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: 0906366
• 负责人: Allan Peter Young
• 金额: $ 30万
• 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: 2009
• 资助国家: 美国
• 起止时间: 2009-09-15 至 2013-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0906366&HistoricalAwards=false
• 关键词: Numerical; Simulations; Quantum; Computers; Disordered

TECHNICAL SUMMARYThis award supports computational and theoretical research and education applying the tools of statistical mechanics to questions on the overall expected performance of a quantum computer and to key conceptual questions on the nature of spin glasses.A major problem in quantum computing is whether an eventual quantum computer would be able to solve a broad range of problems more efficiently than a classical computer. The PI will investigate whether the time taken, the complexity, for the quantum adiabatic algorithm to solve an ?optimization" problem on a quantum computer varies as a power of the number of variables, N, or exponentially with N. The emphasis will be on the size dependence of the minimum gap as the control parameter in the quantum adiabatic algorithm is varied. In order to determine the complexity at large N, the PI plans to develop new algorithms which will allow simulations of larger sizes than in the earlier work, and also to modify the quantum models in order to make the asymptotic dependence appear for smaller sizes.The PI will investigate numerically, the most extensively studied type of system with disorder and frustration, the ?spin glass.? Spin glass physics applies to a wide range of problems in science. Analytical calculations are very hard; so much of what is known has come from simulations. The PI will investigate several key questions: (i) Is there a line of transitions, the ?Almeida-Thouless" line, in a magnetic field?(ii) What is the nature of transition in the Heisenberg spin glass?(iii) Is there an ?ideal glass transition" in structural glasses? Most of the work will actually be carried out on a model in one-dimension with interactions which, on average, fall off as a power of the distance. The advantages of this model are (i) that large sizes can be studied, and (ii) the model is analogous to a short-range model in a finite dimension, and changing the power is equivalent to changing the dimension of the short range model. Hence spin glass physics can, in effect, be studied over a wide range of dimensions by using this model.This proposal will support the education of students in developing state of the art algorithms for large-scale computer simulations. The research will enable them to pursue scientific careers in many related fields. Techniques used in the research will be incorporated into courses on computational physics offered to both undergraduate and graduate students.NON-TECHNICAL ABSTRACTThis award supports computational and theoretical research and education applying the tools of statistical mechanics to questions on the overall expected performance of a quantum computer and to key conceptual questions on the nature of spin glasses.There is great excitement and experimental effort to determine whether a quantum computer can be made. A quantum computer would work through the preparation and manipulation of quantum mechanical states. It has been shown that for certain tasks, a quantum computer would be vastly faster than the fastest existing computers. But can they solve general problems faster than existing computers? The PI will apply computational techniques developed for the problems of Statistical Physics to understand if a proposed general purpose algorithm for a quantum computer executed on a quantum computer is more efficient than algorithms for a classical computer for large problems. This research speaks to the general performance one can expect from a quantum computer and may have impact on how the field of quantum computing evolves.The PI will also study ?spin glasses", which are archetypes for interacting systems with frustration ? systems where there is a strong competition between interactions. Spin glasses are important 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, structural glasses ? ?window glass,? etc. 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 models that succumb to computation. Understanding spin glasses will contribute to our understanding of a wide range of problems that cross disciplinary boundaries.This proposal will support the education of students in developing state of the art algorithms for large-scale computer simulations. The research will enable them to pursue scientific careers in many related fields. Techniques used in the research will be incorporated into courses on computational physics offered to both undergraduate and graduate students.

技术总结该奖项支持计算和理论研究及教育，将统计力学工具应用于有关量子计算机总体预期性能的问题和有关自旋玻璃性质的关键概念问题。量子计算的一个主要问题是，最终的量子计算机是否能够比经典计算机更有效地解决广泛的问题。PI将调查量子绝热算法在量子计算机上解决最优化问题所花费的时间和复杂性是随变量数N的幂变化还是随N的指数变化。重点是随着量子绝热算法中控制参数的变化，最小间隙的大小关系。为了确定大N的复杂性，PI计划开发新的算法，允许比以前的工作更大规模的模拟，并修改量子模型，使渐近依赖出现在更小的规模上。PI将数值研究最广泛研究的无序和受挫类型的系统--自旋玻璃。自旋玻璃物理学适用于科学中的广泛问题。分析计算非常困难；已知的很多东西都来自于模拟。PI将研究几个关键问题：(I)在磁场中是否存在一条相变线，即阿尔梅达-索利斯(Almeida-Thouless)线？(Ii)海森堡自旋玻璃中的相变是什么？(Iii)在结构玻璃中是否存在理想的玻璃相变？大部分工作实际上将在一维模型上进行，相互作用平均而言，随着距离的增加而减弱。该模型的优点是：(1)可以研究大尺度模型；(2)该模型类似于有限维的短程模型，改变幂相当于改变短程模型的维度。因此，使用这个模型可以有效地研究自旋玻璃物理。这项建议将支持学生开发用于大规模计算机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。这项研究中使用的技术将被纳入为本科生和研究生提供的计算物理课程。该奖项支持计算和理论研究和教育，将统计力学工具应用于量子计算机总体预期性能的问题和关于自旋玻璃性质的关键概念问题。在确定是否可以制造量子计算机方面，有非常令人兴奋的事情和实验工作。量子计算机将通过量子力学状态的准备和操作来工作。已经证明，对于某些任务，量子计算机将比现有最快的计算机快得多。但它们能比现有计算机更快地解决一般问题吗？PI将应用为统计物理问题开发的计算技术，以了解拟议的用于在量子计算机上执行的量子计算机的通用算法是否比用于大型问题的经典计算机的算法更有效。这项研究谈到了人们可以期望的量子计算机的一般性能，并可能对量子计算领域的演变产生影响。PI还将研究？自旋眼镜，这是具有挫折感的交互系统的原型？交互之间存在激烈竞争的系统。自旋玻璃之所以重要，是因为为它们开发的想法适用于广泛的复杂系统，如计算机科学中的组合优化问题、生物学中的蛋白质折叠、结构玻璃、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，并且可以用屈从于计算的模型在理论上表示。了解自旋眼镜将有助于我们理解一系列跨学科边界的广泛问题。这项建议将支持学生为大规模计算机模拟开发最先进的算法的教育。这项研究将使他们能够在许多相关领域从事科学事业。研究中使用的技术将被纳入为本科生和研究生提供的计算物理课程。