Geometric Phase Of Two-particle System In Open System

In 1982, Feynman proposed using the principle of superposition of quantum States creating quantum computers that can be parallel computing. However, large-scale quantum size calculation process have Decoherence effects because of inevitably affected by environmental, manufacturing controlled qubit become difficultly in technical. Such that the geometric phase is fault tolerant has become the object of study. In this dissertation, we focused on geometric phase of two-qubit system in open system and the influence of environmental factors. Main contents:Firstly, drew geometric phase under different parameters, Hamiltonian and Lindblad equation can be described in a Markov approximation, when we considered the destructive effects of the environment to superconducting two-particle system in open system. By solving the density matrix formulation of the Lindblad equation, and taking into account the two-qubit entanglement in different degrees, we had investigated the evolution rule of time associated Pancharatnam phase. We known that ideal geometric phase has the advantage of a cyclical and prone phenomenon of Decoherence in the time evolution process, by observing the Pancharatnam geometry evolution with time, we selected the best parameter for controlling qubit to provide references.Secondly, by analysis the significance of phase transitions in the evolution over time of geometric phase. Through observation geometric phase change in the time evolution of the multiple sets of parameters, we found a phase transition. It existed a bit of instant decay phenomena in early superconducting quantum coherence, there are many rules associated with the geometric phase transformation.These results will help in numerical prediction and control of geometric phase of evolution.