CAREER: Algebraic and Semiclassical Methods for Quantum Computing

职业：量子计算的代数和半经典方法

• 批准号: 0747526
• 负责人: Willem van Dam
• 金额: $ 32万
• 依托单位: University of California-Santa Barbara
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-02-01 至 2015-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0747526&HistoricalAwards=false
• 关键词: CAREER; Algebraic; Semiclassical; Methods; Quantum

This project explores the power and limitations of quantum computers using new analytical techniques from algebraic geometry and the physics of semi-classical systems. Whether or not we decide to spend large amounts of resources on the construction of a scalable quantum computer will depend largely on the expected benefits of such a machine, but our current understanding of this issue is still very limited. The research of this project should give us a better picture of the usefulness of processing information in a quantum mechanical way by providing a dictionary between the properties of quantum circuits and some of the more intuitive ideas in geometry. The outreach component consists of the design and implementation of an authoritative, annotated bibliography of online sources of information on quantum computing, which will be made freely available to those outside of academia.The evolution of a quantum computer is best described as a weighted sum of classical computations, where each weight is a complex valued probability amplitude. As a result, the overall probabilities of the quantum computation can be calculated using the corresponding exponential sums of amplitudes, which is a concept that has been studied extensively in algebraic geometry. In this project we translate the geometric and topological ideas behind these exponential sums to the properties of the corresponding quantum circuits. From a physical point of view, the phase of an amplitude is proportional to its `action', which, through the Least Action Principle, plays a crucial role in connecting quantum mechanics with classical mechanics. We use this viewpoint to relate quantum computation to its sum of classical computational paths.

该项目使用代数几何形状和半古典系统物理学的新分析技术探索量子计算机的功能和局限性。我们是否决定花费大量资源来构建可扩展量子计算机的计算机，这在很大程度上取决于这种机器的预期收益，但是我们目前对此问题的理解仍然非常有限。该项目的研究应该使我们可以更好地了解以量子机械方式处理信息的有用性，通过在量子电路的属性与几何形状中一些更直观的思想之间提供词典。外展部分包括设计和实施量子计算的在线信息来源的权威，带注释的书目，该参考书目将免费提供给学术界以外的人。量子计算机的演变最好将其描述为经典计算的加权总和，在每个重量都具有复杂的阀门概率上。结果，可以使用相应的振幅指数总和来计算量子计算的总体概率，这是在代数几何形状中进行广泛研究的概念。在这个项目中，我们将这些指数总和背后的几何和拓扑思想转化为相应的量子电路的属性。从物理的角度来看，振幅的阶段与其“作用”成正比，该动作通过最少的动作原理在将量子力学与经典力学联系起来中起着至关重要的作用。 我们使用此观点将量子计算与其经典计算路径的总和相关联。