We propose an extension to the Pauli stabiliser formalism that includes fractional $2\pi/N$ rotations around the $Z$ axis for some integer $N$. The resulting generalised stabiliser formalism – denoted the XP stabiliser formalism – allows for a wider range of states and codespaces to be represented. We describe the states which arise in the formalism, and demonstrate an equivalence between XP stabiliser states and 'weighted hypergraph states' – a generalisation of both hypergraph and weighted graph states. Given an arbitrary set of XP operators, we present algorithms for determining the codespace and logical operators for an XP code. Finally, we consider whether measurements of XP operators on XP codes can be classically simulated.

中文翻译：

---

XP 稳定器形式主义：具有任意相位的泡利稳定器形式主义的推广

我们提出了对泡利稳定器形式主义的扩展，其中包括对某个整数 $N$ 围绕 $Z$ 轴的分数 $2\pi/N$ 旋转。由此产生的广义稳定器形式主义——表示为 XP 稳定器形式主义——允许表示更广泛的状态和代码空间。我们描述了形式主义中出现的状态，并证明了 XP 稳定器状态和“加权超图状态”之间的等价性——超图和加权图状态的概括。给定任意一组 XP 运算符，我们提出了用于确定 XP 代码的代码空间和逻辑运算符的算法。最后，我们考虑是否可以经典地模拟 XP 码对 XP 算子的测量。