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Topics in complex nonlinear systems.

机译：复杂非线性系统中的主题。

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摘要

In the dissertation, I include two topics of my research in nonlinear dynamic systems. In the first topic, we use numerical optimization techniques to investigate the behavior of the success rates for two- and three-qubit entangling gates, first for perfect fidelity, and then extended to imperfect gates. We find that as the perfect fidelity condition is relaxed, the maximum attainable success rates increase in a predictable fashion depending on the size of the system, and we compare that rate of increase for several gates. Finally, we propose an experiment to test our imperfect LOQC gates using number-resolving photon detectors. We suggest a relatively simple physical apparatus capable of producing CZ gates with controllable fidelity less than 1 and success rates higher than the current theoretical maximum (S=2/27) for perfect fidelity. These experimental setups are within the reach of many experimental groups and would provide an interesting experiment in photonic quantum computing.;In the second topic, we quantitatively study nonlinear effects on the evolution of surface gravity waves on the ocean, to explore systematically the effects of various input parameters on the probability of rogue wave formation. The fourth-order current-modified nonlinear Schrödinger equation (CNLS4) is employed to describe the wave evolution. First, we show that when the average wave steepness is small and nonlinear wave effects are subleading, the wave height distribution is well explained by a single “freak index” parameter, which describes the strength of (linear) wave scattering by random currents relative to the angular spread of the incoming random sea. When the average steepness is large, the wave height distribution takes a very similar functional form, but the key variables determining the probability distribution are the steepness, and the angular and frequency spread of the incoming waves. Then, we obtain quantitative predictions for the wave height distribution as a function of those key environmental conditions. Additionally, we explore the spatial dependence of the wave height distribution, associated with the buildup of nonlinear development. Finally, even greater probability of extreme wave formation is predicted when linear and nonlinear effects are acting together.
机译：在论文中，我包括了我在非线性动力学系统中研究的两个主题。在第一个主题中，我们使用数值优化技术研究两个和三个量子位纠缠门的成功率行为，首先是获得完美保真度，然后再扩展到不完美的门。我们发现，随着理想保真度条件的放松，根据系统的大小，可达到的最大成功率将以可预测的方式增加，并且我们比较了几个门的增长率。最后，我们提出了一个使用数分辨光子探测器测试不完善的LOQC门的实验。我们建议使用一种相对简单的物理设备，该设备能够产生可控保真度小于1且成功率高于当前理论最大保真度（S = 2/27）的CZ门。这些实验设置在许多实验组的研究范围之内，将为光子量子计算提供有趣的实验。在第二个主题中，我们定量研究非线性对海洋表面重力波演化的影响，以系统地探索各种输入参数对流氓波形成的概率的影响。使用四阶电流修正非线性薛定ding方程（CNLS4）来描述波的演化。首先，我们表明，当平均波陡度较小且非线性波影响次导时，波高分布可以通过单个“奇异指数”参数很好地解释，该参数描述了随机电流相对于（线性）波的（线性）波散射强度传入随机海的角展。当平均陡度很大时，波高分布采用非常相似的函数形式，但是决定概率分布的关键变量是陡度以及入射波的角度和频率扩展。然后，我们获得了作为这些关键环境条件的函数的波高分布的定量预测。此外，我们探索了波高分布的空间依赖性，以及非线性发展的建立。最终，当线性和非线性效应共同作用时，预计会形成更大的极端波。

著录项

  • 作者

    Ying, Linghang.;

  • 作者单位

    Tulane University School of Science and Engineering.;

  • 授予单位 Tulane University School of Science and Engineering.;
  • 学科 Geophysics.;Computer Science.;Physics Fluid and Plasma.
  • 学位 Ph.D.
  • 年度 2012
  • 页码 182 p.
  • 总页数 182
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 物理化学（理论化学）、化学物理学;
  • 关键词

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