1. NCCU Academic Hub
  2. Publications
  3. College of Science
  4. Theses
  5. Item

Publications-Theses

Article View/Open

Publication Export

Google ScholarTM

NCCU Library

Citation Infomation

Related Publications in TAIR

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 Chengen_US
dc.contributor.author (Authors) 黃湘喻zh_TW
dc.contributor.author (Authors) Huang, Hsiang Yuen_US
dc.creator (作者) 黃湘喻zh_TW
dc.creator (作者) Huang, Hsiang Yuen_US
dc.date (日期) 2014en_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) G0101755005en_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) 101755005zh_TW
dc.description (描述) 103zh_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/#G0101755005en_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 deviceen_US
dc.subject (關鍵詞) quantum annealingen_US
dc.subject (關鍵詞) simulated annealingen_US
dc.subject (關鍵詞) Kibble-Zurek mechanismen_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 annealingen_US
dc.type (資料類型) thesisen
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