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| 研究生： |
李佳豪 Lee, Jia-Hao |
|---|---|
| 論文名稱： |
以量子電腦模擬量子自旋鏈 Simulating quantum spin chains on a quantum computer |
| 指導教授： |
林瑜琤
Lin, Yu-Cheng 許琇娟 Hsu, Hsiu-Chuan |
| 口試委員: |
林瑜琤
Lin, Yu-Cheng 許琇娟 Hsu, Hsiu-Chuan 高英哲 Kao, Ying-Jer 黃琮暐 Huang, Tsung-Wei |
| 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： | 2020 |
| 畢業學年度： | 108 |
| 語文別： | 中文 |
| 論文頁數： | 40 |
| 中文關鍵詞： | 量子電路 、量子自旋鏈 、變分量子特徵值解法 、量子糾纏 、量子費雪訊息 |
| 外文關鍵詞： | IBM-Q, Qiskit, Quantum circuit, Quantum spin chain, Variational Quantum Eigensolver (VQE), Quantum Fisher information |
| DOI URL： | http://doi.org/10.6814/NCCU202001614 |
| 相關次數： | 點閱：192 下載：74 |
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我們利用雲端 IBM-Q 量子電腦及其搭配的程式套件 Qiskit 來探討量子自旋鏈的基態性質及淬火動力學。我們先在傳統電腦上運用變分量子特徵值解法求得自旋鏈的近似基態波函數，再以量子電腦或 Qiskit 提供的模擬器測量磁化量、量子費雪訊息等觀察量。我們根據所得的結果討論變分法及目前量子電腦在處理量子多體問題上的侷限。
We study ground-state properties and quench dynamics of the quantum Ising chain using IBM’s cloud-based quantum computer and its programming framework Qiskit. The approximate ground states of the spin chain are obtained by means of the Variational Quantum Eigensolver (VQE), implemented on conventional computers. Measurements of several observables, such as magnetization and quantum Fisher information, for the ground states are then carried out on a quantum computer or on a simulator provided by Qiskit. Based on our results, we discuss some limitations of the VQE and its implementation on a quantum computer for solving the quantum many-body problem.
致謝 i
摘要 iii
Abstract v
Contents vii
1 量子計算工具簡介 1
1.1 量子電腦 1
1.2 Qiskit 環境中的量子電路 1
2 問題及方法 9
2.1 量子易辛（Ising）自旋鏈 9
2.2 變分量子特徵值解法 10
2.3 時間演化 13
2.3.1 Trotter 分解法 14
2.3.2 實現時間演化的量子電路 15
3 量子易辛自旋鏈模擬結果 17
3.1 基態的模擬 17
3.2 基態的序參數 21
3.3 量子糾纏性質 26
3.4 淬火的模擬 31
4 結論與展望 37
參考文獻 39
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