Feynman Diagrams and the Semantics of Quantum Computation

费曼图是作为一种工具来显示粒子如何相互作用的，但类似的图描述了其他量子系统中的信息流。最近的工作已经展示了这种图如何描述量子计算中的信息流。 该项目的第一个方面将是创建一个通用的量子编程语言，称为“量子lambda演算”。 我们希望证明所有其他量子编程语言都可以翻译成这一种。而且，用这种语言写的任何程序都可以翻译成上述类型的图。这些图将为量子编程语言提供一个“语义”，也就是说，一个系统的方法来研究这些语言中的程序实际上是做什么的。 这项研究的第二个方面将是在目前正在开发的“拓扑量子计算机”的框架内进行研究。 这种计算机是基于分数量子霍尔效应，它允许被称为“任意子”的准粒子在磁场中的超导薄膜上形成。图解法非常适合描述这种计算机。这项工作的更广泛的影响是，拟议的工作也应该有助于理解与拓扑量子场论中的思想的联系，以及量子引力工作中产生的其他数学模型;此外，应该对当前有前途的拓扑量子计算工作产生深刻的见解

Feynman diagrams were developed as a tool to show how particles interact, but similar diagrams describe the the flow of information in other quantum systems. Recent work has shown how such diagrams can describe the information flow in quantum computation. The first aspect of this project will be to create a universal quantum programming language called the 'quantum lambda calculus'. We hope to show that all other quantum programming languages can be translated into this one. Moreover, any program written in this language can be translated into a diagram of the above sort. These diagrams will give a 'semantics' for quantum programming languages that is, a systematic method for studying what programs in these languages actually do. The second aspect of this research will be a study within this framework of the 'topological quantum computers' currently under development. Such computers are based on the fractional quantum Hall effect, which allows quasiparticles called 'anyons' to form on a thin superconducting film in a magnetic field. Diagrammatic methods are perfectly suited to describing such computers. The broader implications of this workare that the proposed work should also contribute to understanding the links with the ideas in topological quantum field theories, and other mathematical models arising from the work on quantum gravity; and moreover, should yield insights on the promising current work on topological quantum computing