抽象数据类型的量化
Quantisation of Abstract Data Types
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中文总结 AI 辅助
本文在泛代数框架下提出抽象量子数据类型概念，将经典数据类型量化并保留其结构关系，以量子数组、纠错码为例说明应用，为量子编程的数据抽象提供代数基础。
中文摘要 AI 辅助
本文在泛代数框架内引入了抽象量子数据类型的概念，该概念为描述量子编程中的数据抽象提供了代数基础。我们形式化定义了经典数据类型的量化，并证明其等式规范可被合理提升至量子场景。经典函数的两种标准量化方法，即比特预言机（bit oracle）和相位预言机（phase oracle），是该通用构造的特例。我们通过量子数组和量子纠错码的应用示例说明该框架，展示如何通过数据类型量化的视角理解它们。我们进一步建立了量化保持经典数据类型的结构关系与构造的条件，包括嵌入、同构和乘积。
英文摘要
In this paper, we introduce a notion of abstract quantum data type within the framework of universal algebra. This notion provides an algebraic foundation for describing data abstraction in quantum programming. We formally define a quantisation of classical data types and show that their equational specifications can be soundly lifted to the quantum setting. Two standard quantisation methods for classical functions, namely the bit oracle and the phase oracle, arise as special cases of this general construction. We illustrate the framework with applications to quantum arrays and quantum error-correcting codes, showing how they can be understood through the lens of data-type quantisation. We further establish conditions under which quantisation preserves structural relationships and constructions of classical data types, including embeddings, isomorphisms, and products.
