量子态控制中的矩阵的分解

Decomposition of matrix in quantum state control

综述了量子态的控制和矩阵分解之间的关系。着重介绍了近年采用的新的分解技术:基于群论的Cartan分解和基于数值线性代数的cosine-sine分解。介绍了用这些矩阵分解技术在量子信息科学特别是量子线路研究方面所取得的成果。这些研究成果对量子纠缠动力学、量子态的控制、量子网络的优化起到了很大的作用。最后具体地对2-qutrit门的Cartan分解作了讨论,并将它们写成指数形式。

The relationship between quantum state control and matrix decomposition is reviewed. The matrix decomposition newly applied in quantum information science, i.e. Cartan decomposition based on group theory and cosine-sine decomposition based on numerical linear algebra, is introduced firstly. Then the current research situation and the results in this area are reviewed. These results play important roles in quantum entanglement dynamics, the control of quantum states and optimization of quantum circuit Finally, the Cartan decomposition of a 2-qutrit logic gate is given .