arXivDaily arXiv每日学术速递 周一至周五更新
arXiv周末暂无论文更新,休息一下吧,周末愉快~~
arXiv 2004.13472cs.PLcs.LOmath.CTquant-ph
收藏

量子编程语言的线性依赖类型理论

Linear Dependent Type Theory for Quantum Programming Languages

Peng Fu, Kohei Kishida, Peter Selinger

AI总结:

本文提出量子编程语言需要线性依赖类型理论,通过幺半范畴纤维化定义语义,并扩展Proto-Quipper-M实现依赖类型,提供操作语义和原型。

摘要:

现代量子编程语言将量子资源与经典控制相结合。一方面,它们必须采用线性类型化以反映量子资源的不可克隆性。另一方面,高级且实用的语言还应支持量子电路作为一等公民,以及由某些经典参数索引的电路族。因此,量子编程语言需要线性依赖类型理论。本文通过幺半范畴的特定纤维化定义了这种类型理论的通用语义结构。Rios和Selinger(2017)提出的量子电路描述语言Proto-Quipper-M的范畴模型构成了这种纤维化的一个实例,这意味着该语言可以轻松地与依赖类型集成。随后,我们设计了通用的线性依赖类型系统以及Proto-Quipper-M的依赖类型扩展,并为其提供了操作语义和原型实现。

英文摘要:

Modern quantum programming languages integrate quantum resources and classical control. They must, on the one hand, be linearly typed to reflect the no-cloning property of quantum resources. On the other hand, high-level and practical languages should also support quantum circuits as first-class citizens, as well as families of circuits that are indexed by some classical parameters. Quantum programming languages thus need linear dependent type theory. This paper defines a general semantic structure for such a type theory via certain fibrations of monoidal categories. The categorical model of the quantum circuit description language Proto-Quipper-M by Rios and Selinger (2017) constitutes an example of such a fibration, which means that the language can readily be integrated with dependent types. We then devise both a general linear dependent type system and a dependently typed extension of Proto-Quipper-M, and provide them with operational semantics as well as a prototype implementation.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑