本論文介紹量子計算的基本原理，並探討其在量子退火與量子機器學習兩大領域中的應用。第一部分中，我們透過將旅行推銷員問題（Traveling Salesman Problem, TSP）轉換為二次無約束二元最佳化（Quadratic Unconstrained Binary Optimization, QUBO）問題，應用量子退火進行求解，展現量子方法處理NP-困難問題的能力。
第二部分中，我們回顧了數種量子機器學習演算法，包括量子卷積神經網路（Quantum Convolutional Neural Network, QCNN）與量子支援向量機（Quantum Support Vector Machine, QSVM）。最後，我們展示如何將量子演算法應用於實際的印刷電路板（PCB）缺陷檢測任務，並與傳統方法進行效能比較。實驗結果顯示，量子計算在理論分析與實務問題解決方面皆展現出相當潛力。

In this thesis, we present the fundamentals of quantum computing and explore its applications in both quantum annealing and machine learning. In Part 1, we apply quantum annealing to solve the Traveling Salesman Problem (TSP) by formulating it into a Quadratic Unconstrained Binary Optimization (QUBO) problem. This demonstrates the capability of quantum methods to address NP-hard problems.
In Part 2, we then review several quantum machine learning algorithms, including the quantum convolutional neural network (QCNN) and the quantum support vector machine (QSVM). Finally, we demonstrate how quantum algorithms can be applied to a practical PCB defect detection task, comparing their performance with classical approaches. The results highlight the potential of quantum computing in both theoretical and real-world problem domains.

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