Preparation Of Quantum Gates By Control Theoretic Methods

This Thesis focuses on the implementation of quantum gates using the methods from control theory and engineering.Since,realization of robust quantum gates is very important for the realization of working quantum computers,methods of controlling quantum systems for quantum gate preparation are very important for the realization of working quantum computer.In this thesis,Lyapunov based method has studied for the realization of one qubit quantum gates and optimal control based methods has been used to realize two qubit quantum gates.For the implementation of one qubit quantum gates,we employed Lyapunov based method due to fact that one qubit systems are simplest possible quantum systems and evolution of one qubit systems either lies on or inside the Bloch Sphere,which is very which is very simple geometric structure,evolution of this kind of systems is similar to classical rotations on or inside a sphere.Multi-qubit quantum systems differ from one qubit systems in the sense that we cannot consider their evolution as evolution on spheres only,this is due to effect of interaction which results into phenomenon entanglement in multi-qubit quantum systems,this is the main reason that we did not extend our Lyapunov based approach to multi-qubit systems.For the implementation of coherent control for multi-qubit qubit quantum systems,most widely employed approach is optimal quantum control.Optimal Control based strategies have advantage that experimental constraints like control frequency band limitations and amplitude limitations can also be considered in the implementation.Therefore,for two qubit quantum gate synthesis we applied optimal control methods like Krotov method,GRAPE,CRAB and Combination of CRAB and gradient based method.In this thesis all these approaches are studied and compared for the preparation of Controlled-NOT gate in closed two qubit quantum systems with Ising type drift.It has also been shown in this thesis that,gradient based optimal control approaches for quantum gate design perform better than non-gradient approaches.