Quantum Mathematics and Geometry

量子数学与几何

• 批准号: 1013079
• 负责人: Greg Kuperberg
• 金额: $ 27.56万
• 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: 2010
• 资助国家: 美国
• 起止时间: 2010-07-01 至 2014-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1013079&HistoricalAwards=false
• 关键词: Quantum; Mathematics; Geometry

The proposed research will explore the mathematical ideas of quantum computation and quantum information theory, and related ideas in mathematics itself. A defining feature of the mathematics of quantum theory is non-commutativity, the idea the "A times B" does not always equal "B times A". This is reflected in experiments in quantum mechanics that the outcomes of measurements depends on the order in which they are measured; moreover, measurements in quantum mechanics are inherently statistical. The phenomenon of non-commutativity leads to surprising new algorithms that could run on quantum computers if they are one day constructed. In mathematics itself, quantum-style non-commutativity has led to many new ideas in geometry, such as new notions of symmetry, and in topology, such as new methods to describe and distinguish knots and similar topological objects. The PI plans to investigate connections and new constructions among all of these types of quantum mathematics.

拟议的研究将探讨量子计算和量子信息理论的数学思想以及数学本身中相关的思想。 量子理论数学的一个定义特征是非共同性，“ A Times B”的想法并不总是等于“ B倍A”。 这反映在量子力学的实验中，测量结果取决于测量的顺序。此外，量子力学的测量本质上是统计的。 非交换性的现象会导致令人惊讶的新算法，如果量子计算机有一天构建，它们可能会在量子计算机上运行。 在数学本身中，量子风格的非交换性导致了许多新想法，例如新的对称性概念，以及拓扑结构，例如描述和区分结和类似拓扑对象的新方法。 PI计划在所有这些类型的量子数学中调查连接和新结构。