We develop a semantic framework for higher-order quantum computation based on a boundary-centric presentation of compact closed categories, building on Kelly--Laplaza and Abramsky.Morphisms are polarized boundary linkings composed by execution, with a unit-free monoidal sum providing reversible control and branching. We identify a notion of \emph{essential unitarity} generalizing unitarity from first-order processes to higher-order interfaces;at first order it coincides with standard unitarity, and at higher order it characterizes when information is preserved relative tothe boundary. Essential unitarity is the unique predicate compatible with dagger-monoidal structure, coherence reindexing, and currying, and reducing to ordinary unitarity at first order. Every morphism of the quantum core is essentially unitary. The framework realizes the coherent quantum switch and other one-slot, equal-ratio, purity-preserving supermaps as coherent pure-comb dilations. Extended Abstract appears in QPL 2026

翻译：我们基于闭紧幺半范畴的边界中心表示，发展了一个高阶量子计算的语义框架，该框架建立在Kelly–Laplaza与Abramsky的工作之上。态射是由执行过程组合的极化边界连接，并利用无单位幺半和运算实现可逆控制与分支。我们提出了“本质幺正性”的概念，将幺正性从一阶过程推广至高阶接口；在一阶情形下，它与标准幺正性一致，而在高阶情形下，它刻画了信息相对于边界得以保持的条件。本质幺正性是唯一与dagger-幺半结构、余指标重排及柯里化相容的谓词，并且在一阶时退化为通常的幺正性。量子核心中的每个态射都是本质幺正的。该框架实现了相干量子开关及其他单插槽、等比率、保纯度超映射作为相干纯组合膨胀。扩展摘要见QPL 2026。