Theoretical Study On The Optimal Transfer Control Of The Quantum State Population

The establishment of quantum control theory can greatly promotes much development of the fields such as quantum physics, bond selective chemistry, and quantum information. However, due to the complexity and properties of quantum systems themselves, reach on quantum control still need to pay an untiring endeavor of the scholars in various domains.Under such a background, on the basis of reviewing the background of papers and the development status of the quantum control theory, from the viewpoint of the control theory this thesis studies the applications of optimal control theory to quantum systems, including population transfer control, maintaining of coherence and quantum fidelity. The main contents are as follows.1) Based on closed quantum systems, the population transfer control problem is researched. Because of the reliability or the efficiency of a general optimal control scheme leave much to be desired, the thesis presents a general method for formulating monotonically convergent algorithms to iteratively improve control fields. At last, we theoretically proved the effectiveness of the design, which are verified by numerical simulations experiments.2) Based on closed quantum systems, we propose a time-optimized method to control the unitary time evolution in a quantum unitary gate using the Heisenberg model. For two class of states00> and01>, the time-optimized generation of any target states under a uniform magnetic field is analyzed, and a new strategy based on the time-optimized method to generate two qubit entangled states is also suggested. We theoretically proved the effectiveness of the design, which are verified by numerical simulations experiments.3) The methods of population transfer control for open quantum systems are studied. At first, the orthogonal basis of geometric algebra is used to convert the quantum master equation into the state-space model; using the Pontryagin maximum principle, the idea of optimal control of population transfer is designed with a time minimum cost functional. According to the dissipative dynamics of open quantum systems, an optimal control method without iteration is proposed to transfer the population. According to the Lindblad form of open quantum systems with relaxation and dissipation, a optimal control laws without iterations is designed to achieve the population transfer. Lastly, we theoretically proved the effectiveness of all designs, which are verified by numerical simulations experiments.