CDI Type-I: Quantum Diffusion and Quantum Random Walks in Physical Systems

CDI Type-I：物理系统中的量子扩散和量子随机行走Alexander Russell (PI)、Robin Côt´e 康涅狄格大学 B.项目摘要 90 年代末的一项令人震惊的理论发现表明，直接利用量子力学定律的计算设备可以在许多重要的计算问题上显着超过任何经典计算机。这引发了广泛、持续的努力，以实现此类系统并了解其全部计算能力。该项目重点关注量子随机游走和量子扩散。量子随机游走是重要的算法工具，例如，出现在最有效的已知量子算法中，用于解决元素独特性（即确定一个元素（例如名称或数字）是否在长列表中出现两次的问题）和某些逻辑电路的评估等基本问题。从实现的角度来看，量子随机游走特别有吸引力，因为它们可能比通用量子计算机更容易忠实地实现。特别是，它们与量子扩散（超冷原子物理学的一个领域）有直接联系。我们的目标是对现实的量子随机游走进行首次严格分析，从而明确表明用于实现此类游走的候选量子系统。智力价值。在这个提案中，我们打算结合计算机科学和物理学的两个新子领域，即量子随机游走（QRW）和超冷原子系统。更准确地说，我们将探索为研究简单模型中的量子随机游走而开发的工具如何适应与感兴趣的物理系统相对应的更现实的情况。相反，我们将研究现实的物理系统，这些系统可以被设计为与可通过量子随机游走求解的模型相对应。这两种互补的方法将有助于深入了解量子扩散至关重要的系统的复杂潜在行为。此外，凝聚态物理和原子、分子和光学物理中的一大类系统？例如高温超导体或量子磁体？被认为是通过模型来描述的，例如玻色-哈伯德模型或其许多概括之一，其中量子扩散起着关键作用。我们计划探索如何控制此类系统，以便利用简化的实验装置（例如超冷里德伯原子或超冷原子离子混合物）来模拟已知量子随机游走（以及量子扩散）解决方案的简单模型。更广泛的影响。我们将通过 REU 计划（我们已经向数十名学生介绍了真正的研究课题）和研究生研究指导继续我们成功的培训工作。此外，PI 将开发并教授一门名为“量子信息和计算”的多学科课程。在 KAST（孩子们也是科学家）（面向 4 至 9 年级学生的为期 5 天的项目）中，我们将根据孩子们对技术和计算机的迷恋构建新模块。此外，PI 将继续参与达芬奇项目，该项目向高中教师介绍可以纳入高中科学课程的工程、数学和物理主题。B-1

CDI Type-I: Quantum Diffusion and Quantum RandomWalksin Physical SystemsAlexander Russell (PI), Robin C?ot´eUniversity of ConnecticutB. Project SummaryA shocking theoretical discovery of the late 90?s demonstrated that a computational apparatus directly harnessing the laws of quantum mechanics could dramatically outpace any classical computer for a number of important computational problems. This instigated a broad, ongoing effort both to implement such systems and to understand their full computational power.This project focuses on quantum random walks and quantum diffusion. Quantum random walks are important algorithmic tools appearing, for example, in the the most efficient known quantum algorithms for basic problems such as element distinctness (that is, the problem of determining if an element?such as a name or a number?appears twice in a long list) and evaluation of certain logic circuits. Quantum random walks are particularly attractive from the standpoint of implementation as they are presumably simpler to faithfully implement than a general purpose quantum computer. In particular, they possess a direct connection to quantum diffusion, an area of ultracold atomic physics. Our goal is to give the first rigorous analysis of a realistic quantum random walk and, thus, a clear indication of a candidate quantum system for implementing such walks.Intellectual merit. In this proposal, we intend to join forces of two new subfields of computer science and physics, namely quantum random walks (QRW) and ultracold atomic systems. More precisely, we will explore how the tools developed to investigate quantum random walks in simple models can be adapted to more realistic situations corresponding to physical systems of interest. Conversely, we will study realistic physical systems that could be engineered to correspond to models solvable with quantum random walks.These two complementary approaches will lead to insight about the complex underlying behavior of systems where quantum diffusion is crucial. Additionally, a large class of systems in condensed matter physics andatomic, molecular, and optical physics ? such as high-temperature superconductors or quantum magnets ? are thought to be described by models, such as the Bose-Hubbard model or one of its many generalizations,where quantum diffusion plays a key role. We plan to explore how one can control such systems so that simplified experimental setups, such as ultracold Rydberg atoms or ultracold atom-ion mixtures, can be exploited to mimic the simple models where the solutions to quantum random walks (and thus quantumdiffusion) are known.Broader impacts. We will continue our successful training efforts via the REU program (we have introduced dozens of students to real research topics) and graduate research guidance. Additionally, the PIs will develop and teach a multidisciplinary course entitled ?Quantum information and computation.?Within KAST (Kids Are Scientists Too), a 5-day program for 4th through 9th grade students, we will build new modules based on children?s fascination with technologies and computers. Additionally, the PIs will continue involvement in the DaVinci project, a program introducing high-school teachers to topics inengineering, mathematics, and physics that can be integrated into their high school science curricula.B-1