论文标题
根据施密特等级和CNOT大门构建三分之三的统一大门
Constructing three-qubit unitary gates in terms of Schmidt rank and CNOT gates
论文作者
论文摘要
众所周知，每一个两分的统一操作都有施密特排名一，两个或四个，而在施密特等级方面，建造三量的统一大门仍然是一个开放的问题。我们明确地构建了施密特的大门从1到7。事实证明，三分之二的toffoli和弗雷德金门分别使施密特排名第二和四。作为应用程序，我们使用CNOT门的量子电路以及局部的Hadamard和Flip门实现了门。特别是，三个CNOT门的集体使用可以从乘法复杂性中的已知strassen张量来生成Schmidt排名第七的三分位单位门。我们的结果暗示了用于实施多QUAT门的CNOT门数与其Schmidt等级之间的联系。
It is known that every two-qubit unitary operation has Schmidt rank one, two or four, and the construction of three-qubit unitary gates in terms of Schmidt rank remains an open problem. We explicitly construct the gates of Schmidt rank from one to seven. It turns out that the three-qubit Toffoli and Fredkin gate respectively have Schmidt rank two and four. As an application, we implement the gates using quantum circuits of CNOT gates and local Hadamard and flip gates. In particular, the collective use of three CNOT gates can generate a three-qubit unitary gate of Schmidt rank seven in terms of the known Strassen tensor from multiplicative complexity. Our results imply the connection between the number of CNOT gates for implementing multiqubit gates and their Schmidt rank.
