量子電腦是近年來量子控制的熱門領域，其中實現的方法是製造一個二階系統(two-level system)來實現一個量子位元(qubit)，利用電子穿隧的約瑟芬元件便是其中之一；本論文透過複數力學(Complex mechanics)這個具有因果內涵的量子理論，詮釋約瑟芬元件中無法利用「軌跡」來詮釋的電子穿隧現象。在傳統量子力學的架構之下，只有對一個系統的機率描述，而無粒子動態的概念；而現今科技已可達到奈米製程的等級，在分析上需要一套同時考慮古典粒子運動以及微小尺度下會產生量子效應的理論工具，以往卻未曾有人利用「軌跡」來分析約瑟芬元件。在複數力學的架構之下，不但可以很直觀地呈現電子在穿隧時的動態表現，更可以在設計階段時，提供材料的係數，利用電腦事先模擬出此材料參數對粒子穿隧程度的效益，對於未來在發展製程上將會是一套有利的工具。最後我們利用外加電壓改變電子的動能，進而改變電子的動態，達到控制穿隧的目的。在具有古典力學的動態特性的複數力學架構之下，將來更可以直接引入古典控制的理論來對約瑟芬元件穿隧的穩定性來做各種分析，提供量子控制領域一套更直觀的新工具。

Quantum computer has been the most popular topic in these few years. By making a two-level system, such as a “Josephson junction”, we can realize a quantum bit called “qubit”. In this present, we will use complex mechanics, which is a quantum theory used particle path instead of probability density to describe a quantum system. Under the framework of complex mechanics, we can not only provide the dynamic of the electron to show how the tunneling is in progress, but also do the simulation of tunneling with all the parameters of material before design work. This will be very useful and necessary for the manufacturing process in the future. In the last part of this present, we add an extra voltage to the system to make an affect in the electron’s Hamiltonian. By adjusting this parameter, we can control the dynamics of the electrons to make the tunneling happened. This will be a new and intuitive method in quantum control theory, and in the future, we even can use the classic control theory to analysis the stability of electron’s dynamics with the present of trajectories.

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