本論文的目的是利用『非線性H_∞強健控制數值求解』的方式，將H_∞控制應用於微觀世界的量子系統。電子在互相糾纏時會傳遞量子訊息，這是量子電腦與量子通訊的一切基礎，因此量子狀態的操縱與控制變得極為重要。本論文將考慮多電子自旋耦合系統的模型，引入外擾並設計H_∞量子控制器，透過H_∞控制的強健功能，使得量子系統在外界環境的干擾下，能夠保持量子態的穩定。
目前國際上對電子自旋耦合模型的討論僅侷限於單一電子或雙電子，本論文將擴展現有文獻的成果，建立描述N個電子自旋耦合的模型，並透過磁場的加入，實現以『磁場控制電子』的方法。論文的主要工作是將薛丁格方程式化成多電子自旋耦合的雙線性系統，接著將Hamilton-Jacobi PDE方程式化簡成等義的狀態相依Riccati方程式，透過數值疊代的求解建立H_∞量子控制器，並引入複數化外擾來模擬量子系統的環境外擾。最後以雙電子、三電子和四電子自旋來驗證量子系統H_∞控制的強健性，同時檢測在各種環境外擾的作用下，量子H_∞強健控制是否能確保量子態的穩定。

The main purpose of this thesis is to apply a numerical solution of nonlinear H_∞ robust control to the microscopic quantum system. When electrons are entangled with each other, quantum information is transmitted. This is the basis of quantum computers and quantum communication. Therefore, the manipulation and control of quantum states become extremely important. This thesis considers the nonlinear control of multi-electron spin coupling system in the presence of external disturbances. Through the robustness of H_∞ control, the quantum system is shown to remain stable under the disturbance of the external environment.
At present, the discussion of the electron spin coupling model is limited to a single electron or two electrons. This thesis will generalize the results of the existing literature to establish a model describing N spin-coupling electron, and realize the H_∞ control through the addition of a magnetic field. The main work of the thesis is to transform the Schrödinger equation into a multi-electron bilinear equation. Then the Hamilton-Jacobi PDE is reduced to the equivalent state-dependent Riccati equation, and the H_∞ quantum controller is solved by numerical iteration. Furthermore, complex external disturbances are introduced to establish the environmental disturbances of quantum systems. Finally, two-electron, three-electron and four-electron spin coupling models are used to verify the robustness of the H_∞ control by testing whether it can ensure the stability of the quantum system under the influence of various external disturbances.

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