Quantum Mechanics at the Complexity Frontier

复杂性前沿的量子力学

• 批准号: 1656234
• 负责人: Christopher Laumann
• 金额: $ 27.64万
• 依托单位: Trustees of Boston University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-07-01 至 2018-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1656234&HistoricalAwards=false
• 关键词: Quantum; Mechanics; Complexity; Frontier

The development of quantum information technology promises to revolutionize both fundamental and applied science. For example, on the fundamental side, we expect that quantum devices will efficiently simulate poorly understood quantum mechanical theories, providing insight into their behavior. On the applied side, such simulations would allow for the design of new nanomaterials and biochemical molecules. The first experimental step in developing quantum devices has been to bring single quanta under complete control. This has mostly been accomplished over the last two decades. Laboratories around the world now routinely trap, isolate and probe individual atoms, ions, electrons, spins and photons. These systems form 'qubits', the elementary building blocks of quantum computers. The next step is to put these qubits together to form quantum circuits, simulators, networks and eventually computers. However, as the number of qubits in a device grows, so too does the complexity of describing and controlling the properties of that device. This complexity underlies the potential power of quantum technology but also brings many theoretical and experimental challenges. This project seeks to address two of these challenges. First, what physical mechanisms can stabilize the multi-qubit systems so as to make them usable quantum devices? One possibility is provided by a recently discovered phenomenon called 'many-body localization'. Usually, the unavoidable presence of disorder in experiments leads to difficulties controlling the qubits. Counter-intuitively, it seems that putting in more disorder can actually help by 'localizing' the quantum information, preventing it from escaping into the environment as noise. Many of the fundamental features of localization remain unknown. By a combination of classical computational and analytical studies, the group aims to elucidate the conditions under which the many-body localized phase arises, the near-term experimental consequences and its potential as an intrinsic platform for quantum computing. Second, what kinds of problems can we expect a quantum computer to be able to solve? There are efficient quantum algorithms for particular problems, such as simulating molecular structure and breaking cryptographic codes. However, the most general optimization problems are believed to be hard even for a quantum computer. What distinguishes these hard problems from the tractable ones is an outstanding open question whose answer has profound consequences. The aim is to develop a better understanding of typical quantum optimization problems through a case study of a canonical example: quantum satisfiability. It is expected that insights into this problem will lead to new heuristic quantum algorithms. A similar line of inquiry in classical computation led to important classical optimization algorithms, such as simulated annealing and belief propagation.From a somewhat more technical point of view, these two projects are related by their reliance on the techniques of disordered statistical mechanics and spin glass theory. Their study will rely on both numerical simulations using large scale classical computer clusters and analytic study using the cavity method and its quantum generalizations. This latter method was developed previously for the study of quantum spin glasses. The projects will help train one to two graduate students in the relevant physics and techniques.

量子信息技术的发展将给基础科学和应用科学带来革命性的变化。例如，在基本面上，我们期望量子设备能够有效地模拟人们知之甚少的量子力学理论，从而深入了解它们的行为。在应用方面，这种模拟将允许设计新的纳米材料和生物化学分子。开发量子器件的第一个实验步骤是将单量子置于完全控制之下。这主要是在过去二十年中完成的。现在，世界各地的实验室都在定期捕获、隔离和探测单个原子、离子、电子、自旋和光子。这些系统形成了“量子比特”，量子计算机的基本构建模块。下一步是将这些量子比特放在一起，形成量子电路、模拟器、网络，最终形成计算机。然而，随着设备中量子比特数量的增加，描述和控制该设备属性的复杂性也在增加。这种复杂性是量子技术潜在力量的基础，但也带来了许多理论和实验挑战。本项目旨在应对其中两项挑战。首先，什么样的物理机制可以稳定多量子比特系统，使它们成为可用的量子器件？一种可能性是最近发现的一种称为“多体定位”的现象。通常，实验中不可避免的无序会导致难以控制量子位。与直觉相反的是，似乎增加无序度实际上可以帮助量子信息“局部化”，防止它作为噪声逃逸到环境中。本地化的许多基本特征仍然未知。通过经典计算和分析研究的结合，该小组的目标是阐明多体局域相产生的条件，近期的实验结果及其作为量子计算内在平台的潜力。第二，我们期望量子计算机能够解决什么样的问题？对于特定的问题，例如模拟分子结构和破解密码，存在有效的量子算法。然而，最一般的优化问题被认为是困难的，即使是量子计算机。这些难题与容易处理的难题的区别在于一个悬而未决的问题，这个问题的答案具有深远的影响。目的是通过一个典型的例子：量子可满足性的案例研究，更好地理解典型的量子优化问题。预计对这个问题的深入了解将导致新的启发式量子算法。 经典计算中类似的研究路线导致了重要的经典优化算法，如模拟退火和置信传播。从更技术的角度来看，这两个项目是相关的，因为它们依赖于无序统计力学和自旋玻璃理论的技术。他们的研究将依赖于使用大规模经典计算机集群的数值模拟和使用腔方法及其量子推广的分析研究。后一种方法是以前为研究量子自旋玻璃而开发的。这些项目将帮助培训一到两名相关物理和技术的研究生。