Numerical Simulations of Quantum Computers and Disordered Systems

量子计算机和无序系统的数值模拟

• 批准号: 1207036
• 负责人: Allan Peter Young
• 金额: $ 33万
• 依托单位: University of California-Santa Cruz
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-15 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1207036&HistoricalAwards=false
• 关键词: Numerical; Simulations; Quantum; Computers; Disordered

TECHNICAL SUMMARYThis award supports theoretical research and education to study two fields where computer simulations can give important information: quantum computers and spin glasses.It is well known that there are certain specialized problems which can be solved much more efficiently on a quantum computer than on a classical computer. The question addressed in this project is whether an eventual quantum computer could, in addition, solve a broad range of optimization problems more efficiently than a classical computer using the Quantum Adiabatic Algorithm. Results already obtained by the PI for several optimization problems indicate that the simplest application of this algorithm does not give an improvement over classical algorithms for large problem sizes. The PI will therefore use the inherent flexibility of the quantum adiabatic algorithm to see if modifications to it give a significant improvement, and also apply the algorithm to other types of problem. In particular, the PI will investigate if quantum algorithms will be helpful in the field of machine learning.The PI will also investigate several questions in the field of spin glasses, which are systems with disorder and frustration. The study of spin glasses is important far beyond the rather narrow field of dilute magnetic alloys where they were first studied, because ideas developed for them have applicability to a wide range of complex systems, such as combinatorial optimization problems in computer science, protein folding in biology, and structural glasses (e.g. window glass). Spin glasses are a convenient system in which to study this class of problems since they can be probed in fine detail in experiments by applying a magnetic field, and can be represented theoretically by simplified models which are amenable to computer simulation. Understanding spin glasses will help our understanding of these other problems as well. In particular, the PI will apply optimization methods developed using spin glass ideas to solve other optimization problems.This award will support the education of students in developing state-of-the-art algorithms for large-scale numerical simulations. The research will enable them to pursue scientific careers in many related fields and become part of a scientifically sophisticated workforce. Recent students of the PI have gone on to apply the ideas learned under his supervision in both academia and industry. The PI will also continue to teach techniques used in his research as part of courses on computational physics, which are offered to both undergraduates and graduate students.NON-TECHNICAL SUMMARYThis award supports theoretical research and education to study two fields where computer simulations can give important information: quantum computers and spin glasses Information in a computer is stored as "bits" which take values 1 or 0. It has been proposed that certain problems could be solved more efficiently on a quantum computer in which the bits are replaced by "qubits" which follow the laws of quantum mechanics and can be simultaneously in states 1 and 0, which is called a superposition. So far, it has proved very difficult to build a useful quantum computer because a small amount of external noise destroys superposition. However, it is still of interest to study what problems could be solved efficiently on a quantum computer if and when a quantum computer can be built. The PI will study whether a particular broad class of problems, known as optimization problems, can be solved more efficiently on a quantum computer than on a classical computer. Since we do not have a quantum computer, the PI will emulate the behavior of a quantum computer by doing numerical simulations on a classical computer.The PI will also study a class of systems called "spin glasses" which exhibit glassy behavior at low temperatures, that is, they do not come to equilibrium but are always evolving with time. Ideas developed for spin glasses have applicability to a wide range of complex systems, such as some optimization problems in computer science, protein folding in biology, and structural glasses (e.g. window glass). Spin glasses are a convenient system in which to study this class of problems since they can be probed in fine detail in experiments, and can be represented theoretically by simplified models which are amenable to computer simulations. Understanding spin glasses will help our understanding of these other problems as well.This award will support the education of students in developing state-of-the-art algorithms for large-scale numerical simulations. The research will enable them to pursue scientific careers in many related fields and become part of a scientifically sophisticated workforce. Recent students of the PI have gone on to apply the ideas learned under his supervision in both academia and industry. The PI will also continue to teach techniques used in his research as part of courses on computational physics, which are offered to both undergraduates and graduate students.

技术总结该奖项支持理论研究和教育，以研究计算机模拟可以提供重要信息的两个领域：量子计算机和自旋玻璃。众所周知，某些特殊问题在量子计算机上可以比在经典计算机上更有效地解决。这个项目涉及的问题是，最终的量子计算机是否还能比使用量子绝热算法的经典计算机更有效地解决广泛的优化问题。PI对几个优化问题的计算结果表明，对于大问题，该算法的最简单应用并不能给出比经典算法更好的结果。因此，PI将利用量子绝热算法固有的灵活性来查看对其进行修改是否会带来显著改进，并将该算法应用于其他类型的问题。特别是，PI将调查量子算法是否将有助于机器学习领域。PI还将调查自旋玻璃领域的几个问题，这些系统具有无序和受挫。自旋玻璃的研究远远超出了最初研究它们的相当狭窄的稀磁合金领域，因为为它们开发的想法适用于广泛的复杂系统，例如计算机科学中的组合优化问题，生物学中的蛋白质折叠，以及结构玻璃(例如窗户玻璃)。自旋玻璃是研究这类问题的一种方便的系统，因为它们可以通过施加磁场在实验中进行详细的探索，并且可以用易于计算机模拟的简化模型来表示。了解自旋眼镜也将有助于我们理解这些其他问题。特别是，PI将应用利用自旋玻璃思想开发的优化方法来解决其他优化问题。该奖项将支持学生开发用于大规模数值模拟的最先进算法的教育。这项研究将使他们能够在许多相关领域从事科学职业，并成为科学熟练劳动力的一部分。国际和平研究所最近的学生继续将在他的指导下学到的想法应用到学术界和工业界。PI还将继续教授他的研究中使用的技术，作为计算物理课程的一部分，这门课对本科生和研究生都有。非技术总结这个奖项支持理论研究和教育，研究计算机模拟可以提供重要信息的两个领域：量子计算机和自旋眼镜计算机中的信息被存储为取值为1或0的“位”。有人提出，在量子计算机上，某些问题可以更有效地解决，在这种计算机中，比特被符合量子力学定律并可以同时处于1和0态的“量子比特”取代，这被称为叠加。到目前为止，建造一台有用的量子计算机已经被证明是非常困难的，因为少量的外部噪音会破坏叠加。然而，如果能够建造量子计算机，那么在量子计算机上可以有效地解决哪些问题仍然是人们感兴趣的。PI将研究是否可以在量子计算机上比在经典计算机上更有效地解决一类特定的问题，即所谓的优化问题。由于我们没有量子计算机，PI将通过在经典计算机上进行数值模拟来模拟量子计算机的行为。PI还将研究一类在低温下呈现玻璃化行为的系统--自旋玻璃，即它们不会达到平衡，而是总是随着时间的推移而演变。发展自旋玻璃的想法适用于广泛的复杂系统，如计算机科学中的一些优化问题，生物学中的蛋白质折叠，以及结构玻璃(例如窗户玻璃)。自旋玻璃是研究这类问题的一种方便的系统，因为它们可以在实验中进行详细的探索，并且可以用易于计算机模拟的简化模型在理论上表示。了解自旋眼镜也将有助于我们理解这些其他问题。该奖项将支持学生开发用于大规模数值模拟的最先进算法的教育。这项研究将使他们能够在许多相关领域从事科学职业，并成为科学熟练劳动力的一部分。国际和平研究所最近的学生继续将在他的指导下学到的想法应用到学术界和工业界。PI还将继续教授他的研究中使用的技术，作为计算物理课程的一部分，这些课程同时面向本科生和研究生。