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    Efficient quantum approximation : examining the efficiency of select universal gate sets in approximating 1-qubit quantum gates.

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    Quantum computation is of current ubiquitous interest in physics, computer science, and the public interest. In the not-so-distant future, quantum computers will be relatively common pieces of research equipment. Eventually, one can expect an actively quantum computer to be a common feature of life. In this work, I study the approximation efficiency of several common universal quantum gate sets at short sequence lengths using an implementation of the Solovay-Kitaev algorithm. I begin by developing from almost nothing the relevant formal mathematics to rigorously describe what one means by the terms universal gate set and covering efficiency. I then describe some interesting results on the asymptotic covering properties of certain classes of universal gate sets and discuss the theorem which the Solovay-Kitaev algorithm is based on. Moving from mathematical introduction to experimental method, I then describe how sets will be compared. I use the commonly studied sets H+T, Pauli+V, V, and Clifford+T to determine which is the most efficient at approximating randomly generated unitaries. By doing so, we get an understanding of how well each set would perform in the context of a general quantum computer processor. This was accomplished by using the same implementation of the Solovay-Kitaev algorithm throughout, with roughly equal-sized preprocessed libraries formed from each gate set, over approximations for 10,000 randomly generated unitary matrices at algorithm depth n=5. Ultimately, the Pauli+V and V sets were the most efficient and had similar performance qualities. On average the Pauli+V set produced approximations of length 15,491 and accuracy 0.0002686. The V basis produced approximations of average sequence length 16,403 and accuracy 0.0001465. This performance is about equal given this particular implementation of the Solovay-Kitaev algorithm. We conclude that this result is somewhat surprising as the general behavior and efficiency of these particular choices of gate set are expected to be similar. It is possible though that the asymptotic efficiencies of these gate sets vary by a relatively wide margin and this has effected the experiment. It is also possible that some aspect of a naive implementation of the Solovay-Kitaev algorithm resulted in the Hadamard gate based sets performing more poorly than the V basis sets overall. Due to constraints on computational power, this result could also be limited to this particular accuracy regime and could even out as tolerance is taken to be arbitrarily small. Further possibilities of this result as well as further work are then discussed

    Survival of small populations under demographic stochasticity

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    We estimate the mean time to extinction of small populations in an environment with constant carrying capacity but under stochastic demography. In particular, we investigate the interaction of stochastic variation in fecundity and sex ratio under several different schemes of density dependent population growth regimes. The methods used include Markov chain theory, Monte Carlo simulations, and numerical simulations based on Markov chain theory. We find a strongly enhanced extinction risk if stochasticity in sex ratio and fluctuating population size act simultaneously as compared to the case where each mechanism acts alone. The distribution of extinction times deviates slightly from a geometric one, in particular for short extinction times. We also find that whether maximization of intrinsic growth rate decreases the risk of extinction or not depends strongly on the population regulation mechanism. If the population growth regime reduces populations above the carrying capacity to a size below the carrying capacity for large r (overshooting) then the extinction risk increases if the growth rate deviates from an optimal r-value

    Adversarial robustness of deep learning enabled industry 4.0 prognostics

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    The advent of Industry 4.0 in automation and data exchange leads us toward a constant evolution in smart manufacturing environments, including extensive utilization of Internet-of-Things (IoT) and Deep Learning (DL). Specifically, the state-of-the-art Prognostics and Health Management (PHM) has shown great success in achieving a competitive edge in Industry 4.0 by reducing maintenance cost, downtime, and increasing productivity by making data-driven informed decisions. These state-of-the-art PHM systems employ IoT device data and DL algorithms to make informed decisions/predictions of Remaining Useful Life (RUL). Unfortunately, IoT sensors and DL algorithms, both are prone to cyber-attacks. For instance, deep learning algorithms are known for their susceptibility to adversarial examples. Such adversarial attacks have been extensively studied in the computer vision domain. However, it is surprising that their impact on the PHM domain is yet not explored. Thus, modern data-driven intelligent PHM systems pose a significant threat to safety- and cost-critical applications. Towards this, in this thesis, we propose a methodology to design adversarially robust PHM systems by analyzing the effect of different types of adversarial attacks on several DL enabled PHM models. More specifically, we craft adversarial attacks using Fast Gradient Sign Method (FGSM) and Basic Iterative Method (BIM) and evaluate their impact on Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), Convolutional Neural Network (CNN), Bi-directional LSTM, and Multi-layer perceptron (MLP) based PHM models using the proposed methodology. The obtained results using NASA's turbofan engine, and a well-known battery PHM dataset show that these systems are vulnerable to adversarial attacks and can cause a serious defect in the RUL prediction. We also analyze the impact of adversarial training using the proposed methodology to enhance the adversarial robustness of the PHM systems. The obtained results show that adversarial training is successful in significantly improvising the robustness of these PHM models.Includes bibliographical references (pages 80-98)

    An age-dependent branching process with arbitrary state space II

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    Compaction and Porosity Based Pore Pressure Prediction in the “Cappe Field”, Coastal Swamp Depobelt, Niger Delta, Nigeria

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    Three wells of the “Cappe” Field in the offshore part of the Coastal Swamp depobelt I, Niger Delta, were evaluated primarily to determine the impact of compaction on reservoir quality and to determine possible over-pressured zones in the Benin and Agbada formations. Sandstone porosity-depth plots of the three wells show a linear trend of gradual porosity reduction with depth for the top of the wells 1, 2 and 3 (r2 = 0.26, 0.42 and 0.73 at 4500-5900ft, 3940-5000ft and 2500-5350ft respectively). Two variations from this simple trend were observed. 1: Intervals of insignificant porosity reduction (well 1; 6500-7950ft, r2 = 0.00003 and well 2; 5760-7911ft, r2 = 0.008), due to hydrocarbon entrapment. 2: A reversal in the trend (well 3; 5450-9658ft, r = -0.89) indicated by an increase in porosity as a result of overpressure. A number of factors such as compaction, fluid content and pore pressure affect the porosity-depth trends of the Agbada Formation. A decrease in porosity with depth generally holds true for shales (well 1: r2 = 0.74 and well 2: r2 = 0.81) except for an increase in porosity (r2 = -0.596) observed in well 3. Compaction factor is significant in sandstone porosity reduction in the Benin Formation (well 1: 58.3% and well 2: 68.9%) than in the Agbada Formation (well 1: 25.64% and well 2: 25.29%). Sandstone porosities predicted at the base of the wells are generally low (well 1: 5.86%, well 2: 7.52%), implying uneconomical reservoirs.KEY WORDS: Pore Pressure, Overpressure, Porosity, Compactio
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