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題名 基於重要性採樣在量子電腦上的糾纏熵量測
Measuring entanglement entropy with importance sampling on quantum computers作者 林敬軒
Lin, Ching-Hsuan貢獻者 許琇娟
Hsu, Hsiu-Chuan
林敬軒
Lin, Ching-Hsuan關鍵詞 量子計算
量子糾纏
機器學習
類神經網路
Metropolis 演算法
重要性採樣
純度估算
Randomized Measurement
Quantum computing
Quantum entanglement
Machine learning
Neural network
Metropolis sampling
Importance sampling
Purity estimation
Randomized measurement日期 2023 上傳時間 1-Sep-2023 16:28:20 (UTC+8) 摘要 測量量子態的物理量在日漸進步的量子計算研究中扮演十分重要的角色，當問題擴展至更複雜或龐大的量子系統時，對現行的量子電腦的使用環境和硬體限制仍是一大挑戰。本研究基於已被廣泛使用的 Randomized Measurement，設計一針對純度估算之工具。其架構結合古典端方法和量子端的 RandomizedMeasurement，追求純度估算時擁有低統計誤差。透過古典機器學習近似高運算資源消耗的量子電路測量，並在估算量子子系統純度時引入重要性採樣，其相對於均勻採樣的優勢讓系統可以顯著的減少對運算資源和時間的需求。本文將完整的介紹我們的系統架構，接著，從虛擬機和真實機上Product state、GHZ state 實驗開始，延伸至較複雜的 Bell state 之淬火動力學的純度估算結果。我們利用此工具實現精準且高效率的糾纏熵測量，展望在日後亦可被推廣至其他量子系統和物理量的計算。
Measuring the properties of a quantum state plays an important role in the rapidly developing field of quantum computing researches nowadays. When expanding the goal on large-scale or complex quantum systems, one may find it challenging to utilize quantum computers under current hardware conditions and environments.In this research, we designed a toolbox for purity estimation based on the widely used randomized measurement protocol. A combination of classical machine learning and randomized measurements on the quantum states enables us to pursue low statistical error on purity estimation on both quantum simulators and real machines.This toolbox improves the efficiency of measuring purity on quantum circuits via classical machine learning and importance sampling. It’s advantage over uniform sampling is the significant reduction on the demand of computational resources and time.In this thesis, we provide a detailed introduction of the system’s structure. Starting from the product state and GHZ state, we further perform experiments on quench dynamics of Bell state, which exhibits longer range entanglement. Finally, we show that this toolbox realizes measurements of entanglement entropy with higher precision and efficiency. This study is expectedto be applied to other quantum systems and physical quantities in the future.參考文獻 [1] John Preskill. Quantum computing 40 years later, 2023. arXiv:2106.10522.[2] Richard P. Feynman. Simulating physics with computers. International Journal of Theoretical Physics, 21(6):467, Jun 1982.[3] Kishor Bharti, Alba Cervera-Lierta, Thi Ha Kyaw, Tobias Haug, Sumner Alperin Lea, Abhinav Anand, Matthias Degroote, Hermanni Heimonen, Jakob S. Kottmann, Tim Menke, Wai-Keong Mok, Sukin Sim, Leong-Chuan Kwek, and Alá n Aspuru Guzik. Noisy intermediate-scale quantum algorithms. Reviews of Modern Physics, 94(1), Feb 2022.[4] John Preskill. Quantum Computing in the NISQ era and beyond. Quantum, 2:79, Aug 2018.[5] The ibm quantum development roadmap, 2022. https://research.ibm.com/blog/ibm-quantum-roadmap-2025, accessed on 05/30/2023.[6] Vikas Hassija, Vinay Chamola, Vikas Saxena, Vaibhav Chanana, Prakhar Parashari, Shahid Mumtaz, and Mohsen Guizani. Present landscape of quantum computing.IET Quantum Communication, 1(2):42–48, 2020.[7] Qiskit contributors. Qiskit: An open-source framework for quantum computing, 2023. https://qiskit.org/, accessed on 07/20/2023.[8] 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. arXiv:1809.03452.[9] Qiskit terra api reference. https://qiskit.org/documentation/apidoc/terra.html,accessed on 06/01/2023.[10] Ryszard Horodecki, Paweł Horodecki, Michał Horodecki, and Karol Horodecki. Quantum entanglement. Reviews of Modern Physics, 81(2):865–942, Jun 2009.[11] Tiff Brydges, Andreas Elben, Petar Jurcevic, Benoî t 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, Apr 2019.[12] Andreas Elben, Benoît Vermersch, Christian F. Roos, and Peter Zoller. Statistical correlations between locally randomized measurements: A toolbox for probing entanglement in many-body quantum states. Physical Review A, 99(5), May 2019.[13] Aniket Rath, Rick van Bijnen, Andreas Elben, Peter Zoller, and Benoît Vermersch. Importance sampling of randomized measurements for probing entanglement. Phys. Rev. Lett., 127:200503, Nov 2021.[14] Adriano Barenco, Charles H. Bennett, Richard Cleve, David P. DiVincenzo, Norman Margolus, Peter Shor, Tycho Sleator, John A. Smolin, and Harald Weinfurter. Elementary gates for quantum computation. Physical Review A, 52(5):3457–3467, Nov 1995.[15] Bing Xu, Naiyan Wang, Tianqi Chen, and Mu Li. Empirical evaluation of rectified activations in convolutional network, 2015. arXiv:1505.00853.[16] Michael A. Nielsen and Isaac L. Chuang. Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, 2010.[17] Po-Yao Chang. Topology and entanglement in quench dynamics. Physical Review B, 97(22), Jun 2018.[18] Joseph Vovrosh and Johannes Knolle. Confinement and entanglement dynamics on a digital quantum computer. Scientific Reports, 11(1), Jun 2021.[19] Francesco Mezzadri. How to generate random matrices from the classical compact groups, 2007. arXiv:math-ph/0609050 描述 碩士
國立政治大學
應用物理研究所
110755003資料來源 http://thesis.lib.nccu.edu.tw/record/#G0110755003 資料類型 thesis dc.contributor.advisor 許琇娟 zh_TW dc.contributor.advisor Hsu, Hsiu-Chuan en_US dc.contributor.author (Authors) 林敬軒 zh_TW dc.contributor.author (Authors) Lin, Ching-Hsuan en_US dc.creator (作者) 林敬軒 zh_TW dc.creator (作者) Lin, Ching-Hsuan en_US dc.date (日期) 2023 en_US dc.date.accessioned 1-Sep-2023 16:28:20 (UTC+8) - dc.date.available 1-Sep-2023 16:28:20 (UTC+8) - dc.date.issued (上傳時間) 1-Sep-2023 16:28:20 (UTC+8) - dc.identifier (Other Identifiers) G0110755003 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/147297 - 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) 110755003 zh_TW dc.description.abstract (摘要) 測量量子態的物理量在日漸進步的量子計算研究中扮演十分重要的角色，當問題擴展至更複雜或龐大的量子系統時，對現行的量子電腦的使用環境和硬體限制仍是一大挑戰。本研究基於已被廣泛使用的 Randomized Measurement，設計一針對純度估算之工具。其架構結合古典端方法和量子端的 RandomizedMeasurement，追求純度估算時擁有低統計誤差。透過古典機器學習近似高運算資源消耗的量子電路測量，並在估算量子子系統純度時引入重要性採樣，其相對於均勻採樣的優勢讓系統可以顯著的減少對運算資源和時間的需求。本文將完整的介紹我們的系統架構，接著，從虛擬機和真實機上Product state、GHZ state 實驗開始，延伸至較複雜的 Bell state 之淬火動力學的純度估算結果。我們利用此工具實現精準且高效率的糾纏熵測量，展望在日後亦可被推廣至其他量子系統和物理量的計算。 zh_TW dc.description.abstract (摘要) Measuring the properties of a quantum state plays an important role in the rapidly developing field of quantum computing researches nowadays. When expanding the goal on large-scale or complex quantum systems, one may find it challenging to utilize quantum computers under current hardware conditions and environments.In this research, we designed a toolbox for purity estimation based on the widely used randomized measurement protocol. A combination of classical machine learning and randomized measurements on the quantum states enables us to pursue low statistical error on purity estimation on both quantum simulators and real machines.This toolbox improves the efficiency of measuring purity on quantum circuits via classical machine learning and importance sampling. It’s advantage over uniform sampling is the significant reduction on the demand of computational resources and time.In this thesis, we provide a detailed introduction of the system’s structure. Starting from the product state and GHZ state, we further perform experiments on quench dynamics of Bell state, which exhibits longer range entanglement. Finally, we show that this toolbox realizes measurements of entanglement entropy with higher precision and efficiency. This study is expectedto be applied to other quantum systems and physical quantities in the future. en_US dc.description.tableofcontents 第一章 導論 1第一節 量子電腦的起源和現今發展 1第二節 Qiskit 2第三節 量子糾纏 4第二章 系統模型 6第一節 記號 6第二節 系統模型簡介 7第三章 實作 9第一節 機器學習 9第二節 重要性採樣-Metropolis演算法 13第三節 純度估算 14第四章 實驗數據和結果 16第一節 Product state和GHZ state 18第二節 淬火動力學 31第五章 結論 40附錄 42參考文獻 51 zh_TW dc.format.extent 4828752 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0110755003 en_US dc.subject (關鍵詞) 量子計算 zh_TW dc.subject (關鍵詞) 量子糾纏 zh_TW dc.subject (關鍵詞) 機器學習 zh_TW dc.subject (關鍵詞) 類神經網路 zh_TW dc.subject (關鍵詞) Metropolis 演算法 zh_TW dc.subject (關鍵詞) 重要性採樣 zh_TW dc.subject (關鍵詞) 純度估算 zh_TW dc.subject (關鍵詞) Randomized Measurement zh_TW dc.subject (關鍵詞) Quantum computing en_US dc.subject (關鍵詞) Quantum entanglement en_US dc.subject (關鍵詞) Machine learning en_US dc.subject (關鍵詞) Neural network en_US dc.subject (關鍵詞) Metropolis sampling en_US dc.subject (關鍵詞) Importance sampling en_US dc.subject (關鍵詞) Purity estimation en_US dc.subject (關鍵詞) Randomized measurement en_US dc.title (題名) 基於重要性採樣在量子電腦上的糾纏熵量測 zh_TW dc.title (題名) Measuring entanglement entropy with importance sampling on quantum computers en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) [1] John Preskill. Quantum computing 40 years later, 2023. arXiv:2106.10522.[2] Richard P. Feynman. Simulating physics with computers. International Journal of Theoretical Physics, 21(6):467, Jun 1982.[3] Kishor Bharti, Alba Cervera-Lierta, Thi Ha Kyaw, Tobias Haug, Sumner Alperin Lea, Abhinav Anand, Matthias Degroote, Hermanni Heimonen, Jakob S. Kottmann, Tim Menke, Wai-Keong Mok, Sukin Sim, Leong-Chuan Kwek, and Alá n Aspuru Guzik. Noisy intermediate-scale quantum algorithms. Reviews of Modern Physics, 94(1), Feb 2022.[4] John Preskill. Quantum Computing in the NISQ era and beyond. Quantum, 2:79, Aug 2018.[5] The ibm quantum development roadmap, 2022. https://research.ibm.com/blog/ibm-quantum-roadmap-2025, accessed on 05/30/2023.[6] Vikas Hassija, Vinay Chamola, Vikas Saxena, Vaibhav Chanana, Prakhar Parashari, Shahid Mumtaz, and Mohsen Guizani. Present landscape of quantum computing.IET Quantum Communication, 1(2):42–48, 2020.[7] Qiskit contributors. Qiskit: An open-source framework for quantum computing, 2023. https://qiskit.org/, accessed on 07/20/2023.[8] 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. arXiv:1809.03452.[9] Qiskit terra api reference. https://qiskit.org/documentation/apidoc/terra.html,accessed on 06/01/2023.[10] Ryszard Horodecki, Paweł Horodecki, Michał Horodecki, and Karol Horodecki. Quantum entanglement. Reviews of Modern Physics, 81(2):865–942, Jun 2009.[11] Tiff Brydges, Andreas Elben, Petar Jurcevic, Benoî t 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, Apr 2019.[12] Andreas Elben, Benoît Vermersch, Christian F. Roos, and Peter Zoller. Statistical correlations between locally randomized measurements: A toolbox for probing entanglement in many-body quantum states. Physical Review A, 99(5), May 2019.[13] Aniket Rath, Rick van Bijnen, Andreas Elben, Peter Zoller, and Benoît Vermersch. Importance sampling of randomized measurements for probing entanglement. Phys. Rev. Lett., 127:200503, Nov 2021.[14] Adriano Barenco, Charles H. Bennett, Richard Cleve, David P. DiVincenzo, Norman Margolus, Peter Shor, Tycho Sleator, John A. Smolin, and Harald Weinfurter. Elementary gates for quantum computation. Physical Review A, 52(5):3457–3467, Nov 1995.[15] Bing Xu, Naiyan Wang, Tianqi Chen, and Mu Li. Empirical evaluation of rectified activations in convolutional network, 2015. arXiv:1505.00853.[16] Michael A. Nielsen and Isaac L. Chuang. Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press, 2010.[17] Po-Yao Chang. Topology and entanglement in quench dynamics. Physical Review B, 97(22), Jun 2018.[18] Joseph Vovrosh and Johannes Knolle. Confinement and entanglement dynamics on a digital quantum computer. Scientific Reports, 11(1), Jun 2021.[19] Francesco Mezzadri. How to generate random matrices from the classical compact groups, 2007. arXiv:math-ph/0609050 zh_TW
