Application Of Optimal Control Method In Quantum Logic Gates

Nuclear magnetic resonance played a big role in the scientific research,as one of the important technology of modern analysis and testing. It is widely applied in physics,chemistry, biology, geology, medicine, material science and so on.Quantum system is vulnerable to deference from the external environment, which leads to decoherence in the system. So the duration of pulse sequence should be as short as possible. optimal control is one of the methods to optimize pulse sequence.We introduce two kinds of optimization control method. one is obtained by creating desired spin order in terms of the computing geodesics on a sphere under a special metric. Another one is numerical algorithms based on GRAPE algorithm.The first method requires the use of the geometric ideas, and calculate the length of the Geodesics by using Lagrange equation and other mathematical methods, so as to get the minimum time of the pulse sequence. The second one is numerical calculation method.Concerning the two methods mentioned above, the former converts the evolution process of quantum system into other calculation process by certain transformations, avoiding the complex computation evolution of the Hamiltonian, while the latter remarkably save the computing time with the use of GRAPE algorithm. They both effectively shorten the pulse time and improve the fidelity of quantum gate.