论文标题
克利福德·盖茨（Clifford Gates）生成的四个量子位
Four qubits generated by Clifford gates
论文作者
论文摘要
Clifford组是由受控门，Hadamard Gate和P = {{1,0}，{0，I}} Gate生成的一组门。我们会说，如果可以使用克利福德·盖茨（Clifford Gates）准备，则N Qubit State是Clifford州。在本文中，我们研究了所有四个Qubit Clifford州的集合。我们证明有293760个州，其纠缠熵必须为0、2/3、1、4/3和5/3。我们还表明，这些状态中的任何一对都可以使用本地门和最多3个cnot大门连接。我们通过将293760个状态分为18组来实现这一目标，其中一组可以与本地克利福德门连接。然后，我们研究不同的CNOT门如何对18组作用。我们还在克利福德（Clifford Gates）的子组C_R的作用下研究了克利福德国家（Clifford State），具有真实的条目。这次，我们表明，每对具有真实条目的克利福德状态最多都可以连接到C_R中的5个CNOT门和本地门。链接https://youtu.be/42mi6ks2_eu导致YouTube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 controlled not gates, the Hadamard gate and the P={{1,0},{0,i}} gate. We will say that a n-qubit state is a Clifford state if it can be prepared using Clifford gates. In this paper we study the set of all 4-qubit Clifford states. We prove that there are 293760 states and their entanglement entropy must be either 0, 2/3, 1, 4/3 and 5/3. We also show that any pair of these states can be connected using local gates and at most 3 CNOT gates. We achieve this by splitting the 293760 states into 18 groups where each pair of states in a group can be connected with a local Clifford gate. We then study how the different CNOT gates act on the 18 groups. We also study the Clifford states with real entries under the action of the subgroup C_R of Clifford gates with real entries. This time we show that every pair of Clifford states with real entries can be connected with at most 5 CNOT gates and local gates in C_R. The link https://youtu.be/42MI6ks2_eU leads to a YouTube video that explains the most important results in this paper.
