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研究生： 陳渝翔
Yu-Hsiang Chen
論文名稱： 分散式秀爾演算法之模擬分析研究
Simulation Analysis of Distributed Shor's Algorithm
指導教授： 林嘉慶
Jia-Chin Lin
口試委員:
學位類別： 碩士
Master
系所名稱： 資訊電機學院 - 通訊工程學系
Department of Communication Engineering
論文出版年： 2023
畢業學年度： 111
語文別： 中文
論文頁數： 41
中文關鍵詞： 分散式計算 、量子演算法 、秀爾演算法
外文關鍵詞： Distributed computing, quantum algorithms, Shor's algorithm
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    • 本論文針對分散式秀爾演算法的模擬與分析進行了研究。首先，在緒論中，
    我們介紹了量子演算法的演進，旨在提供對該領域的背景和相關研究的概述。
    其次，第二章介紹了傳統的秀爾演算法，分析了其運作原理和應用領域。然
    後，第三章介紹了如何達成分散式秀爾演算法。最後，我們在第四章中分別使
    用前面介紹的量子演算法去實際分解數字 15 與 21，並對模擬實驗的結果並進行
    了討論。這些模擬實驗旨在驗證分散式秀爾演算法的性能和效能。我們通過比
    較兩種不同算法，評估了分散式秀爾演算法的優勢。最後，我們討論了未來可
    能的研究方向，以進一步改進和擴展分散式秀爾演算法的應用。

    This paper presents a study on the simulation and analysis of distributed Shor's
    algorithm. The introduction provides an overview of the evolution of quantum
    algorithms, offering background information and related research in the field. The
    second chapter introduces the traditional Shor's algorithm, introducing its
    operating principles and application domains. The third chapter focuses on the
    introduction of the distributed Shor's algorithm, which is an algorithm based on
    distributed computing frameworks, offering higher efficiency and scalability.
    Lastly, in the fourth chapter, we report the results of simulation experiments and
    engage in discussions. These simulation experiments aim to validate the
    performance and effectiveness of the distributed Shor's algorithm. By comparing
    algorithms, we evaluate the advantages and limitations of the distributed Shor's
    algorithm. Finally, we discuss potential future research directions to further
    improve and expand the application of the distributed Shor's algorithm.

    目錄 摘要................................................... i Abstract.............................................. ii 目錄.................................................. iii 圖目錄................................................. iv 第一章 緒論 ............................................1 1.1 研究背景............................................1 1.2 研究動機............................................2 1.3 研究大綱............................................3 第二章 秀爾演算法 .......................................4 2.1 秀爾演算法介紹.......................................4 2.2 量子週期尋找程式.....................................6 2.2.1 量子傅立葉變換.....................................6 2.2.2 量子相位估計.......................................8 第三章 分散式秀爾演算法..................................12 3.1 分散式秀爾演算法介紹.................................12 3.2 量子隱形傳態........................................12 第四章 模擬實驗結果與討論................................17 4.1 模冪函數電路架構....................................17 4.2 秀爾演算法量子電路..................................19 4.2.1 秀爾演算法量子電路(a=4,N=15)......................19 4.2.2 分散式秀爾演算法量子電路(a=4,N=15).................21 4.2.3 秀爾演算法量子電路(a=4,N=21)......................23 4.2.4 分散式秀爾演算法量子電路(a=4,N=21)................26 第五章 結論與未來展望...................................29 參考文................................................30

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