Use Of The Preparation Of A Trapped Ion In The Ion Trap Quantum Logic Gate Operations And Quantum States

A combination of quantum mechanics and computer science yields an interesting new subject, quantum computers. The field of quantum computers has been revolutionized by the work of Shor on factorization of large numbers. Quantum computers can solve efficiently some of the problems that cannot be attacked by any classical computers, since for these problems there are superfast quantum algorithms thanks to quantum parallelism. In view of these advantages, we are pursuing to bring the quantum computer into being to our best. The most promising formalism we use for quantum computation, which we call a quantum "gate array", was introduced by Deutsch, who showed that a simple generalization of the Tof-foli gate suffices as a universal gate for quantum computing. The quantum gate array is the natural quantum generalization of acyclic combinational logic "circuit" studied in conventional computational complexity theory. In 1995, Barenco showed that almost any two-bit gate is universal, so building a feasible two-bit logic gate is the first step to engineer a quantum computer. In principle, the quantum bit can be carried by any two states system. Due to the importance of the interferometer in implementing the logic gate operations, the coherent time of the system used as quantum bit must be as long as that to carry out the logic gate operations at least. The trapped ions meet the above demands, so it is the best candidate. Since the trapped ion was originally proposed by Cirac and Zoller in 1995 as a system to carry out quantum computation, many experimental schemes have been tasted and succeeded. Based on the models used to deal with the interaction between the trapped ions and the laser, we investigate the physical foundation under the ion-trap computing and the evolution of the states of the trapped ions. In the "hot" trapped ions scheme, transition paths involving different unpopulated vibrational states interfere destructively to eliminate the dependence of rates and revolution frequencies on vibrational quantum numbers, so the implementation is both insensitive to thevibrational state and robust against changes in the vibrational motion occurring during operation. In consequence, quantum computation becomes feasible with ions whose vibrations are strongly coupled to a thermal reservoir. Using the evolution method, by solving the master equation analytically, we find that as the accuracy to implemente the logic gate operation is improved, the time needed is prolonged. We also give some plots showing the evolution of the probability of the states of the system. At last, we propose a method to generate two mode SU(1,1) intelligent states for the center of mass and relative motional modes for two trapped ions. In our scheme, only three laser beams are employed, and their directions are all the same as the direction of the two trapped ions' alignment. Under some initial conditions, our desired states are obtained as the steady-state solution to the master equation of the system. This method avoids the trouble in controlling the conditions during the evolution, so it is very flexible.