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題名 以模擬量子退火過程探索自旋系統的基態
Approaching ground states of spin systems via simulated quantum annealing作者 黃湘喻
Huang, Hsiang Yu貢獻者 林瑜琤
Lin, Yu Cheng
黃湘喻
Huang, Hsiang Yu關鍵詞 D-Wave 計算機
量子退火
模擬退火
Kibble-Zurek 機制
D-Wave device
quantum annealing
simulated annealing
Kibble-Zurek mechanism日期 2014 上傳時間 1-Dec-2014 14:27:31 (UTC+8) 摘要 專為解決最佳化問題設計的程式化量子退火計算機 ---D-Wave 系統 --- 已於近年問世。為瞭解 D-Wave 退火過程的性質，許多研究團隊進行各類型的測試，試圖將 D-Wave 計算機運算效能與其它古典及量子模擬退火演算法作比較。本論文利用量子蒙地卡羅(quantum Monte Carlo) 計算模擬橫場下的易辛模型，並探討藉降低橫場（量子擾動）逼近量子臨界點的退火動力學之標度行為。我們的結果顯示，隨模擬時間進行退火的動力過程並不反應真實的量子動力現象。我們因此建議，比較量子退火與古典退火的計算測試待需更嚴謹的實驗設計。
Recently, a programmable quantum annealing device, the D-Wave system, has been built that attempts to solve optimization problems by adiabatically quenching quantum fluctuations. In order to get insights into the nature of the D-Wave annealing process, different research teams have performed several tests of the D-Wave and compared its performance to other classical and quantum simulated annealing algorithms. In this thesis we use quantum Monte Carlo method to simulate quantum annealing in the transverse-field Ising model, and study scaling aspects of the quantum phase transition approached by changing the transverse field as a function of simulation time. We find that quenching quantum fluctuations in simulation time does not access the true quantum dynamics. Our results therefore show a careful design of benchmark tests is needed for comparing a quantum annealer to a simulated classical annealer.參考文獻 [1] G. E. Santoro, R. Martonak, E. Tosatti, and R. Car, Science 295, 2427 (2002). [2] R. Martonak, G. E. Santoro, and E. Tosatti, Phys. Rev. B 66, 094203 (2002). [3] S. Kirkpatrick et al., science 220, 671 (1983). [4] T. W. Kibble, Physics Reports 67, 183 (1980). [5] W. Zurek, Nature 317, 505 (1985). [6] A. Polkovnikov, Phys. Rev. B 72, 161201 (2005). [7] C.-W. Liu, A. Polkovnikov, and A. W. Sandvik, Phys. Rev. B 89, 054307 (2014). [8] B. Friedrich and D. Herschbach, Physics Today 56, 53 (2003). [9] D. S. Fisher and D. A. Huse, Phys. Rev. Lett. 56, 1601 (1986). [10] D. S. Fisher and D. A. Huse, Phys. Rev. B 38, 386 (1988). [11] G. Parisi, Phys. Rev. Lett. 43, 1754 (1979). [12] G. Parisi, Phys. Rev. Lett. 50, 1946 (1983). [13] M. Mezard, G. Parisi, N. Sourlas, G. Toulouse, and M. Virasoro, Phys. Rev. Lett. 52, 1156 (1984). [14] D. Bitko, T. F. Rosenbaum, and G. Aeppli, Phys. Rev. Lett. 77, 940 (1996). [15] A. Messiah, Quantum Mechanics, Volume II, Wiley, New York, 1976. [16] E. Farhi et al., Science 292, 472 (2001). [17] J. G. Andrew M. Childs, Edward Farhi and S. Gutmann, Quantum Information and Computation 2, 181 (2002). [18] T. Kadowaki and H. Nishimori, Phys. Rev. E 58, 5355 (1998). [19] N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, J. Chem. Phys. 21, 1087 (1953). [20] G. E. Santoro and E. Tosatti, Journal of Physics A: Mathematical and General 39, R393 (2006). [21] S. Boixo et al., Nature Physics 10, 218 (2014). [22] V. Bapst and G. Semerjian, Journal of Physics: Conference Series 473, 012011 (2013). [23] R. J. Baxter, Exactly solved models in statistical mechanics, Courier Dover Publications, 2007. [24] J. Cardy, Scaling and renormalization in statistical physics, volume 5, Cambridge University Press, 1996. [25] S. Sachdev, Quantum phase transitions, Wiley Online Library, 2007. [26] R. P. Feynman, Reviews of Modern Physics 20, 367 (1948). [27] T. W. Kibble, Journal of Physics A: Mathematical and General 9, 1387 (1976). [28] W. H. Zurek, Physics Reports 276, 177 (1996). [29] J. Dziarmaga, Phys. Rev. Lett. 95, 245701 (2005). [30] W. H. Zurek, U. Dorner, and P. Zoller, Phys. Rev. Lett. 95, 105701 (2005). [31] H. F. Trotter, Proc. Am. Math. Soc. 10, 545 (1959). [32] M. Suzuki, Prog. Theor. Phys. 56, 1454 (1976). [33] T. F. Rønnow et al., Science 345, 420 (2014). [34] R. H. Swendsen and J.-S. Wang, Physical review letters 58, 86 (1987). 描述 碩士
國立政治大學
應用物理研究所
101755005
103資料來源 http://thesis.lib.nccu.edu.tw/record/#G0101755005 資料類型 thesis dc.contributor.advisor 林瑜琤 zh_TW dc.contributor.advisor Lin, Yu Cheng en_US dc.contributor.author (Authors) 黃湘喻 zh_TW dc.contributor.author (Authors) Huang, Hsiang Yu en_US dc.creator (作者) 黃湘喻 zh_TW dc.creator (作者) Huang, Hsiang Yu en_US dc.date (日期) 2014 en_US dc.date.accessioned 1-Dec-2014 14:27:31 (UTC+8) - dc.date.available 1-Dec-2014 14:27:31 (UTC+8) - dc.date.issued (上傳時間) 1-Dec-2014 14:27:31 (UTC+8) - dc.identifier (Other Identifiers) G0101755005 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/71760 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 應用物理研究所 zh_TW dc.description (描述) 101755005 zh_TW dc.description (描述) 103 zh_TW dc.description.abstract (摘要) 專為解決最佳化問題設計的程式化量子退火計算機 ---D-Wave 系統 --- 已於近年問世。為瞭解 D-Wave 退火過程的性質，許多研究團隊進行各類型的測試，試圖將 D-Wave 計算機運算效能與其它古典及量子模擬退火演算法作比較。本論文利用量子蒙地卡羅(quantum Monte Carlo) 計算模擬橫場下的易辛模型，並探討藉降低橫場（量子擾動）逼近量子臨界點的退火動力學之標度行為。我們的結果顯示，隨模擬時間進行退火的動力過程並不反應真實的量子動力現象。我們因此建議，比較量子退火與古典退火的計算測試待需更嚴謹的實驗設計。 zh_TW dc.description.abstract (摘要) Recently, a programmable quantum annealing device, the D-Wave system, has been built that attempts to solve optimization problems by adiabatically quenching quantum fluctuations. In order to get insights into the nature of the D-Wave annealing process, different research teams have performed several tests of the D-Wave and compared its performance to other classical and quantum simulated annealing algorithms. In this thesis we use quantum Monte Carlo method to simulate quantum annealing in the transverse-field Ising model, and study scaling aspects of the quantum phase transition approached by changing the transverse field as a function of simulation time. We find that quenching quantum fluctuations in simulation time does not access the true quantum dynamics. Our results therefore show a careful design of benchmark tests is needed for comparing a quantum annealer to a simulated classical annealer. en_US dc.description.tableofcontents 謝辭 i 中文摘要 ii 英文摘要 iii 1 引言 1 2 自旋模型 3 2.1 自旋1/2................................... 3 2.2 具交互作用的自旋模型 .......................... 6 3 量子退火法 10 3.1 量子緩漸演化 ............................... 10 3.2 模擬量子退火法 .............................. 11 4 相變臨界點的標度 14 4.1 簡述相變及臨界現象 ........................... 14 4.2 淬火的標度行為 .............................. 19 5 易辛模型的模擬量子退火演算 22 5.1 量子-古典易辛模型的對映 ....................... 22 5.2 連續虛數時間的蒙地卡羅方法 ...................... 25 5.3 以標度分析檢驗量子退火法 ....................... 30 6 總結與展望 38 zh_TW dc.format.extent 1466339 bytes - dc.format.mimetype application/pdf - dc.language.iso en_US - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0101755005 en_US dc.subject (關鍵詞) D-Wave 計算機 zh_TW dc.subject (關鍵詞) 量子退火 zh_TW dc.subject (關鍵詞) 模擬退火 zh_TW dc.subject (關鍵詞) Kibble-Zurek 機制 zh_TW dc.subject (關鍵詞) D-Wave device en_US dc.subject (關鍵詞) quantum annealing en_US dc.subject (關鍵詞) simulated annealing en_US dc.subject (關鍵詞) Kibble-Zurek mechanism en_US dc.title (題名) 以模擬量子退火過程探索自旋系統的基態 zh_TW dc.title (題名) Approaching ground states of spin systems via simulated quantum annealing en_US dc.type (資料類型) thesis en dc.relation.reference (參考文獻) [1] G. E. Santoro, R. Martonak, E. Tosatti, and R. Car, Science 295, 2427 (2002). [2] R. Martonak, G. E. Santoro, and E. Tosatti, Phys. Rev. B 66, 094203 (2002). [3] S. Kirkpatrick et al., science 220, 671 (1983). [4] T. W. Kibble, Physics Reports 67, 183 (1980). [5] W. Zurek, Nature 317, 505 (1985). [6] A. Polkovnikov, Phys. Rev. B 72, 161201 (2005). [7] C.-W. Liu, A. Polkovnikov, and A. W. Sandvik, Phys. Rev. B 89, 054307 (2014). [8] B. Friedrich and D. Herschbach, Physics Today 56, 53 (2003). [9] D. S. Fisher and D. A. Huse, Phys. Rev. Lett. 56, 1601 (1986). [10] D. S. Fisher and D. A. Huse, Phys. Rev. B 38, 386 (1988). [11] G. Parisi, Phys. Rev. Lett. 43, 1754 (1979). [12] G. Parisi, Phys. Rev. Lett. 50, 1946 (1983). [13] M. Mezard, G. Parisi, N. Sourlas, G. Toulouse, and M. Virasoro, Phys. Rev. Lett. 52, 1156 (1984). [14] D. Bitko, T. F. Rosenbaum, and G. Aeppli, Phys. Rev. Lett. 77, 940 (1996). [15] A. Messiah, Quantum Mechanics, Volume II, Wiley, New York, 1976. [16] E. Farhi et al., Science 292, 472 (2001). [17] J. G. Andrew M. Childs, Edward Farhi and S. Gutmann, Quantum Information and Computation 2, 181 (2002). [18] T. Kadowaki and H. Nishimori, Phys. Rev. E 58, 5355 (1998). [19] N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, J. Chem. Phys. 21, 1087 (1953). [20] G. E. Santoro and E. Tosatti, Journal of Physics A: Mathematical and General 39, R393 (2006). [21] S. Boixo et al., Nature Physics 10, 218 (2014). [22] V. Bapst and G. Semerjian, Journal of Physics: Conference Series 473, 012011 (2013). [23] R. J. Baxter, Exactly solved models in statistical mechanics, Courier Dover Publications, 2007. [24] J. Cardy, Scaling and renormalization in statistical physics, volume 5, Cambridge University Press, 1996. [25] S. Sachdev, Quantum phase transitions, Wiley Online Library, 2007. [26] R. P. Feynman, Reviews of Modern Physics 20, 367 (1948). [27] T. W. Kibble, Journal of Physics A: Mathematical and General 9, 1387 (1976). [28] W. H. Zurek, Physics Reports 276, 177 (1996). [29] J. Dziarmaga, Phys. Rev. Lett. 95, 245701 (2005). [30] W. H. Zurek, U. Dorner, and P. Zoller, Phys. Rev. Lett. 95, 105701 (2005). [31] H. F. Trotter, Proc. Am. Math. Soc. 10, 545 (1959). [32] M. Suzuki, Prog. Theor. Phys. 56, 1454 (1976). [33] T. F. Rønnow et al., Science 345, 420 (2014). [34] R. H. Swendsen and J.-S. Wang, Physical review letters 58, 86 (1987). zh_TW
