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康涅狄格大学B. 90年代末一个令人震惊的理论发现？他的研究表明，直接利用量子力学定律的计算装置在解决许多重要的计算问题时，可以大大超过任何经典计算机。这激发了一个广泛的，持续的努力，既要实现这样的系统，并了解他们的全部计算能力。量子随机游走是重要的算法工具，例如，在最有效的已知量子算法中出现的基本问题，如元素独特性（即，确定元素是否存在的问题）。比如一个名字或者一个号码在一个长列表中出现两次）和某些逻辑电路的评估。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，它们与超冷原子物理学领域的量子扩散有直接联系。我们的目标是给出第一个严格的分析，一个现实的量子随机行走，因此，一个明确的指示，一个候选的量子系统实现这样的行走。在这个提议中，我们打算联合计算机科学和物理学的两个新的子领域，即量子随机行走（QRW）和超冷原子系统。更确切地说，我们将探索如何开发工具来研究简单模型中的量子随机游走，以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成对应于量子随机游走可解的模型。这两种互补的方法将导致对量子扩散至关重要的系统的复杂潜在行为的洞察。此外，凝聚态物理学、原子物理学、分子物理学和光学物理学中的一大类系统？比如高温超导体或者量子磁体被认为是由模型描述的，例如玻色-哈伯德模型或其许多推广之一，其中量子扩散起着关键作用。我们计划探索如何能够控制这样的系统，以便简化的实验设置，如超冷里德伯原子或超冷原子-离子混合物，可以用来模拟简单的模型，其中量子随机行走（从而量子扩散）的解决方案是已知的。我们将继续通过REU计划（我们已经向数十名学生介绍了真实的研究课题）和研究生研究指导我们成功的培训工作。此外，PI将开发和教授一门多学科课程，名为？量子信息与计算在KAST（孩子们也是科学家），一个为期5天的计划，为4日至9年级的学生，我们将建立新的模块基于儿童？他对技术和计算机的迷恋。此外，PI将继续参与达芬奇项目，这是一个向高中教师介绍工程、数学和物理主题的项目，这些主题可以融入他们的高中科学课程。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