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游走

• 批准号: 0835735
• 负责人: Alexander Russell
• 金额: $ 55.05万
• 依托单位: University of Connecticut
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-09-15 至 2012-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0835735&HistoricalAwards=false
• 关键词: CDI; Type; Quantum; Diffusion; Random

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

CDI类型1：物理系统中的量子扩散和量子随机行走（PI）， Robin C？康涅狄格大学90年代末令人震惊的理论发现？S证明了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大大超过任何经典计算机。这激发了一项广泛的、持续的努力，既要实现这样的系统，又要了解它们的全部计算能力。本项目主要研究量子随机漫步和量子扩散。量子随机漫步是重要的算法工具，例如，在已知最有效的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）？比如名字或号码？在长列表中出现两次)和对某些逻辑电路的评估。从实现的角度来看，量子随机漫步特别有吸引力，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，它们与量子扩散有直接联系，量子扩散是超冷原子物理学的一个领域。我们的目标是给出一个现实的量子随机漫步的第一个严格的分析，因此，一个明确的候选量子系统实现这种行走的指示。知识价值。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，即量子随机漫步（QRW）和超冷原子系统。更准确地说，我们将探索如何开发用于研究简单模型中的量子随机漫步的工具，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与量子随机漫步可解的模型相对应。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，在凝聚态物理、原子、分子和光学物理中有一个大类的系统？比如高温超导体或量子磁体？都被认为是由模型来描述的，比如玻色-哈伯德模型或它的许多推广之一，其中量子扩散起着关键作用。我们计划探索如何控制这样的系统，以便简化实验装置，如超冷里德伯原子或超冷原子-离子混合物，可以用来模拟量子随机漫步（因此量子扩散）的解已知的简单模型。更广泛的影响。我们将通过REU项目（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将开发和教授一门多学科课程，名为？量子信息与计算。在为期5天的面向4 ~ 9年级学生的KAST （Kids Are Scientists Too）项目中，我们将建立以儿童为基础的新模块。美国人对科技和计算机的迷恋。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，可以整合到他们的高中科学课程中。b - 1