Zeta演算
The Zeta Calculus
摘要：
我们提出了一种量子编程语言，推广了$λ$ -演算。语言是非线性的;重复变量表示，不是克隆量子数据，而是共享量子位的状态;也就是说，产生一对纠缠的量子位，其振幅相对于所选的基是相同的。该语言有两个抽象运算符，$ζ$和$ξ$，分别对应于Z基和X基;每个抽象运算符也由一个相位参数化，表示在共享之前应用于输入的旋转。我们给出了ZX-演算语言的语义，并证明了它的等式理论的声音。我们展示了这种语言如何在量子世界中提供高阶函数的良好表示。
英文摘要：
We propose a quantum programming language that generalizes the $λ$-calculus. The language is non-linear; duplicated variables denote, not cloning of quantum data, but sharing a qubit's state; that is, producing an entangled pair of qubits whose amplitudes are identical with respect to a chosen basis. The language has two abstraction operators, $ζ$ and $ξ$, corresponding to the Z- and X-bases; each abstraction operator is also parameterised by a phase, indicating a rotation that is applied to the input before it is shared. We give semantics for the language in the ZX-calculus and prove its equational theory sound. We show how this language can provide a good representation of higher-order functions in the quantum world.
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