Researches On Geometry Phase Gate And Quantum Algorithm

Quantum computation and quantum information is an interesting new subject, which is a combination of quantum mechanics and computation or information science. It makes quantum state information carrier, and manages quantum information by state preparation and manipulation. Quantum algorithm is not only the most difficult challenge on quantum computation, but also the reason for lots of research on quantum computation, the discovers of Grover algorithm and Shor algorithm force people devoting into this subject. The inconceivable characters of quantum teleportation and quantum cryptography inspire many people. Since the trapped ions is the very important physical systems by which the theories of quantum information and quantum computation can be demonstrated and tested, the system play very important roles in studying quantum information and quantum computation. The main contents are as follows:1. Realization of geometric phase gates. Quantum logic gates is the basic elements of quantum computation and quantum information, and the research on geometric phase gates which avoids some mistakes has some significance. We propose an alternative scheme for the implementation of geometric phase gate with trapped ions. In the present protocol, the laser beam is tuned to ionic transition frequency, the gate speed is much faster and the system is robust against decoherence. Moreover, we can realize the geometric phase gate without implementing any pure geometric qubit operaion.2. Realization of quantum random walk. Quantum random walk is the generalization of the random walk in quantum system, and it was hoped as a basic to construct a new quantum algorithm. In resent years, a new quantum random walk search algorithm has been found, which nearly has the same speed as the Grover search algorithm. We propose a scheme to implement the quantum random walk on a line in an ion trap, we only use a stand-wave laser pulse and a periodic fastπ/2 pulse to implement the quantum walk, the experiment matter is quite simple.3. Realization of quantum game. Quantum game is an interesting new subject, which is a combination of quantum mechanics and game theory. It has been shown that some problem which cannot be resolved in classical game, can be done well in quantum game. We propose a scheme to realize the two-player quantum Prisoner's Dilemma with hot trapped ions. Based on the interaction between two ions and bichromatic radiation, the vibrational mode in our scheme is only virtually excited so that the system is insensitive to the thermal field.