Study On The Theory Of Quantum Control Of Quantum Decoherence

Quantum computation, a new research field, will bring about great changes in ourfuture life. However, with its development, people find that the adverse effects of quan-tum decoherence, which is inevitable for any realistic quantum system, becomes thebottle-neck problem for the further advancement of quantum computation technology.In recent years, people have tried a lot of ways to conquer the quantum decoherenceand have found some methods to suppress the decoherence effectively. In this thesis, Iwill summarize these work and present the latest advances. In addition, some researchwork of me and my coworkers will be introduced in the last sections.First, we review the development history of quantum computation and quantumcontrol. The connection between them is also presented. Then, we give three differ-ent formalisms to describe quantum decoherence. We show the relations among thesethree formalisms. Especially, we induce the logical relation between the representationof super-operators and quantum master equation in detail after browsing lots of refer-ences. Furthermore, we review the main methods of suppressing quantum decoherencein quantum computation, which are: quantum error correcting, quantum deherence-free-subspace, quantum dynamical decoupling and quantum feedback control. At last,we introduce some concrete applications of the methods of dynamical decoupling andquantum feedback control. The main results are:1)We have studied the dynamical decoupling between the 2-qubit quantum mem-ory and its bath. We analyze and discuss the case of non-ideal condition. Moreover, wegeneralize the results to any N-qubit quantum memory of Ising model, exposed to itsbath.2)We have studied the dynamical decoupling of phase decoherence and amplitudedecoherence for the three-level atoms. We find the bang-bang decoupling operations forthe atom with types of Λ,V ,Cascade. We discuss the relation between the numberof bang-bang control cycles and the decoherence rate under the non-ideal case.3) Quantum localization plays an important role in the preparation and initializa-tion of quantum states. We have also studied the quantum state localization of 2-levelsystems with the quantum feedback principle. The sufficient and necessary conditionof localization is found here and the stability condition is also presented.