable assumptions, we can use the techniques of quantum error correction and fault tolerance to achieve an arbitrary reduction in the noise level.

In this thesis, we look at how additional information about the structure of noise, or "noise bias," can improve or alter the performance of techniques in quantum error correction and fault tolerance. In Chapter 2, we explore the possibility of designing certain quantum gates to be extremely robust with respect to errors in their operation. This naturally leads to structured noise where certain gates can be implemented in a protected manner, allowing the user to focus their protection on the noisier unprotected operations.

In Chapter 3, we examine how to tailor error-correcting codes and fault-tolerant quantum circuits in the presence of dephasing biased noise, where dephasing errors are far more common than bit-flip errors. By using an appropriately asymmetric code, we demonstrate the ability to improve the amount of error reduction and decrease the physical resources required for error correction.

In Chapter 4, we analyze a variety of protocols for distilling magic states, which enable universal quantum computation, in the presence of faulty Clifford operations. Here again there is a hierarchy of noise levels, with a fixed error rate for faulty gates, and a second rate for errors in the distilled states which decreases as the states are distilled to better quality. The interplay of of these different rates sets limits on the achievable distillation and how quickly states converge to that limit.

Effects of Lorentz local field correction on propagation properties of few-cycle pulse in dense Λ-type atomic medium

By solving numerically the full Maxwell-Bloch equations without the slowly varying envelope approximation and the rotating-wave approximation, we investigate the effects of Lorentz local field correction (LFC) on the propagation properties of few-cycle laser pulse in a dense A-type three-level atomic medium. We find that: when the area of the input pulse is larger, split of pulse occurs and the number of the sub-pulses with LFC is larger than that without LFC; at the same distance, the time interval between the first sub-pulse and the second sub-pulse in the case without LFC is longer than that with LFC, the time of pulse appearing in the case without LFC is later than that in the case with LFC, and the two phenomena are more obvious with propagation distance increasing; time evolution rules of the populations of levels vertical bar 1 >, vertical bar 2 > and vertical bar 3 > in the two cases with and without LFC are much different. When the area of the input pulse is smaller, effects of LFC on time evolutions of the pulse and populations are remarkably smaller than those in the case of larger area pulse. (c) 2008 Elsevier B.V. All rights reserved.

Accelerogram processing using reliability bounds and optimal correction methods

This study addresses the problem of obtaining reliable velocities and displacements from accelerograms, a concern which often arises in earthquake engineering. A closed-form acceleration expression with random parameters is developed to test any strong-motion accelerogram processing method. Integration of this analytical time history yields the exact velocities, displacements and Fourier spectra. Noise and truncation can also be added. A two-step testing procedure is proposed and the original Volume II routine is used as an illustration. The main sources of error are identified and discussed. Although these errors may be reduced, it is impossible to extract the true time histories from an analog or digital accelerogram because of the uncertain noise level and missing data. Based on these uncertainties, a probabilistic approach is proposed as a new accelerogram processing method. A most probable record is presented as well as a reliability interval which reflects the level of error-uncertainty introduced by the recording and digitization process. The data is processed in the frequency domain, under assumptions governing either the initial value or the temporal mean of the time histories. This new processing approach is tested on synthetic records. It induces little error and the digitization noise is adequately bounded. Filtering is intended to be kept to a minimum and two optimal error-reduction methods are proposed. The "noise filters" reduce the noise level at each harmonic of the spectrum as a function of the signal-to-noise ratio. However, the correction at low frequencies is not sufficient to significantly reduce the drifts in the integrated time histories. The "spectral substitution method" uses optimization techniques to fit spectral models of near-field, far-field or structural motions to the amplitude spectrum of the measured data. The extremes of the spectrum of the recorded data where noise and error prevail are then partly altered, but not removed, and statistical criteria provide the choice of the appropriate cutoff frequencies. This correction method has been applied to existing strong-motion far-field, near-field and structural data with promising results. Since this correction method maintains the whole frequency range of the record, it should prove to be very useful in studying the long-period dynamics of local geology and structures.

Estudo clínico randomizado duplo cego comparando duas técnicas de plicatura nasal após osteotomias tipo Le Fort I

A correção de deformidades esqueléticas da face por meio de um tratamento ortodôntico-cirúrgico tornou-se uma opção segura e previsível. Os movimentos ósseos são milimetricamente calculados e executados cirurgicamente, assim como a oclusão é meticulosamente engrenada através dos movimentos ortodônticos. Os efeitos que os tecidos moles sofrem com as cirurgias ortognáticas são, no entanto, menos previsíveis, e apesar do principal objetivo da cirurgia ortognática ser uma melhora funcional, o componente estético é sem dúvida de extrema importância. Em especial, a região de base alar apresenta resultados muito variáveis, a despeito dos bons resultados esqueléticos atingidos. O objetivo deste estudo foi comparar 2 diferentes tipos de sutura utilizados na região de base do nariz, e observar qual tipo apresenta um resultado que melhor acompanhe os movimentos realizados pelo tecido esquelético. Trinta e cinco pacientes foram aleatoriamente distribuídos em 2 grupos. O grupo 1 funcionou como controle e os pacientes receberam a plicatura nasal intra-oral, que é o tipo de plicatura nasal mais descrito na literatura. Já os pacientes do grupo 2 receberam plicatura nasal extra-oral. Para análise estatística foram calculadas as médias e desvios padrões dos grupos, e a hipótese nula de que não havia diferença entre os 2 grupos foi testata com o teste T de Student. Em ambos os grupos ocorreu um alargamento da base do nariz, porém a média de alargamento do grupo 1 foi de 2,50 milímetros (mm), enquanto que a média de alargamento do grupo 2 foi de 1,26 mm. Além disso, o desvio padrão foi menor para o grupo 2, e a hipótese nula foi rejeitada (p<0,05), demonstrando que a diferença entre os grupos foi estatisticamente significativa. Pôde-se concluir que quando objetiva-se um controle mais previsível e rigoroso da base do nariz, a plicatura nasal extra-oral cumprirá melhor esta função.