The implementation of controlled adiabatic and nonadiabatic evolutions quantum gates in open systems

Abstract

In the last two decades, theoretical and experimental works on quantum information have achieved noticeable progress. The theoretical results demonstrate that quantum computers can perform computational tasks better than the classical one. However, building a complete quantum computer that can solve real computational problems is still difficult. The main challenge to implement a quantum computer is to come with a model that is very robust to the environment effect. Today, the two fundamental quantum computational models frequently used in the experimental side are the gate model and the adiabatic evolution one. These two models are basically used to implement quantum gates and quantum circuits. Recently, Itay Hen could combine the gate model and the adiabatic one to come with a new model called the controlled adiabatic evolutions. In this thesis, we investigated the robustness of Itay’s model to the external environment. Besides, we proposed a new model similar to Itay’s one that gives a speed advantage to implement quantum gates. We start our work by illustrating the general frame of this research study. After, we provided an overview of the area of quantum computation. We discussed the origins and the history of the field, and the primary application of quantum computing. In the main work, we introduced Itay’s model and illustrated how we could implement the fundamental elementary gates and prepare Bell’s states based on the controlled adiabatic evolutions model. Next, we studied the robustness of Itay’s model to the different type of noise using Monte-Carlo quantum trajectory and Lindblad master equation. As an alternative to Itay’s model, we proposed a new approach similar to his model but with nonadiabatic evolutions. The new model allows speeding the implementation process of the quantum gate. Also, we studied the reliability of our model in the case of the presence of noise using the same approaches used with Itay’s model. We concluded the study by comparing the effectiveness of the controlled adiabatic process with the controlled nonadiabatic one.