Decoherence In Quantum Computers And Control Of Decoherence Subspace Constructed

With the realization of quantum algorithm and the solution of error-avoiding, quantum computing(QC) has attracted many scientists' attention. Based on the properties of quantum superposition and coherence-the essence of quantum mechanics, quantum computing is intended to perform many difficult tasks which cannot be solved by classical computers. However, as the quantum system is correlated with its external environment, it is very difficult to keep coherence of qubits which is used in QC. Therefore, many people try to tackle this problem.In this thesis, the decoherence between the qubits, arisen from the interaction between the quantum system and the environment, is described. Then, the relaxation processes of electron spin in the semi-conductor doped quantum dots by the nuclear hyperfine interactions and the external magnetic field are investigated. Finally, using the subdynamics theory, the construction of the decoherence subspace is discussed.Furthermore, with the use of the kinetic equation of subdynamics and the suitable time ordering rule, a type of irreversible Liouville equation and nonlinear Liouville equation for project/open quantum systems is presented. In addition, a spectral relation for the non-equilibrium statistical distribution, based on the boundary conditions, is determined and the irreversible Liouville equation with the non-perturbative method is solved. The following conclusions can be drawn from the solutions: by using the scaling time period, decoherence disappears and the eigen-projectors are invariant and independent of the interaction in the constructed subspace, thereby making it suitable for performing quantum computing. Furthermore, the decoherence-free condition of the projected subspace is derived. Finally, to show the decoherence-free states, a model of spin-based quantum computing is constructed using the non-perturbative approach.