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| 研究生： |
黃湘喻 Huang, Hsiang Yu |
|---|---|
| 論文名稱： |
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 |
| 指導教授： |
林瑜琤
Lin, Yu Cheng |
| 學位類別： |
碩士
Master |
| 系所名稱： |
理學院 - 應用物理研究所 Graduate Institute of Applied Physics |
| 論文出版年： | 2014 |
| 畢業學年度： | 103 |
| 語文別： | 中文 |
| 論文頁數： | 42 |
| 中文關鍵詞： | D-Wave 計算機 、量子退火 、模擬退火 、Kibble-Zurek 機制 |
| 外文關鍵詞： | D-Wave device, quantum annealing, simulated annealing, Kibble-Zurek mechanism |
| 相關次數： | 點閱：255 下載：88 |
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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.
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
[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).
