本研究主要探討將Transformer模型用於預測糾纏二分量子之近似。量子糾纏是一種基本且重要的量子力學現象，其特性使得量子計算機在某些特定問題上具有高效的計算效率。本研究旨在通過訓練深度學習模型來分解量子密度矩陣，從而縮短計算時間。本研究結果表明，雖然Transformer模型在訓練集上的表現令人滿意，但在測試集上的表現仍有待提高。研究結果和方法對於未來量子計算的應用具有重要意義。

This study mainly explores the application of the Transformer model for predicting the approximation of entangled bipartite quantum systems. Quantum entanglement is a fundamental and significant phenomenon in quantum mechanics, whose properties enable quantum computers to achieve efficient computational performance on certain specific problems. This research aims to decompose quantum density matrices by training a deep learning model, thereby reducing computation time. The results indicate that the Transformer model performs satisfactorily on the training set. However, the performance on the test set still needs improvement. The findings and methods of this research hold significant implications for future applications in quantum computing.

目錄
第一章 緒論 1
1.1 背景 1
1.2 目的 1
第二章 人工智慧與量子糾纏介紹 3
2.1 人工智慧 3
2.2神經網路 4
2.3卷積神經網路 6
2.4 大型語言模型LLM 8
2.5 Transformer 10
2.6 二分量子系統 12
2.7 量子糾纏 13
第三章 研究方法 15
3.1二分量子糾纏數學公式 15
（一）問題說明 15
3.2 Transformer計算方法 15
（一）Scaled Dot-Product Attention 15
（二）Multi-head Attention 16
（三）編碼器與解碼器 17
第四章 研究結果與結論 19
4.1 資料集 19
4.2 資料處理 19
4.3 模型設定 19
4.3 研究結果 20
參考文獻 23

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