论文标题
Clifford组中不受控制的连通性
Controlled not connectivity in the Clifford group
论文作者
论文摘要
Clifford组是由CZ Gate生成的一组门，以及两个本地门：Hadamard和Pi/2相移门。众所周知，对于两个量子系统，Clifford组C2是4乘4个单位矩阵的组92160的子组。众所周知，本地Clifford Gates LC2是组C2组4608的子组。为了更好地理解集合C2，如果u_1 = vu_2在LC2中的某些V中，则在C2等效中制作两个矩阵U1和U2。我们表明，这种等价关系将C2分解为20个轨道O1，...，O20，每个元素具有4608个元素。此外，对于每个轨道OI，Czoi与9个不同的轨道OI1，...，OI9相交。此外，Oij和Czoi的交点为每个J = 1,2，...，，9。链接https://www.youtube.com/watch?v=lcytb2tnxfw&t=685s将您带到YouTube视频，该视频解释了本文中最重要的结果。
The Clifford group is the set of gates generated by the CZ gate, and the two local gates: the Hadamard and the Pi/2 phase shift gate. It is known that, for a two qubit system, the Clifford group C2 is a subgroup of order 92160 of the group of 4 by 4 unitary matrices. It is also known that the local Clifford gates LC2 is a subgroup of order 4608 of the group C2. In order to better understand the set C2, we make two matrices U1 and U2 in C2 equivalent if U_1=VU_2 for some V in LC2. We show that this equivalence relation splits C2 into 20 orbits, O1, ..., O20, each with 4608 elements. Moreover, for each orbit Oi, CZOi intersects 9 different orbits Oi1, ...,Oi9. Moreover, the intersection of Oij and CZOi has 512 matrices for each j=1,2, ..., ,9. The link https://www.youtube.com/watch?v=lcYtB2tnXFw&t=685s leads you to a YouTube video that explains the most important results in this paper.
