Geometric Quantum Computation And The Study Of Problems Of Quantum Information Transmission

Quantum computation and quantum information is an interdiciphne of quantum mechanics, computer and information sciences. During the past two decases, it has been continuing to be one of the focus points attended by many researchers who work in the physical and information science field. On one hand, realizing and controlling a quantum logic gate is attended by people because of its inportance for quantum computation. How to realize quantum computation, the schemes are not a few. But the problem is that controlling and manipulating on microscopic quantum states in experiment is very difficult. The schemes which are puted forward at'present have mainly made use of the interaction of atoms and optical-cavity, cold trapped ion, electronics spin or nuclear magnetic resonance, quantum dots manipulation and superconducting quantum interference etc. . Now it is hard to say that which kind of schemes is much useful. However, the quantum dots and superconducting Jbsephsdn junction schemes are suitable for integration and miniaturization. Taking this problem into account, we propose a new geometric quantum computation method. On the other hand, because of the novel nature of quantum teleportation and the importance of the accessible information of quantun signal resource ensembles in quantum communication field, which provide a powerful tool and method for the proof of security of quantum key distribution, enhancing the research of this aspect has the important realistic meaning and practical value to the development of quantum information. In practice, this dissertation focuses on the study of the aforementioned two problems, we have investigated and analyzed the controlling mechanism of the adiabatic conditional geometric quantum phase-shift gates for two-qubit, and realized the geometric quantum computation by making use of the nonadiabatic geometric phase of quantum states of the superconducting Josephson junctions quantum interference device system. We have also discussed the accessible information of quantum signal resource ensemble, and studied the teleportation of an arbitrary d-dimensional TV-particle unknown state via a partially-entangled quantum channel;This dissertation comes in four parts. The first part includes chapter 1 and 2. In chapter 1, a brief review about the development of quantum computation and quantum information is given. The basic content of the study of quantum computation and quantum information is summarized. In chapter .2, the foundation knowledge of classical computation and classical information theory, and also quantum computation and quantum information theory are reviewed. In order to study geometric phaseexpediently in chapter 3 and 4, we have discussed the Berry phase of quantum state evolving adiabatically and the Aharnonov-Anandan phase of quantum state evolving nonadiabatically.The second part, which includes chapter 3 and 4, is designed to discuss the problem about geometric quantum computation: the study of the effective controlling and manipulating on the two-qubit conditional geometric quantum phase-shift gate and the realization of the two-qubit nonadiabatic conditional geometric quantum phase gate. In chapter 3, we focus our attention on discussing the geometric phase(Berry phase) of quantum state evolving adiabatically and the controlling mechanism about the two-qubit conditional geometric quantum phase-shift gate realized by using of the adiabatic geometric phase-shift. We also show the relationships between the frequency of the external laser fields and the transition of the qubit in the two-qubit conditional geometric quantum phase-shift gate, explaining in detail how the transition of the qubit depends on the the external laser fields and the states of the controlling qubit. We also detail the theoretical ideas which explain how to control effectivly the two-qubit conditional geometric quantum phase-shift gates through external laser fields. In chapter 4, We propse a method to control the dc-SQUID (superconducting quantum interference device) system b...