A Simulation of Some Parameters for Linear Paul Trap to Optimize Quantum Computer Operation

Abstract

Quantum computation is a new technology with the potential for providing exponential parallelism. The feasibility of a quantum computer is limited by different sources of errors. One of the most promising proposals in this field is the Trapped Ion Quantum Computer (TIQC) that suggested by Cirac in 1995. This thesis uses simulation to investigate the feasibility of implementing this proposed model. The linear Paul trap that suggested by Paul was used in this work. and levels of the are chose as a quantum bits in this work. The effect of the errors in different physical and geometrical parameters was studied. In the TIQC each laser pulse can be represented as a mathematical transformation. These transformations can rotate the quantum register state in the Hilbert space with a desired angle. For the ideal case, to get a certain rotation, a certain arguments of the transformation can be imposed. In fact these arguments depend on many physical and geometrical parameters like angle of incident of laser, laser wavelength, trap frequency and others. In this work the effect of the variation of these parameters on the quantum register state is taken in account. The fidelity criterion is adopted in all of the results in this thesis to detect the matching between the two forms of a certain transformation. The results of this work are classified into three main classes. First the dependency of the fidelity on the laser wavelength, second the dependency of the fidelity on the laser pulse time and finally the fidelity dependency on the Rabi oscillations. From these results, the unity value of the fidelity can be achieved in different cases which can be the optimum set values of both the geometrical and physical parameters. Each set of these parameters can be considered as the best values for both the design and operation of the linear Paul trap.