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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/30243完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 顏嗣鈞 | |
| dc.contributor.author | Yu-Han Yang | en |
| dc.contributor.author | 楊育翰 | zh_TW |
| dc.date.accessioned | 2021-06-13T01:46:01Z | - |
| dc.date.available | 2008-07-19 | |
| dc.date.copyright | 2007-07-19 | |
| dc.date.issued | 2007 | |
| dc.date.submitted | 2007-07-10 | |
| dc.identifier.citation | [1] P. Shor, “Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer,” SIAM J. Comp., 26: 1484-1509, 1997.
[2] L. Grover, “A fast quantum mechanical algorithm for database search,” Proceedings of STOC’96, pp. 212-219. [3] M. A. Nielsen and I. L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, Cambridge, UK, 2000. [4] U. Schöning. “A probabilistic algorithm for k-SAT and constraint satisfaction problems,” Proc. 40th IEEE Symp. Foundations of Computer Science, pp. 410-414, October 1999. [5] D. Meyer. “From quantum cellular automata to quantum lattice gases,” Journal of Statistical Physics, 85: 551-574, 1996. [6] E. Farhi and S. Gutmann. “Quantum computation and decision trees,” Physical Review A, 58: 915-928, 1998. [7] A. Child, E. Farhi, S. Gutmann. “An example of the difference between quantum and classical random walks,” Quantum Information Processing, 1:35, 2002. [8] A. Ambainis, E. Bach, A. Nayak, A. Vishwanath, and J. Watrous. “One-dimensional quantum walks,” Proceedings of STOC’01, pp. 37-49. [9] C. Moore and A. Russell. “Quantum walks on the hypercube,” Proc. RANDOM 2002, pp. 164-178, Cambridge, MA, 2002. Springer. [10] T. D. Mackay, S. D. Bartlett, L. T. Stephenson, and B. C. Sanders. “Quantum walks in higher dimensions,” J. Phys. A: Math. Gen., 35: 2745, 2002. [11] N. Shenvi, J. Kempe, and K. B. Whaley. “A quantum random walk search algorithm,” Physical Review A, 67(5): 052307, 2003. [12] J. Kempe. “Quantum random walks – an introductory overview,” Contemporary Physics, 44: 307-327, 2003. [13] J. Watrous. “Quantum simulations of classical random walks and undirected graph connectivity,” Journal of Computer and System Sciences, 62(2): 376-391, 2001. [14] V. Kendon. “Quantum walks on general graphs,” quant-ph/0306140, unpublished. [15] A. Ambainis. 'Quantum walks and their algorithmic applications'. International Journal of Quantum Information, 1(2003), pages 507-518. [16] G. Tanner, “From quantum graphs to quantum random walks”, Non-Linear Dynamics and Fundamental Interactions, 2006. also quant-ph/0504224. [17] R. P. Feynman and A. R. Hibbs, “Quantum mechanics and path integrals,” International series in pure and applied physics. McGraw-Hill, New York, 1965 [18] D. Aharonov, A. Ambainis, J. Kempe, and U. Vazirani. “Quantum walks on graphs.” In Proc. 33th STOC, pages 50-59, New York, NY, 2001. ACM. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/30243 | - |
| dc.description.abstract | 在文獻中，有幾個量子演算法已被證明具有優越性超過其相對應之傳統演算法。最近的一個是量子隨機漫步。我們提出一個量子隨機漫步於一般圖形的統一架構。引進單一標籤的概念進入量子隨機漫步演算法。如果單一約束都無法滿足，我們還提供另一種中間量測的方法。我們並以幾個例子說明了所設計的演算法能保持量子干涉性質。 | zh_TW |
| dc.description.abstract | In the literature, several quantum computation algorithms have been shown to have superiority over their classical counterparts. The most recent one is quantum random walks. We propose a unified framework for quantum walk algorithms on general graphs. We introduce the concept of unitary labeling into the quantum walk algorithm, and also provide another solution with intermediate measurement if the unitary constraint is not satisfied. We also demonstrate that the designed algorithms maintain the quantum interfering property with a few examples. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-13T01:46:01Z (GMT). No. of bitstreams: 1 ntu-96-R93921023-1.pdf: 640067 bytes, checksum: 9c7302aa2f9b8bc88e6f264bf9b2b632 (MD5) Previous issue date: 2007 | en |
| dc.description.tableofcontents | Chapter 1 Introduction 1
Chapter 2 Preliminaries 4 2.1 Quantum Computation 4 2.1.1 Quantum Bit 5 2.1.2 Quantum Gates 7 2.1.3 Quantum Algorithms 8 2.2 Random Walk 10 Chapter 3 Quantum Random Walk 12 3.1 Quantum Random Walk on a Line 12 3.2 Quantum Random Walk on Higher Dimensions 14 3.3 Quantum Random Walk on General Graph 16 Chapter 4 Quantum Random Walk on General Graphs 19 4.1 Regular Graph 19 4.2 Unitary Labeling 20 4.3 Quantum Walk with Unitary Labeling (QWUL) Algorithm 21 4.4 Edge-coloring 25 4.5 Quantum Walk with Intermediate Measurement (QWIM) Algorithm 28 Chapter 5 Simulation Results 32 5.1 QWUL on a Finite Line 32 5.2 QWIM on a Grid 34 Chapter 6 Conclusion and Future Work 39 References 40 | |
| dc.language.iso | en | |
| dc.subject | 量子演算法 | zh_TW |
| dc.subject | 隨機漫步 | zh_TW |
| dc.subject | random walk | en |
| dc.subject | quantum algorithm | en |
| dc.title | 量子隨機漫步於一般圖形的統一架構 | zh_TW |
| dc.title | A Unified Framework for Quantum Random Walk Algorithms on General Graphs | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 95-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 雷欽隆,莊仁輝,黃秋煌 | |
| dc.subject.keyword | 量子演算法,隨機漫步, | zh_TW |
| dc.subject.keyword | quantum algorithm,random walk, | en |
| dc.relation.page | 41 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2007-07-11 | |
| dc.contributor.author-college | 電機資訊學院 | zh_TW |
| dc.contributor.author-dept | 電機工程學研究所 | zh_TW |
| 顯示於系所單位： | 電機工程學系 | |
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