标题： 量子cpos的类别 显示英文标题

标题： Categories of quantum cpos

摘要： 本文结合了两个研究方向。 第一个方向涉及寻找量子编程语言及其类型系统的范畴模型。 第二个方向是数学结构的量化程序，这相当于寻找这些结构的非交换推广（也称为量子推广）。 使用一种称为离散量化的量化方法，这本质上相当于在冯·诺依曼代数和量子关系的范畴中内化结构，我们找到了一种非交换推广的$\omega$-完备偏序集（cpos），称为量子cpos。 cpos在域理论中处于核心地位，并被广泛用于构建编程语言的范畴模型。 我们证明了量子cpos具有与cpos类似的范畴性质，因此适合用于构建量子编程语言的范畴模型，这通过一些示例进行了说明。 因此，量子cpos可能成为未来量子域理论的骨干。 显示英文摘要

摘要： This paper unites two research lines. The first involves finding categorical models of quantum programming languages and their type systems. The second line concerns the program of quantization of mathematical structures, which amounts to finding noncommutative generalizations (also called quantum generalizations) of these structures. Using a quantization method called discrete quantization, which essentially amounts to the internalization of structures in a category of von Neumann algebras and quantum relations, we find a noncommutative generalization of $\omega$-complete partial orders (cpos), called quantum cpos. Cpos are central in domain theory, and are widely used to construct categorical models of programming languages. We show that quantum cpos have similar categorical properties to cpos and are therefore suitable for the construction of categorical models for quantum programming languages, which is illustrated with some examples. For this reason, quantum cpos may form the backbone of a future quantum domain theory.