Research On Coherence Preserving Control Strategies In Master Equation Based Open Quantum Systems

The combination of classical information theory and the quantum theory has given birth to the quantum information theory, which is expected to complete many tasks which can not be completed by the classical information processing capabilities. Its development may bring about epoch-making changes in the computer science, which has aroused widespread concerns in the scientific community. In recent years, some quantum computing programme has been realized in the laboratory, some into practical use of quantum logic devices has also started taking shape in front of us.But to see these brilliant results at the same time, we must pay more and more attention to the new challenges: as the very foundation of the quantum information processing, the coherence effects and the entanglement properties are so fragile that can easily be damaged during the interaction between the states of the system and the environment. This environment-induced, dynamical destruction of quantum coherence is called decoherence, which is the most severe obstacle to achieve quantum computation. It leads to a dynamical selection of a distinguish set of pure states of the open quantum system and counteracts the superposition principle in the Hilbert Space. So overcoming the decoherence effects and constructing the highly controllable quantum processes for fault-tolerant operation is the key to achieve high-performance quantum computing.Against the problem, based on the analysis of the relationship between the quantum control and the suppression of quantum decoherence, strategies are investigated to keep the coherence in several typical open quantum systems, emphasis are placed on the specific decoherence factors such as the dissipation, the drift and the decay of the systems. The main work and contributions are as follows:(1) The quantum stochastic differential equation derived from the Lindblad form quantum master equation is mainly investigated. The general formulation in terms of environment operators representing the quantum state diffusion is given. The constructive decoherence Lindblads' compact on the evolution and the dynamics of the system including drift and dissipation is analyzed separately. The numerical simulation algorithm for stochastic process of direct photodetection of a driven two-level system on high performance computer is provided to predict the dynamical behavior. Its superiority is verified compared with the classical Runge-Kutta algorithm, followed by further discussions on the convergence of the algorithm. The purpose of this part is to provide a theoretical basis and programme guidance to make sure that the follow-up strategies can control various forms of decoherence to maintain the coherent feature.(2) An optimal control strategy to suppress the unexpected decoherence effect with general description in the quantum master equation is put forward. Practical considerations are raised to find a simpler solvable form of the master equation from which the control strategy can be easier to derive. The orthogonal basis of geometric algebra is used to convert the quantum master equation into the state-space model; in which the useful coherent vector can be attained to quantify the coherence properties of the general systems. Then the corresponding recursive algorithm is designed to achieve both the maximal suppression of decoherence and the control energy minimizing in a typical two-level quantum system. Afterwards, some tips on how to choose the parameters are discussed. Simulation results have verified its effectiveness and superiority to coherence-preserving.(3) Expand the general decoherence formulation to some typical lindblad form which stands for some specific physical meaning of the decoherence factors arised from the interaction with the environment including the dissipation, drift or decay of the system information, etc. And then correspond control method is designed for suppress the decoherence terms. Special attention is paid to the following two systems—A cavity-QED model in the presence of atomic radiation and the spontaneous emissions. The other one is the three-level atom system with decoherence due to the spontaneous atomic radiation caused by coherent spontaneous emission. In order to handle these two issues, the solutions are as follows:a. Rabi oscillation is analyzed, as well as the conditions to keep it from vanishing. In order to eliminate the unexpected decoherence effect to the Rabi oscillation, the transfer function of Rabi oscillation is deduced using optical Bloch equations, in which one of the important cause of decoherence in Cavity QED-the atom's spontaneous emission is considered especially. A root locus based compensation system is set up to realize coherence preserving via Rabi oscillation stabilization. And what is more, a quantum tomography technology combined physical realization is put forward in succession.b. For reducing the unexpected decoherence effect in a A-typed three-level atom system, the master equation of an atomic system is investigated to find a set of states that had zero spontaneous decay rates. Two laser fields are introduced to prepare the decoherence-free state via DFS strategy to suppress spontaneous emission for the decoupling of the system's state and the environment.