Numerical Simulations of Quantum Computers and Disordered Systems

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，在量子计算机上可以比在经典计算机上更有效地解决某些专门问题。在这个项目中解决的问题是，最终的量子计算机是否可以，此外，解决广泛的优化问题，比使用量子绝热算法的经典计算机更有效。PI在若干优化问题上得到的结果表明，该算法最简单的应用并不比经典算法在大问题规模上有任何改进。因此，PI将利用量子绝热算法固有的灵活性，看看对它的修改是否会带来显著的改进，并将该算法应用于其他类型的问题。特别是，PI将研究量子算法在机器学习领域是否有帮助。PI还将研究自旋玻璃领域的几个问题，自旋玻璃是具有无序和挫折的系统。自旋玻璃研究的重要性远远超出了它们最初研究的稀释磁性合金的相当狭窄的领域，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和结构玻璃（例如窗户玻璃）。自旋玻璃是研究这类问题的一个方便的系统，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在理论上表示。理解自旋玻璃也有助于我们理解其他问题。特别是，PI将应用使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事业，并成为科学尖端劳动力的一部分。PI最近的学生在他的指导下将学到的思想应用于学术界和工业界。PI还将继续教授他在研究中使用的技术，作为计算物理课程的一部分，这些课程面向本科生和研究生。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计算机中的信息以“比特”的形式存储，其值为1或0。有人提出，某些问题可以在量子计算机上更有效地解决，在量子计算机上，比特被“量子位”取代，这些量子位遵循量子力学定律，可以同时处于状态1和0，这被称为叠加。到目前为止，由于少量的外部噪声会破坏叠加态，制造有用的量子计算机非常困难。然而，如果量子计算机能够被建造出来，那么在量子计算机上可以有效地解决什么问题仍然是一个值得研究的问题。PI将研究一类特定的广泛问题，即最优化问题，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。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还将研究一类被称为“自旋玻璃”的系统，这种系统在低温下表现出玻璃的行为，也就是说，它们不会达到平衡，但总是随着时间而进化。自旋玻璃的发展理念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和结构玻璃（如窗户玻璃）。自旋玻璃是研究这类问题的一个方便的系统，因为它们可以在实验中进行详细的探索，并且可以用适合计算机模拟的简化模型在理论上表示。理解自旋玻璃也有助于我们理解其他问题。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事业，并成为科学尖端劳动力的一部分。PI最近的学生在他的指导下将学到的思想应用于学术界和工业界。PI还将继续教授他在研究中使用的技术，作为计算物理课程的一部分，这些课程面向本科生和研究生。

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.