In fault-tolerant quantum computation and quantum error-correction one is interested on Pauli matrices that commute with a circuit/unitary. We provide a fast algorithm that decomposes any Clifford gate as a $\textit{minimal}$ product of Clifford transvections. The algorithm can be directly used for finding all Pauli matrices that commute with any given Clifford gate. To achieve this goal, we exploit the structure of the symplectic group with a novel graphical approach.

翻译：在容错量量计算和量子误差校正中,人们感兴趣的是使用电路/统一处理的保利矩阵。我们提供了一种快速算法,将任何克里福德门分解成克里福德转换器的$\ textit{minimal}$产品。该算法可以直接用于寻找与任何特定克里福德门通勤的所有保利矩阵。为了实现这一目标,我们用新的图形方法利用随机组的结构。