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| 研究生： |
張淮竣 Chang, Huai-Chun |
|---|---|
| 論文名稱： |
於近期量子計算機量測糾結熵 Probing Entanglement Entropy on Near-term Quantum Computers |
| 指導教授： |
許琇娟
Hsu, Hsiu-Chuan |
| 口試委員: |
林瑜琤
Lin, Yu-Cheng 高英哲 Kao, Ying-Jer 王喬萱 Wang, Chiao-Hsuan |
| 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： | 2024 |
| 畢業學年度： | 112 |
| 語文別： | 中文 |
| 論文頁數： | 134 |
| 中文關鍵詞： | 嘈雜中等規模量子機器 、IBM Quantum 、淬火動力學 、Su–Schrieffer–Heeger 模型 、任尼熵 、隨機測量 、錯誤緩解 |
| 外文關鍵詞： | Noisy Intermediate-Scale Quantum Device, IBM Quantum, Quench dynamics, Su–Schrieffer–Heeger model, Renyi entropy, Randomized measurement, Error mitigation |
| 相關次數： | 點閱：57 下載：15 |
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在本篇論文中，我們在嘈雜中等規模量子機器（Noisy Intermediate-Scale Quantum Device， 簡稱NISQ 機器） 上模擬了Su–Schrieffer–Heeger 模型。主要運用了IBM Quantum 上所提供的量子電腦，透過隨機測量進行第二任尼熵（second-order Renyi entropy）的量測。為了在NISQ 機器上處理部分二聚化淬火哈密頓量，我們應用了適應性時間步長的Trotter decomposition 以減少電路深度。同時我們也考慮了完全二聚化極限淬火哈密頓量，其中時間演化算子可以精確地映射到量子閘，因此降低了嘈雜的影響。在錯誤緩解之後，糾纏熵的振盪模式與理論很好地吻合。為了有效地處理隨機測量所需的大量量子電路板和數據，我們開發了一個名為Qurry 的Python 套件工具，用於處理前述實驗的工作流程的管理、自動化、以及運用平行化計算進行後處理。最後我們還研究了隨機量測任尼熵的誤差標度分析，及其在模擬更大系統時會面臨的挑戰。
In this thesis, we explore the quench dynamics of the Su–Schrieffer–Heeger (SSH) model and quantum entanglement using Noisy Intermediate-Scale Quantum (NISQ) computers, specifically on the IBM Quantum platform. We investigate the second-order Renyi entropy through randomized measurements to characterize the entanglement of quantum states. To simulate partial-dimerized quench Hamiltonians, we employ Trotter decomposition with an adaptive step size to reduce circuit depth. In the fully dimerized limit, the time evolution operator is exactly mapped to quantum gates, which minimizes noise. After applying error mitigation techniques, we find that the entanglement entropy oscillations align with theoretical predictions. Additionally, we developed a Python package called Qurry to manage workflows and facilitate parallel post-processing. Finally, we analyze the error scaling of Renyi entropy measurements and discuss the challenges encountered when simulating larger systems.
誌謝...................................... i
Acknowledgements.......................... ii
摘要....................................... iii Abstract................................... iv Contents................................... v ListofFigures.............................. viii ListofTables .............................. xvi
1 導論....................................... 1
1.1 研究背景................................. 1
1.2 Qiskit ................................. 2
2 實驗方法................................... 4
2.1 記號表 .................................. 4
2.2 模型介紹................................. 5
2.3 隨機量測................................. 6
2.3.1 量測子系統 ............................ 8
2.3.2 量測整個系統 .......................... 9
2.4 誤差緩解................................. 10
2.5 Qurry ................................... 11
3 實作....................................... 13
3.1 適應性時間步長............................. 14
3.2 使用適應性時間步長後的效果 ................. 17
4 誤差標度分析 ............................... 21
4.1 早期嘗試.................................. 21
4.2 實作..................................... 23
4.3 量測次數與計算時間之關係 .................. 30
4.3.1 量子態Cat的計算時間...................... 30
4.3.2 Python、Cython、Rust的計算時間對比........ 31
4.3.3 以效率最好的 Rust 實作為基準的計算時間對比 ... 33
5 結論........................................ 35
5.1 適應性時間步長的優勢 ....................... 35
5.2 當前隨機量測已然到來的計算瓶頸 .............. 36
Reference 37
A 資料附錄..................................... 40
B 所有未列出的資料.............................. 55
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