隨著量子領域快速發展，量子系統控制有許多方法被提出，本論文以量子Lyapunov控制及量子滑動模式控制作為主要兩個控制量子糾纏的方法。在Lyapunov函數控制中，選定末態，進行控制以達到目標糾纏態。在滑動模式控制中，吾人將糾纏測量函數視為滑動面，再以切換控制的方式將系統控制到滑動面上，進而達到穩定。本研究先建立滑動模式控制與量子糾纏的關係，再根據Lyapunov函數穩定法則，推導出滑動模式控制律，將任意狀態控制到目標糾纏態。本論文在滑動控制中加入不確定性參數，使系統在滑動面附近來回做切換，以探討不確定性參數對滑動控制的影響。論文最後比較Lyapunov控制與滑動模式控制運用在量子糾纏應用的優劣性。本論文貢獻有三，一是透過量子Lyapunov控制方法，使二位元純態量子系統達到吾人想要的目標糾纏態，二是建立滑動模式控制與量子糾纏函數之間的橋樑，最後是基於滑動模式控制，使得二位元純態量子系統由任意狀態出發，最後到達目標糾纏態。

With the rapid development in the field of quantum, numerous methods for controlling quantum systems have been proposed. This paper focuses on two main approaches for controlling quantum entanglement: quantum Lyapunov control and quantum sliding mode control. In Lyapunov function control, a target entangled state is selected, and control is applied to achieve the desired entangled state. In sliding mode control, we treat the entanglement measurement function as a sliding surface and use switching control to guide the system onto the sliding surface, thereby achieving stability. This study first establishes the relationship between sliding mode control and quantum entanglement, and then derives the sliding mode control law based on the Lyapunov stability theorem, which enables arbitrary states to be controlled to the target entangled state. Uncertainty parameters are introduced into the sliding control to explore their impact on the control near the sliding surface. Finally, a comparison is made between Lyapunov control and sliding mode control regarding their advantages and disadvantages in quantum entanglement applications. The contributions of this paper can be summarized as follows: firstly, the quantum Lyapunov control method allows two-qubit pure state quantum systems to achieve the desired target entangled state; secondly, a bridge is established between sliding mode control and quantum entanglement function; and lastly, based on sliding mode control, two-qubit pure state quantum systems can be guided from arbitrary initial states to the target entangled state.

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