The Study Of Geometric Phase In Quantum Systems

The phase has important significant even more than the probability amplitude in quantum mechanics. In the past decades, a lot of studies such as Pancharatnam phase, A-B effect, A-C effect, Berry phase and its promotion and application, which have drawn our attention to a fact that geometric phase is a part of wave function in quantum mechanics. Nowadays, the study of geometric phase has spilled over into many branches of physics, including optics, molecular physics, nuclear physics, and condensed matter physics.Quantum information is the combination of quantum mechanics and informatics. Quantum bits have more properties such as superposition and entanglement, which bring the brilliant prospect to quantum information. However, there are some obstacles on the implement of quantum computer:In the real physical world, quantum system could be spontaneous radiation or interact with environment inevitable, which lead to decoherent. Therefore, geometric quantum computation emerged. The main contents are as follows:1. Based on the A-C effect, we deducing the wave function of system whether earth’s rotation exists respectively by using Foucault pendulum’s Hamiltonian. From the discussion of the wave functions in two situations, we demonstrate the clockwise rotation of pendulum is caused by the earth’s rotation. In addition, we propose an improvement scheme about neutron interference experiment, which would observe the geometric effect.2. Since universal quantum logic gates can be constitutive of single-qubit gates and two-qubit controlled phase gates, we discuss the universal geometric quantum logic gates. Moreover, we deduce the geometric phase in quantum composite system, and figure out the connection between it and parameters.3. We briefly discuss the quantum description of pure state and mixed state in quantum computing, and its corresponding representation on Bloch sphere and Poincare sphere. Combining with geometric effect, we discuss the global phase of pure state from geometric structure, and then extended to the case of mixed state.