Graphical description of the action of Clifford operators on stabilizer states
Graphical description of the action of Clifford operators on stabilizer states
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Clifford 算子对稳定器状态的作用的图形描述
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
C. Caves
中科院分区：
文献类型：
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作者：
M. Elliott;Bryan Eastin;C. Caves
我们引入了稳定器状态的图形表示，并将Clifford算符在稳定器状态上的作用转化为相应的稳定器-状态图上的图操作。我们的稳定器图是由实心和中空节点构成的，节点之间有(无向)边，每个节点上都有环和符号。我们发现，局部Clifford变换可以用节点上和沿边的局部互补、回路互补以及节点类型或符号的变化来完整地描述。此外，我们证明了一个小的等价规则集生成对应于给定稳定器状态的所有图；我们通过构造一个有效的程序来测试任意两个稳定器图的等价性来实现这一点。
We introduce a graphical representation of stabilizer states and translate the action of Clifford operators on stabilizer states into graph operations on the corresponding stabilizer-state graphs. Our stabilizer graphs are constructed of solid and hollow nodes, with (undirected) edges between nodes and with loops and signs attached to individual nodes. We find that local Clifford transformations are completely described in terms of local complementation on nodes and along edges, loop complementation, and change of node type or sign. Additionally, we show that a small set of equivalence rules generates all graphs corresponding to a given stabilizer state; we do this by constructing an efficient procedure for testing the equality of any two stabilizer graphs.