Abstract
The thesis consists of two parts for investigating protection of quantum bits(qubits). For this purpose, the first part deals with the ubiquitous decoherence problem for the spin-based qubits. Spin as a building block of qubit(s) in open systems is explored. In particular, we develop a highly efficient method within the dynamical decoupling scenario against the disturbance from the outside world. This method aims at solving the general decoherence problem arising from the Heisenberg-like spin-spin interaction. In the second part, we investigate the Majorana modes which are known to be robust. Motivated by experimental indications, we study the phase diagram of high-Tc superconductors in the presence of the Rashba spin-orbit interaction. Besides, we find a topological phase transition driven by the fact: the dk vector from the spin-triplet pairing is nonparallel to the gk vector in the Rashba spin-orbit interaction. This effect was overlooked in the previous studies. Though the tran- sition point is beyond the mean-field parameter space, this single-particle Hamiltonian without any disorders, two-particle interactions and even external field is the minimal model which reveals that topological phase transition does not need a full gap closing and reopening process. This is contradictory to the generic concept of topological phase transition. We also study the transport properties in N-S junctions and Josephson junctions. Particularly, we point out that the momentum dependent critical length lc(ky) plays a crucial role for the detection of Majorana fermions in high-Tc cuprate superconductors.