分散式秀爾演算法之模擬分析研究

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：49

、訪客IP：18.191.166.122

姓名

陳渝翔(Yu-Hsiang Chen) 查詢紙本館藏

畢業系所

通訊工程學系

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)

相關論文

★ 運用SIFT特徵進行光學影像目標識別	★ 語音關鍵詞辨識擷取系統
★ 適用於筆記型電腦之WiMAX天線研究	★ 應用於凱氏天線X頻段之低雜訊放大器設計
★ 適用於802.11a/b/g WLAN USB dongle曲折型單極天線設計改良	★ 應用於行動裝置上的雙頻(GPS/BT)天線
★ SDH設備單體潛伏性障礙效能分析與維運技術	★ 無風扇嵌入式觸控液晶平板系統小型化之設計
★ 自動化RFID海關通關系統設計	★ 發展軟體演算實現線性調頻連續波雷達測距系統之設計
★ 近場通訊之智慧倉儲管理	★ 在Android 平台上實現NFC 室內定位
★ Android應用程式開發之電子化設備巡檢	★ 鏈路預算估測預期台灣衛星通訊的發展
★ 在中上衰落通道中分集結合技術之二階統計特性	★ 先進長程演進系統中載波聚合技術的初始同步

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

[檢視]

[下載]

本電子論文使用權限為同意立即開放。
已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

摘要(中)

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。

摘要(英)

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.

關鍵字(中)

★ 分散式計算
★ 量子演算法
★ 秀爾演算法

關鍵字(英)

★ Distributed computing
★ quantum algorithms
★ Shor′s algorithm

論文目次

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

參考文獻

[1] E.R. Johnson, N. Harrigan, and M. Gimeno-Segovia, Programming Quantum
Computers, O’Reilly Media, Boston, MA (2019)
[2] C. Bernhardt, Quantum computing for everyone, MIT Press, Cambridge, MA
(2019)
[3] H. T. Larasati and H. Kim, "Simulation of Modular Exponentiation Circuit for
Shor′s Algorithm in Qiskit," 2020 14th International Conference on
Telecommunication Systems, Services, and Applications
[4] Thomas Monz et al. ,Realization of a scalable Shor algorithm.Science351,1068-
1070(2016).
[5] H. Singh, D. Gupta, and A. Singh, “Quantum key distribution protocols:
A review,” Journal of Computational Information Systems, vol. 8, pp.
2839–2849, 2012.
[6] P.W. Shor, Algorithms for quantum computation: discrete logarithms and
factoring, in: Proceedings of the 35th Annual Symposium on Foundations of
Computer Science, 1994, pp. 124–134.
[7] P.W. Shor, Polynomial-time algorithms for prime factorization and discrete
logarithms on a quantum computer, Siam Review 41 (2) (1999)pp.303–332.
[8] D. K. Kumar, E. H. Venkata Krishna, R. Ushasri, V. Jahnavi, K. B. Prakash and S.
Imambi, "Implementation Of Grover′s and Shor′s Algorithms In Quantum
Machine Learning," 2023 International Conference on Intelligent and Innovative
Technologies in Computing, Electrical and Electronics (IITCEE), Bengaluru,
India, 2023, pp. 967-972
[9] C. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters,
Teleporting an unknown quantum state via dual classical and ´Einstein-Podolsky-Rosen channels, Physiscal Review Letters, 70 (13) (1993)
pp.1895–1899
[10] G. R. Mounica, G. Manimaran, L. B. Jerome and P. Bhattacharjee,
"Implementation of 5-Qubit approach-based Shor′s Algorithm in IBM Qiskit,"
2021 IEEE Pune Section International Conference (PuneCon), Pune, India, 2021,
pp. 1-6,
[11] Skosana, U., Tame, M. Demonstration of Shor’s factoring algorithm for N =
21 on IBM quantum processors. Sci Rep 11, 16599 (2021)
[12]Jr. Samuel J. Lomonaco, A. Yimsiriwattana. "Distributed quantum computing: A
distributed Shor algorithm" (2004)
[13]J. Avron, O. Casper, I. Rozen, Quantum advantage and noise reduction in
distributed quantum computing, Physical Review A, 104 (5) (2021)
052404.
[14] Xiao, Ligang, et al. "Distributed Shor′s algorithm." arXiv preprint
arXiv:2207.05976 (2022).
[15] Peng, Xinhua, et al. "Quantum adiabatic algorithm for factorization and its
experimental implementation." Physical review letters 101.22 (2008): 220405.
[16] Vidal, Guifré. "Efficient classical simulation of slightly entangled quantum
computations." Physical review letters 91.14 (2003): 147902.
[17] Griffiths, R. B. & Niu, C.-S. Semiclassical Fourier transform for quantum
computation. Phys. Rev. Lett. 76, 3228–3231 (1996).
[18] Lu, C.-Y., Browne, D. E., Yang, T. & Pan, J.-W. Demonstration of a compiled
version of Shor’s quantum factoring algorithm using photonic qubits. Phys. Rev.
Lett. 99, 250504 (2007).
- 32 -
[19] Amico, M., Saleem, Z. H. & Kumph, M. An experimental study of Shor’s
factoring algorithm on ibm q. Phys. Rev. A 100, 012305 (2019).
[20] IBM Experience, Shor’s Algorithm, (https://quantumcomputing.ibm.com/docs/iqx/guide/shors-algorithm)
[21] IBM Qiskit Experience (https://quantum-computing.ibm.com/).

指導教授

林嘉慶(Jia-Chin Lin)

審核日期

2023-7-20

推文