Quantum methods in mathematics and computer science

数学和计算机科学中的量子方法

• 批准号: 1319245
• 负责人: Greg Kuperberg
• 金额: $ 35.85万
• 依托单位: University of California-Davis
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-09-01 至 2018-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1319245&HistoricalAwards=false
• 关键词: Quantum; methods; mathematics; computer; science

The aim of this project is to explore theoretical ideas in mathematics and computer science that are related to quantum mechanics. Quantum mechanics is a physical theory that, notably, requires a new model of probability theory that can be called quantum probability, and this in turn leads to the theory of quantum computing and the possibility of building quantum computers. The project will investigate quantum algorithms (algorithms that could be run on quantum computers) for problems in topology, for example determining whether two knots are equivalent or different. The project will also investigate quantum error correction (a new kind of error correction that would be needed by quantum computers) in the setting of a new kind of geometry, "quantum metric spaces", in which distances are defined in the language of quantum probability. Finally the project will explore quantum algebra, which is a kind of modern algebra with non-commuting variables also inspired by quantum mechanics and which has relations to quantum computing.This project will have at least two and potentially three broader impacts. First, all work will be disseminated on the arXiv, a widely used preprint server that includes most work in quantum computing, and the principal investigator will help support the arXiv. Second, the project will include development of lecture notes, which could be made into a future graduate textbook, on quantum probability, quantum computing, and quantum mechanics. Third, if quantum computers are ever build, they will have an extremely broad impact, and the ideas in this project will play a role.

该项目的目的是探索与量子力学相关的数学和计算机科学的理论思想。量子力学是一种物理理论，值得注意的是，它需要一种新的概率论模型，可以称为量子概率，这反过来又导致了量子计算理论和构建量子计算机的可能性。 该项目将研究拓扑问题的量子算法（可以在量子计算机上运行的算法），例如确定两个结是否相等或不同。 该项目还将在一种新型几何学“量子度量空间”的设置中研究量子纠错（量子计算机所需的一种新型纠错），其中距离用量子概率的语言定义。 最后，该项目将探索量子代数，这是一种具有非交换变量的现代代数，也受到量子力学的启发，并且与量子计算有关。该项目将产生至少两个、可能三个更广泛的影响。 首先，所有工作都将在 arXiv 上传播，arXiv 是一种广泛使用的预印本服务器，其中包括量子计算方面的大部分工作，首席研究员将帮助支持 arXiv。 其次，该项目将包括编写关于量子概率、量子计算和量子力学的讲义，这些讲义可以被制作成未来的研究生教科书。 第三，如果量子计算机建成，它们将产生极其广泛的影响，这个项目中的想法将发挥作用。

项目成果

Computational complexity and 3–manifolds andzombies

计算复杂性和 3 流形和僵尸

• DOI: 10.2140/gt.2018.22.3623
• 发表时间: 2018
• 期刊: Geometry & Topology
• 影响因子: 2
• 作者: Kuperberg, Greg;Samperton, Eric
• 通讯作者: Samperton, Eric