量子管弦乐队：递归混合程序的具体语义
Quantum Orchestras: a Concrete Semantics for Recursive Hybrid Programs
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中文总结 AI 辅助
研究为扩展经典基础语言的量子编程语言构建指称语义的方法，通过定义基于量子仪器形式主义的量子管弦乐队单子，它是经典状态单子和概率幂域单子的自然扩展，可解释发散混合程序并研究扩展到量子非交换情况的微妙之处。
中文摘要 AI 辅助
许多量子编程语言通过扩展经典基础语言来表示混合量子计算，其中量子比特通过引用访问，量子操作被理解为改变外部量子态。然而，这种量子计算观点的语义仍未充分发展，特别是当语言允许中途测量和非终止时。在这项工作中，我们通过定义量子管弦乐队单子来为这类语言构建指称语义，它基于量子仪器形式主义，精确捕捉这种量子效应风格。该单子有具体表示，作用于范畴DCPO，能解释发散的混合程序，是经典状态单子和概率幂域单子的自然扩展。我们研究了将这些定义天真扩展到量子非交换情况时的一些微妙之处。
英文摘要
Many production quantum programming languages represent hybrid quantum computations by extending a classical base language with a quantum effect, where qubits are addressed by reference, and quantum operations are understood to mutate some external quantum state. However, the semantics of this view of quantum computation remains underdeveloped, especially when the language allows mid-circuit measurements and non-termination. In this work, we provide a general method for building denotational semantics for such languages, by defining the quantum orchestra monad, which precisely captures this style of quantum effect. The monad has a concrete presentation, being based on the formalism of quantum instruments, a common tool in quantum information theory for capturing the action of a quantum process along with its classical outcomes. It acts on the category DCPO, and so enables the interpretation of divergent hybrid programs. The quantum orchestra monad serves as a natural extension of both the classical state monad and the probabilistic powerdomain monad. We investigate some of the subtleties present when trying to naïvely extend these definitions to the quantum non-commutative case.
