量子比特的门操作与共形映照

Gate Operations of Qubit and Conformal Mapping

一个双态量子体系即量子比特。在忽略一个位相因子的情况下,可以将量子比特表示在Riemann复球面上,即量子比特的Bloch球表示。采用球极射影,可以将量子比特的Bloch球表示等同于扩充复平面的复数表示。考虑一位量子比特的门操作,将幺正变换与复平面上一类特殊的共形映照相联系。研究表明,量子比特的门操作与共形映照有着密切的关系。

A two-level quantum system is a quantum bit（qubit）.Without the consideration of quantum coherence, qubit can be expressed on Riemann complex sphere,i.e. Bloch sphere representation. Identifying the Bloch sphere representation of qubit with the extended complex plane by means of stereographic projection and considering the gate operations of single qubit, we obtain equivalance relation between unitary operations and one special kind of contformal mappings.The investigation shows that there is close relation between gate operations of qubit and conformal mappings.