School of Mathematical Sciences, Capital Normal University, Beijing 100037, P R China.
Sci Rep. 2013;3:2594. doi: 10.1038/srep02594.
Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum computation with n qutrits. We show that the optimal quantum circuits are essentially equivalent to the shortest path between two points in a certain curved geometry of SU(3(n)). As an example, three-qutrit systems are investigated in detail.
确定幺正操作的量子线路复杂度是量子计算中的一个重要问题。我们使用黎曼几何的数学技术，研究了具有 n 个量子比特的量子计算中的有效量子线路。我们表明，最优量子线路本质上等同于 SU(3(n))的某个弯曲几何中的两点之间的最短路径。作为一个例子，我们详细研究了三量子比特系统。
