AI 中文总结
研究能否叠加程序，以量子SWITCH为例。开发新型量子编程语言，通过语义分析找出控制操作行为不当根源是对应问题，用线性类型系统解决，使其能表达量子SWITCH。
AI 中文摘要
与只能取值0或1的经典比特不同，量子比特可以处于0和1的叠加态。这引发了是否不仅能叠加数据还能叠加程序的问题，例如量子SWITCH。用比特控制程序的朴素方法在控制酉操作时有效，但对一般量子通道定义不明确，而量子SWITCH不存在此问题。基于此，本文开发了一种能在量子通道上表达量子SWITCH的新型量子编程语言。通过基于程序变换的语义分析，发现控制操作行为不当的根源是对应问题，即量子条件分支的then-和else-分支中测量缺乏协调。本文用线性类型系统解决此问题，使语言能良好表达量子SWITCH。
英文摘要
In contrast to a classical bit, which can only take the value $0$ or $1$, its quantum counterpart -- a qubit -- can exist in a superposition of $0$ and $1$. This is a superposition of data values, naturally raising the question of whether one can superpose not only data but also programs. For example, a particular superposition of programs, known as the quantum SWITCH, has attracted much attention, and its implementations and computational advantages have been studied extensively within the physics community. A naive way to control a program by a qubit is by means of a controlled operation. Given an operation $F$, this amounts to considering an operation that behaves as $F$ when the control qubit is $|1\rangle$, and as the identity operation when the control qubit is $|0\rangle$. This idea works well when $F$ is a unitary operation, but it is not well-defined for a general quantum channel. By contrast, the quantum SWITCH is free from the well-definedness issue. This contrast leads to the key insight of this paper: controlled operations and the quantum SWITCH should be regarded as different kinds of quantum control mechanisms. Building on this insight, we develop a novel quantum programming language with quantum control and measurement that can express the quantum SWITCH over quantum channels. Using a semantic analysis based on program transformations, we identify the source of the ill-behavedness of controlled operations as the \emph{correspondence problem}: a lack of coordination between the measurements performed in the then- and else-branches of quantum conditional branching. We address this problem with a linear type system that enforces alignment of the quantum operations used in the two branches, yielding a well-behaved language capable of expressing the quantum SWITCH.
Comments56 pages
