标题： 准-克利福德到量子比特映射 显示英文标题

标题： Quasi-Clifford to qubit mappings

摘要： 带有给定(反)交换结构的代数在量子力学中很常见。 这种结构由准 Clifford 代数(QCA)来描述：由$\alpha_1, \dots, \alpha_n$生成的 QCA 由关系$\alpha_i^2 = k_i$和$\alpha_j \alpha_i = (-1)^{\chi_{ij}} \alpha_i \alpha_j$给出，其中$k_i \in \mathbb{C}$和$\chi_{ij} \in \{0, 1\}$。 我们提出了一种从 QCA 到泡利代数的映射，并讨论其在量子信息和计算中的应用。 该映射还提供了具有准 Clifford 结构的矩阵群的 Wedderburn 分解。 这为例如泡利群提供了块对角化，而对于马约拉纳算子，则恢复了 Jordan-Wigner 变换。 讨论了在半定规划的对称性约简和构造最大反对易子集中的应用。 显示英文摘要

摘要： Algebras with given (anti-)commutativity structure are widespread in quantum mechanics. This structure is captured by quasi-Clifford algebras (QCA): a QCA generated by $\alpha_1, \dots, \alpha_n$ is is given by the relations $\alpha_i^2 = k_i$ and $\alpha_j \alpha_i = (-1)^{\chi_{ij}} \alpha_i \alpha_j$, where $k_i \in \mathbb{C}$ and $\chi_{ij} \in \{0, 1\}$. We present a mapping from QCA to Pauli algebras and discuss its use in quantum information and computation. The mapping also provides a Wedderburn decomposition of matrix groups with quasi-Clifford structure. This provides a block-diagonalization for e.g. Pauli groups, while for Majorana operators the Jordan-Wigner transform is recovered. Applications to the symmetry reduction of semidefinite programs and for constructing maximal anti-commuting subsets are discussed.