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題名 於近期量子計算機量測糾結熵
Probing Entanglement Entropy on Near-term Quantum Computers
作者 張淮竣
Chang, Huai-Chun
貢獻者 許琇娟
Hsu, Hsiu-Chuan
張淮竣
Chang, Huai-Chun
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
Noisy Intermediate-Scale Quantum Device
IBM Quantum
Quench dynamics
Su–Schrieffer–Heeger model
Renyi entropy
Randomized measurement
Error mitigation
日期 2024
上傳時間 4-Sep-2024 15:26:35 (UTC+8)
摘要 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.
參考文獻 [1] Tiff Brydges, Andreas Elben, Petar Jurcevic, Benoît Vermersch, Christine Maier, Ben P. Lanyon, Peter Zoller, Rainer Blatt, and Christian F. Roos. Probing rényi entanglement entropy via randomized measurements. Science, 364(6437):260–263, 2019. [2] Huai-Chun Chang. Qurry - the quantum experiment manager for qiskit, 2024. [3] Huai-Chun Chang, Hsiu-Chuan Hsu, and Yu-Cheng Lin. Probing entanglement dy- namics and topological transitions on noisy intermediate-scale quantum computers, 2024. [4] Ivan B. Djordjevic. Quantum Information Processing, Quantum Computing, and Quantum Error Correction. Elsevier, 2nd edition, 2021. [5] Elben, A., Vermersch, B., Roos, C. F., Zoller, and P. Statistical correlations between locally randomized measurements: A toolbox for probing entanglement in many- body quantum states. Phys. Rev. A, 99:052323, May 2019. [6] Feynman and Richard P. Simulating physics with computers. International journal of theoretical physics, 21(6/7):467–488, 1982. [7] GambettaandJay. Ibm quantum roadmap to build quantum-centric supercomputers, May 2022. Accessed: 2024-07-20. [8] IBM Newsroom. Ibm debuts next-generation quantum processor & ibm quantum system two, extends roadmap to advance era of quantum utility, December 2023. Accessed: 2024-07-20. [9] Javadi-Abhari,Ali,Treinish,Matthew,Krsulich,Kevin,Wood,ChristopherJ.,Lish- man, Jake, Gacon, Julien, Martiel, Simon, Nation, Paul D., Bishop, Lev S., Cross, Andrew W., Johnson, Blake R., Gambetta, and Jay M. Quantum computing with Qiskit, 2024. [10] Fujitsu Limited. Fujitsu develops quantum/hpc hybrid computing technology to op- timize solution brokering for customers, Nov 2022. [11] David C. McKay, Thomas Alexander, Luciano Bello, Michael J. Biercuk, Lev Bishop, Jiayin Chen, Jerry M. Chow, Antonio D. Córcoles, Daniel Egger, Stefan Filipp, Juan Gomez, Michael Hush, Ali Javadi-Abhari, Diego Moreda, Paul Nation, Brent Paulovicks, Erick Winston, Christopher J. Wood, James Wootton, and Jay M. Gambetta. Qiskit backend specifications for openqasm and openpulse experiments, 2018. [12] Mikio Morita, Yoshinori Tomita, Junpei Koyama, and Koichi Kimura. Simulator demonstration of large scale variational quantum algorithm on hpc cluster, 2024. [13] Preskill and John. FAULT-TOLERANT QUANTUM COMPUTATION, pages 213– 269. World Scientific, 1997. [14] Preskill and John. Quantum Computing in the NISQ era and beyond. Quantum, 2:79, August 2018. [15] John Preskill. Quantum computing 40 years later, 2023. [16] Su, W. P., Schrieffer, J. R., Heeger, and A. J. Solitons in polyacetylene. Phys. Rev. Lett., 42:1698–1701, Jun 1979. [17] Vovrosh,Joseph,Khosla,KiranE.,Greenaway,Sean,Self,Christopher,Kim,M.S., Knolle, and Johannes. Simple mitigation of global depolarizing errors in quantum simulations. Phys. Rev. E, 104:035309, Sep 2021.
描述 碩士
國立政治大學
應用物理研究所
111755001
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0111755001
資料類型 thesis
dc.contributor.advisor 許琇娟zh_TW
dc.contributor.advisor Hsu, Hsiu-Chuanen_US
dc.contributor.author (Authors) 張淮竣zh_TW
dc.contributor.author (Authors) Chang, Huai-Chunen_US
dc.creator (作者) 張淮竣zh_TW
dc.creator (作者) Chang, Huai-Chunen_US
dc.date (日期) 2024en_US
dc.date.accessioned 4-Sep-2024 15:26:35 (UTC+8)-
dc.date.available 4-Sep-2024 15:26:35 (UTC+8)-
dc.date.issued (上傳時間) 4-Sep-2024 15:26:35 (UTC+8)-
dc.identifier (Other Identifiers) G0111755001en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/153487-
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) 111755001zh_TW
dc.description.abstract (摘要) 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。zh_TW
dc.description.abstract (摘要) 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.en_US
dc.description.tableofcontents 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................................ 55zh_TW
dc.format.extent 92970174 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0111755001en_US
dc.subject (關鍵詞) 嘈雜中等規模量子機器zh_TW
dc.subject (關鍵詞) IBM Quantumzh_TW
dc.subject (關鍵詞) 淬火動力學zh_TW
dc.subject (關鍵詞) Su–Schrieffer–Heeger 模型zh_TW
dc.subject (關鍵詞) 任尼熵zh_TW
dc.subject (關鍵詞) 隨機測量zh_TW
dc.subject (關鍵詞) 錯誤緩解zh_TW
dc.subject (關鍵詞) Noisy Intermediate-Scale Quantum Deviceen_US
dc.subject (關鍵詞) IBM Quantumen_US
dc.subject (關鍵詞) Quench dynamicsen_US
dc.subject (關鍵詞) Su–Schrieffer–Heeger modelen_US
dc.subject (關鍵詞) Renyi entropyen_US
dc.subject (關鍵詞) Randomized measurementen_US
dc.subject (關鍵詞) Error mitigationen_US
dc.title (題名) 於近期量子計算機量測糾結熵zh_TW
dc.title (題名) Probing Entanglement Entropy on Near-term Quantum Computersen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) [1] Tiff Brydges, Andreas Elben, Petar Jurcevic, Benoît Vermersch, Christine Maier, Ben P. Lanyon, Peter Zoller, Rainer Blatt, and Christian F. Roos. Probing rényi entanglement entropy via randomized measurements. Science, 364(6437):260–263, 2019. [2] Huai-Chun Chang. Qurry - the quantum experiment manager for qiskit, 2024. [3] Huai-Chun Chang, Hsiu-Chuan Hsu, and Yu-Cheng Lin. Probing entanglement dy- namics and topological transitions on noisy intermediate-scale quantum computers, 2024. [4] Ivan B. Djordjevic. Quantum Information Processing, Quantum Computing, and Quantum Error Correction. Elsevier, 2nd edition, 2021. [5] Elben, A., Vermersch, B., Roos, C. F., Zoller, and P. Statistical correlations between locally randomized measurements: A toolbox for probing entanglement in many- body quantum states. Phys. Rev. A, 99:052323, May 2019. [6] Feynman and Richard P. Simulating physics with computers. International journal of theoretical physics, 21(6/7):467–488, 1982. [7] GambettaandJay. Ibm quantum roadmap to build quantum-centric supercomputers, May 2022. Accessed: 2024-07-20. [8] IBM Newsroom. Ibm debuts next-generation quantum processor & ibm quantum system two, extends roadmap to advance era of quantum utility, December 2023. Accessed: 2024-07-20. [9] Javadi-Abhari,Ali,Treinish,Matthew,Krsulich,Kevin,Wood,ChristopherJ.,Lish- man, Jake, Gacon, Julien, Martiel, Simon, Nation, Paul D., Bishop, Lev S., Cross, Andrew W., Johnson, Blake R., Gambetta, and Jay M. Quantum computing with Qiskit, 2024. [10] Fujitsu Limited. Fujitsu develops quantum/hpc hybrid computing technology to op- timize solution brokering for customers, Nov 2022. [11] David C. McKay, Thomas Alexander, Luciano Bello, Michael J. Biercuk, Lev Bishop, Jiayin Chen, Jerry M. Chow, Antonio D. Córcoles, Daniel Egger, Stefan Filipp, Juan Gomez, Michael Hush, Ali Javadi-Abhari, Diego Moreda, Paul Nation, Brent Paulovicks, Erick Winston, Christopher J. Wood, James Wootton, and Jay M. Gambetta. Qiskit backend specifications for openqasm and openpulse experiments, 2018. [12] Mikio Morita, Yoshinori Tomita, Junpei Koyama, and Koichi Kimura. Simulator demonstration of large scale variational quantum algorithm on hpc cluster, 2024. [13] Preskill and John. FAULT-TOLERANT QUANTUM COMPUTATION, pages 213– 269. World Scientific, 1997. [14] Preskill and John. Quantum Computing in the NISQ era and beyond. Quantum, 2:79, August 2018. [15] John Preskill. Quantum computing 40 years later, 2023. [16] Su, W. P., Schrieffer, J. R., Heeger, and A. J. Solitons in polyacetylene. Phys. Rev. Lett., 42:1698–1701, Jun 1979. [17] Vovrosh,Joseph,Khosla,KiranE.,Greenaway,Sean,Self,Christopher,Kim,M.S., Knolle, and Johannes. Simple mitigation of global depolarizing errors in quantum simulations. Phys. Rev. E, 104:035309, Sep 2021.zh_TW