We introduce the monoidal closed category qCPO of quantum cpos, whose objects are "quantized" analogs of omega-complete partial orders (cpos). The category qCPO is enriched over the category CPO of cpos, and contains both CPO, and the opposite of the category FdAlg of finite-dimensional von Neumann algebras as monoidal subcategories. We use qCPO to construct a sound model for the quantum programming language Proto-Quipper-M (PQM) extended with term recursion, as well as a sound and computationally adequate model for the Linear/Non-Linear Fixpoint Calculus (LNL-FPC), which is both an extension of the Fixpoint Calculus (FPC) with linear types, and an extension of a circuit-free fragment of PQM that includes recursive types.

中文翻译：

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量子 CPO

我们介绍了量子 cpos 的幺半群闭范畴 qCPO，其对象是 omega 完全偏序 (cpos) 的“量化”类似物。范畴 qCPO 比 cpos 的范畴 CPO 更为丰富，并且包含 CPO 和有限维冯诺依曼代数的范畴 FdAlg 的对立面作为幺半群子范畴。我们使用 qCPO 为通过项递归扩展的量子编程语言 Proto-Quipper-M (PQM) 构建了一个健全的模型，以及为线性/非线性固定点演算 (LNL-FPC) 构建了一个合理且计算充足的模型，它既是具有线性类型的固定点微积分 (FPC) 的扩展，也是包含递归类型的 PQM 无电路片段的扩展。