Quantum Phase And Its Application

Geometric quantum computing is a quantum information processing toconstruct the geometric quantum gate by using the geometric phase in quantumphysics system. Geometric quantum computing is a fault-tolerant quantum computingwith an intrinsic property, which not only can effectively reduce the error in theprocess of computing and communications but also can improve the ability ofresistance to decoherence.On the first part, a novel approach to geometric phase of mixed state is proposedby using the normalized spinorial representation in connecting the density matrix withmixed state vector, in which all the decoherence of the system was studied effectively.On the second part, we seek for an oscillating center solution of the wave functionsatisfying Schr dinger equation for a nonrelativistic charge particle in an arbitraryexternal field, at the same time all the physical system should satisfy Schrodingerequation. We get the wave function in which the center of Landau energy levels is aharmonic oscillator, which successfully explains the sports center of the quantum halleffect. On the last part, by investigating a particle motion in an instructive quantumsystem with moving three dimensional potential barrier, we find that due to analteration of boundary conditions, the wave function pick up an additional Nonlocalphase factor. This phase factor is not dependent on the dynamics of physical system.We show that, especially, the nonlocal feature of quantum behavior can fully bedescribed by the geometric phase.