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題名 透過自動編碼器進行量子錯誤緩解
Quantum Error Mitigation via Autoencoder Neural Networks
作者 林孝道
Lin, Xiao-Dao
貢獻者 許琇娟
Hsu, Hsiu-Chuan
林孝道
Lin, Xiao-Dao
關鍵詞 量子錯誤緩解
深度學習
卷積神經網絡
卷積自動編碼器
Quantum Error Mitigation
Deep learning
Convolutional Neural Networks
Convolutional Autoencoder
日期 2025
上傳時間 1-Sep-2025 16:52:49 (UTC+8)
摘要 近年來，量子計算受到廣泛關注，相關演算法與應用正積極發展。然而，現階段的量子硬體仍面臨多種量子噪聲的限制，包括操作閘不完美、去相干現象以及量測誤差等。為應對這些挑戰，研究者提出了多種量子錯誤緩解（Quantum Error Mitigation）方法，其中不少透過對量測機率分布進行後處理來減少誤差。儘管成效顯著，此類方法往往需要額外的硬體或計算資源。 本論文提出一種基於機器學習的量子錯誤緩解方法，在降低硬體複雜度的同時，提升量測機率分布的準確性。該方法採用最初用於圖像去噪的卷積自動編碼器（Convolutional Autoencoder），並以深度從1至18的4量子位元隨機電路為訓練資料，透過 Qiskit 模擬器分別生成理想與含噪聲的量測結果。訓練過程使用 Kullback-Leibler（KL）散度作為損失函數，採用 Adam 優化器，進行 500 個訓練週期，最終在驗證集上達到平均 95% 的降噪效果，且未出現過擬合跡象。 為進一步檢驗模型對不同量子態與演算法的適用性，本研究在格羅弗演算法（Grover's Algorithm）、量子傅立葉轉換（Quantum Fourier Transform）、Haar 隨機電路以及平凡順磁系統（Trivial Paramagnet）上進行測試。結果顯示，本方法能穩定且有效地抑制量測噪聲，顯示其在噪聲中等規模量子（NISQ）裝置中具有應用潛力。此外，鑑於真實量子電腦擁有不同的噪聲特徵，預訓練模型利用 IBM Quantum（IBMQ）提供的 Sherbrooke 量子處理器生成的小型資料集進行微調（fine-tuning），同樣獲得良好結果，顯示方法的可移植性與適應性。本次研究致力於發展實用、且基於學習的量子噪聲減緩技術。
Quantum computing has witnessed growing interest in recent years, with a variety of quantum algorithms and applications being actively explored. However, the current state of quantum hardware faces significant limitations due to various sources of quantum noise, including gate imperfections, decoherence, readout errors, and etc. To address these challenges, numerous error mitigation strategies have been proposed, typically involving post-processing of measurement probability distributions. While effective, many such approaches introduce additional hardware or computational overhead. This thesis explores a machine learning-based method for quantum error mitigation that minimizes hardware complexity while improving the accuracy of measurement probability distributions. A convolutional neural network (CNN) autoencoder, originally developed for image denoising, was adapted for this purpose. The model was trained using data generated from 4-qubit random circuits of depths ranging from 1 to 18, simulated using Qiskit's simulated backends to obtain both ideal and noise-affected measurement data. The training process employed Kullback-Leibler divergence (KLD) as the loss function and the Adam optimizer for 500 epochs, resulting in an average error suppression of 95% across the validation dataset without signs of overfitting. To evaluate its robustness across different quantum states and algorithms, the model was tested on a broad range of circuits, including Grover's algorithm, the Quantum Fourier Transform, Haar-random circuits, and the Trivial Paramagnet. The results demonstrated consistent and effective denoising of noisy measurement data, indicating that the autoencoder is a promising tool for error mitigation in noisy intermediate-scale quantum (NISQ) devices. Furthermore, owing to different noise characterizations on real quantum machines, the pretrained model was fine-tuned using a small dataset generated by the \texttt{Sherbrooke} backend from IBM Quantum (IBMQ), showing encouraging results and adaptability. This work contributes to the development of practical, learning-based quantum error mitigation techniques.
參考文獻 [1] Richard P. Feynman. Simulating physics with computers. International Journal of Theoretical Physics, 21(6):467–488, Jun 1982. [2] John Preskill. Quantum Computing in the NISQ era and beyond. Quantum, 2:79, August 2018. [3] Suguru Endo, Zhenyu Cai, Simon C. Benjamin, and Xiao Yuan. Hybrid quantum-classical algorithms and quantum error mitigation. Journal of the Physical Society of Japan, 90(3):032001, 2021. [4] Abhinav Kandala, Antonio Mezzacapo, Kristan Temme, Maika Takita, Markus Brink, Jerry M. Chow, and Jay M. Gambetta. Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature, 549(7671):242–246, Sep 2017. [5] K. Mitarai, M. Negoro, M. Kitagawa, and K. Fujii. Quantum circuit learning. Phys. Rev. A, 98:032309, Sep 2018. [6] Piotr Czarnik, Andrew Arrasmith, Patrick J. Coles, and Lukasz Cincio. Error mitigation with Clifford quantum-circuit data. Quantum, 5:592, November 2021. [7] Michael A. Nielsen and Isaac L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, 2000. [8] Ryan LaRose, Andrea Mari, Sarah Kaiser, Peter J. Karalekas, Andre A. Alves, Piotr Czarnik, Mohamed El Mandouh, Max H. Gordon, Yousef Hindy, Aaron Robertson, Purva Thakre, Misty Wahl, Danny Samuel, Rahul Mistri, Maxime Tremblay, Nick Gardner, Nathaniel T. Stemen, Nathan Shammah, and William J. Zeng. Mitiq: A software package for error mitigation on noisy quantum computers. Quantum, 6:774, August 2022. [9] Armands Strikis, Dayue Qin, Yanzhu Chen, Simon C Benjamin, and Ying Li. Learning-based quantum error mitigation. PRX Quantum, 2(4):040330, 2021. [10] Jihye Kim, Byungdu Oh, Yonuk Chong, Euyheon Hwang, and Daniel K Park. Quantum readout error mitigation via deep learning. New Journal of Physics, 24(7):073009, jul 2022. [11] Zhenyu Cai, Ryan Babbush, Simon C. Benjamin, Suguru Endo, William J. Huggins, Ying Li, Jarrod R. McClean, and Thomas E. O’Brien. Quantum error mitigation. Rev. Mod. Phys., 95:045005, Dec 2023. [12] Haoran Liao, Derek S. Wang, Iskandar Sitdikov, Ciro Salcedo, Alireza Seif, and Zlatko K. Minev. Machine learning for practical quantum error mitigation. Nature Machine Intelligence, 6(12):1478–1486, Dec 2024. [13] P. Vincent, H. Larochelle, Y. Bengio, and P. Manzagol. Extracting and composing robust features with denoising autoencoders. Proceedings of the 25th International Conference on Machine Learning, pages 1096–1103, 2008. [14] P. Vincent, H. Larochelle, I. Lajoie, Y. Bengio, and P. Manzagol. Stacked denoising autoencoders: Learning useful representations in a deep network with a local denoising criterion. Journal of Machine Learning Research, 11:3371–3408, 2010. [15] G. Jaiswal, R. Rani, H. Mangotra, and A. Sharma. Integration of hyperspectral imaging and autoencoders: Benefits, applications, hyperparameter tuning and challenges. In Proceedings of an International Conference, 2023. [16] L. Gondara. Medical image denoising using convolutional denoising autoencoders. IEEE 16th International Conference on Data Mining Workshops, pages 241–246, 2016. [17] Y. Zhang. A better autoencoder for image: Convolutional autoencoder. In Proceedings of the International Conference on Image Processing, 2018. [18] Xiao-Dao Lin, Hsi-Ming Chang, Jhih-Shih You, and Hsiu-Chuan Hsu. Quantum error mitigation via autoencoder neural networks. In Proceedings of the IEEE International Conference on Quantum Control, Computing and Learning (IEEE qCCL2025), The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, June 2025. IEEE. To appear; Not yet published as of August 25, 2025. [19] Warren S McCulloch and Walter Pitts. A logical calculus of the ideas immanent in nervous activity. The bulletin of mathematical biophysics, 5:115–133, 1943. [20] Donald Olding Hebb. The organization of behavior: A neuropsychological theory. Psychology press, 2005. [21] Frank Rosenblatt. The perceptron: a probabilistic model for information storage and organization in the brain. Psychological review, 65(6):386, 1958. [22] Marvin Minsky and Seymour A Papert. Perceptrons, reissue of the 1988 expanded edition with a new foreword by Léon Bottou: an introduction to computational geometry. MIT press, 2017. [23] David E Rumelhart, Geoffrey E Hinton, and Ronald J Williams. Learning representations by back-propagating errors. nature, 323(6088):533–536, 1986. [24] Ian Goodfellow, Yoshua Bengio, and Aaron Courville. Deep Learning. MIT Press, 2016. http://www.deeplearningbook.org. [25] Vincent Dumoulin and Francesco Visin. A guide to convolution arithmetic for deep learning. arXiv preprint arXiv:1603.07285, 2016. [26] Matthew D Zeiler, Dilip Krishnan, Graham W Taylor, and Rob Fergus. Deconvolutional networks. In 2010 IEEE Computer Society Conference on computer vision and pattern recognition, pages 2528–2535. IEEE, 2010. [27] Evan Shelhamer, Jonathan Long, and Trevor Darrell. Fully convolutional networks for semantic segmentation. IEEE transactions on pattern analysis and machine intelligence, 39(4):640–651, 2016. [28] Francesco Mezzadri. How to generate random matrices from the classical compact groups. Notices of the American Mathematical Society, 54(5):592–604, 2007. [29] Laurens van der Maaten and Geoffrey Hinton. Visualizing data using t-sne. Journal of machine learning research, 9(Nov):2579–2605, 2008. [30] Xiao-Dao Lin. ae-qem: Autoencoder-based quantum error mitigation sdk. https: //github.com/Y-Frieren-Y/ae-qem, 2025. Version v0.1.0, commit 4531147; License: MIT. [31] Qiskit Contributors. Qiskit: Fake lima backend properties (props_lima.json). https://github.com/Qiskit/qiskit/blob/0.45.3/qiskit/providers/fake_provider/backends/lima/props_lima.json, 2024. Accessed: 2025-07-05.
描述 碩士
國立政治大學
應用物理研究所
112755009
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0112755009
資料類型 thesis
dc.contributor.advisor 許琇娟zh_TW
dc.contributor.advisor Hsu, Hsiu-Chuanen_US
dc.contributor.author (Authors) 林孝道zh_TW
dc.contributor.author (Authors) Lin, Xiao-Daoen_US
dc.creator (作者) 林孝道zh_TW
dc.creator (作者) Lin, Xiao-Daoen_US
dc.date (日期) 2025en_US
dc.date.accessioned 1-Sep-2025 16:52:49 (UTC+8)-
dc.date.available 1-Sep-2025 16:52:49 (UTC+8)-
dc.date.issued (上傳時間) 1-Sep-2025 16:52:49 (UTC+8)-
dc.identifier (Other Identifiers) G0112755009en_US
dc.identifier.uri (URI) https://nccur.lib.nccu.edu.tw/handle/140.119/159396-
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) 112755009zh_TW
dc.description.abstract (摘要) 近年來，量子計算受到廣泛關注，相關演算法與應用正積極發展。然而，現階段的量子硬體仍面臨多種量子噪聲的限制，包括操作閘不完美、去相干現象以及量測誤差等。為應對這些挑戰，研究者提出了多種量子錯誤緩解（Quantum Error Mitigation）方法，其中不少透過對量測機率分布進行後處理來減少誤差。儘管成效顯著，此類方法往往需要額外的硬體或計算資源。 本論文提出一種基於機器學習的量子錯誤緩解方法，在降低硬體複雜度的同時，提升量測機率分布的準確性。該方法採用最初用於圖像去噪的卷積自動編碼器（Convolutional Autoencoder），並以深度從1至18的4量子位元隨機電路為訓練資料，透過 Qiskit 模擬器分別生成理想與含噪聲的量測結果。訓練過程使用 Kullback-Leibler（KL）散度作為損失函數，採用 Adam 優化器，進行 500 個訓練週期，最終在驗證集上達到平均 95% 的降噪效果，且未出現過擬合跡象。 為進一步檢驗模型對不同量子態與演算法的適用性，本研究在格羅弗演算法（Grover's Algorithm）、量子傅立葉轉換（Quantum Fourier Transform）、Haar 隨機電路以及平凡順磁系統（Trivial Paramagnet）上進行測試。結果顯示，本方法能穩定且有效地抑制量測噪聲，顯示其在噪聲中等規模量子（NISQ）裝置中具有應用潛力。此外，鑑於真實量子電腦擁有不同的噪聲特徵，預訓練模型利用 IBM Quantum（IBMQ）提供的 Sherbrooke 量子處理器生成的小型資料集進行微調（fine-tuning），同樣獲得良好結果，顯示方法的可移植性與適應性。本次研究致力於發展實用、且基於學習的量子噪聲減緩技術。zh_TW
dc.description.abstract (摘要) Quantum computing has witnessed growing interest in recent years, with a variety of quantum algorithms and applications being actively explored. However, the current state of quantum hardware faces significant limitations due to various sources of quantum noise, including gate imperfections, decoherence, readout errors, and etc. To address these challenges, numerous error mitigation strategies have been proposed, typically involving post-processing of measurement probability distributions. While effective, many such approaches introduce additional hardware or computational overhead. This thesis explores a machine learning-based method for quantum error mitigation that minimizes hardware complexity while improving the accuracy of measurement probability distributions. A convolutional neural network (CNN) autoencoder, originally developed for image denoising, was adapted for this purpose. The model was trained using data generated from 4-qubit random circuits of depths ranging from 1 to 18, simulated using Qiskit's simulated backends to obtain both ideal and noise-affected measurement data. The training process employed Kullback-Leibler divergence (KLD) as the loss function and the Adam optimizer for 500 epochs, resulting in an average error suppression of 95% across the validation dataset without signs of overfitting. To evaluate its robustness across different quantum states and algorithms, the model was tested on a broad range of circuits, including Grover's algorithm, the Quantum Fourier Transform, Haar-random circuits, and the Trivial Paramagnet. The results demonstrated consistent and effective denoising of noisy measurement data, indicating that the autoencoder is a promising tool for error mitigation in noisy intermediate-scale quantum (NISQ) devices. Furthermore, owing to different noise characterizations on real quantum machines, the pretrained model was fine-tuned using a small dataset generated by the \texttt{Sherbrooke} backend from IBM Quantum (IBMQ), showing encouraging results and adaptability. This work contributes to the development of practical, learning-based quantum error mitigation techniques.en_US
dc.description.tableofcontents 誌謝 i Abstract iii 摘要 v Contents vii List of Figures ix List of Tables xii 1 Introduction 1 2 Theoretical Background 6 2.1 Quantum Computing 6 2.1.1 Quantum State Representation 6 2.1.2 Unitary Evolution 7 2.1.3 Projective Measurement 8 2.1.4 Common Quantum Gates 8 2.1.5 Bloch Sphere Representation 10 2.1.6 Qiskit Implementation 11 2.2 Deep Learning 13 2.2.1 Mimic of Neurons - Perceptron 14 2.2.2 Multi-layers Perceptron 16 2.3 Convolutional Neural Networks (CNN) 18 2.3.1 Convolution Layer 18 2.3.2 Transposed Convolution Layer 23 3 Methodology 28 3.1 Dataset Generation 28 3.2 The Autoencoder Neural Networks 30 3.3 Strategies and Details of Training 33 3.4 Test and Evaluation 34 4 Results and Discussion 40 4.1 Training Results 40 4.2 Model Evaluation on Simulated Datasets 44 4.3 Evaluation on Dataset Generated from a Quantum Backend 47 5 Conclusions 55 6 ae-qem Software Development Kit 57 A Properties of FakeLima Backend 60 B The Model Structures 62 C TSNE 65 D Values of Quantile in Figures 66 Reference 67zh_TW
dc.format.extent 4175738 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0112755009en_US
dc.subject (關鍵詞) 量子錯誤緩解zh_TW
dc.subject (關鍵詞) 深度學習zh_TW
dc.subject (關鍵詞) 卷積神經網絡zh_TW
dc.subject (關鍵詞) 卷積自動編碼器zh_TW
dc.subject (關鍵詞) Quantum Error Mitigationen_US
dc.subject (關鍵詞) Deep learningen_US
dc.subject (關鍵詞) Convolutional Neural Networksen_US
dc.subject (關鍵詞) Convolutional Autoencoderen_US
dc.title (題名) 透過自動編碼器進行量子錯誤緩解zh_TW
dc.title (題名) Quantum Error Mitigation via Autoencoder Neural Networksen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) [1] Richard P. Feynman. Simulating physics with computers. International Journal of Theoretical Physics, 21(6):467–488, Jun 1982. [2] John Preskill. Quantum Computing in the NISQ era and beyond. Quantum, 2:79, August 2018. [3] Suguru Endo, Zhenyu Cai, Simon C. Benjamin, and Xiao Yuan. Hybrid quantum-classical algorithms and quantum error mitigation. Journal of the Physical Society of Japan, 90(3):032001, 2021. [4] Abhinav Kandala, Antonio Mezzacapo, Kristan Temme, Maika Takita, Markus Brink, Jerry M. Chow, and Jay M. Gambetta. Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature, 549(7671):242–246, Sep 2017. [5] K. Mitarai, M. Negoro, M. Kitagawa, and K. Fujii. Quantum circuit learning. Phys. Rev. A, 98:032309, Sep 2018. [6] Piotr Czarnik, Andrew Arrasmith, Patrick J. Coles, and Lukasz Cincio. Error mitigation with Clifford quantum-circuit data. Quantum, 5:592, November 2021. [7] Michael A. Nielsen and Isaac L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, 2000. [8] Ryan LaRose, Andrea Mari, Sarah Kaiser, Peter J. Karalekas, Andre A. Alves, Piotr Czarnik, Mohamed El Mandouh, Max H. Gordon, Yousef Hindy, Aaron Robertson, Purva Thakre, Misty Wahl, Danny Samuel, Rahul Mistri, Maxime Tremblay, Nick Gardner, Nathaniel T. Stemen, Nathan Shammah, and William J. Zeng. Mitiq: A software package for error mitigation on noisy quantum computers. Quantum, 6:774, August 2022. [9] Armands Strikis, Dayue Qin, Yanzhu Chen, Simon C Benjamin, and Ying Li. Learning-based quantum error mitigation. PRX Quantum, 2(4):040330, 2021. [10] Jihye Kim, Byungdu Oh, Yonuk Chong, Euyheon Hwang, and Daniel K Park. Quantum readout error mitigation via deep learning. New Journal of Physics, 24(7):073009, jul 2022. [11] Zhenyu Cai, Ryan Babbush, Simon C. Benjamin, Suguru Endo, William J. Huggins, Ying Li, Jarrod R. McClean, and Thomas E. O’Brien. Quantum error mitigation. Rev. Mod. Phys., 95:045005, Dec 2023. [12] Haoran Liao, Derek S. Wang, Iskandar Sitdikov, Ciro Salcedo, Alireza Seif, and Zlatko K. Minev. Machine learning for practical quantum error mitigation. Nature Machine Intelligence, 6(12):1478–1486, Dec 2024. [13] P. Vincent, H. Larochelle, Y. Bengio, and P. Manzagol. Extracting and composing robust features with denoising autoencoders. Proceedings of the 25th International Conference on Machine Learning, pages 1096–1103, 2008. [14] P. Vincent, H. Larochelle, I. Lajoie, Y. Bengio, and P. Manzagol. Stacked denoising autoencoders: Learning useful representations in a deep network with a local denoising criterion. Journal of Machine Learning Research, 11:3371–3408, 2010. [15] G. Jaiswal, R. Rani, H. Mangotra, and A. Sharma. Integration of hyperspectral imaging and autoencoders: Benefits, applications, hyperparameter tuning and challenges. In Proceedings of an International Conference, 2023. [16] L. Gondara. Medical image denoising using convolutional denoising autoencoders. IEEE 16th International Conference on Data Mining Workshops, pages 241–246, 2016. [17] Y. Zhang. A better autoencoder for image: Convolutional autoencoder. In Proceedings of the International Conference on Image Processing, 2018. [18] Xiao-Dao Lin, Hsi-Ming Chang, Jhih-Shih You, and Hsiu-Chuan Hsu. Quantum error mitigation via autoencoder neural networks. In Proceedings of the IEEE International Conference on Quantum Control, Computing and Learning (IEEE qCCL2025), The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, June 2025. IEEE. To appear; Not yet published as of August 25, 2025. [19] Warren S McCulloch and Walter Pitts. A logical calculus of the ideas immanent in nervous activity. The bulletin of mathematical biophysics, 5:115–133, 1943. [20] Donald Olding Hebb. The organization of behavior: A neuropsychological theory. Psychology press, 2005. [21] Frank Rosenblatt. The perceptron: a probabilistic model for information storage and organization in the brain. Psychological review, 65(6):386, 1958. [22] Marvin Minsky and Seymour A Papert. Perceptrons, reissue of the 1988 expanded edition with a new foreword by Léon Bottou: an introduction to computational geometry. MIT press, 2017. [23] David E Rumelhart, Geoffrey E Hinton, and Ronald J Williams. Learning representations by back-propagating errors. nature, 323(6088):533–536, 1986. [24] Ian Goodfellow, Yoshua Bengio, and Aaron Courville. Deep Learning. MIT Press, 2016. http://www.deeplearningbook.org. [25] Vincent Dumoulin and Francesco Visin. A guide to convolution arithmetic for deep learning. arXiv preprint arXiv:1603.07285, 2016. [26] Matthew D Zeiler, Dilip Krishnan, Graham W Taylor, and Rob Fergus. Deconvolutional networks. In 2010 IEEE Computer Society Conference on computer vision and pattern recognition, pages 2528–2535. IEEE, 2010. [27] Evan Shelhamer, Jonathan Long, and Trevor Darrell. Fully convolutional networks for semantic segmentation. IEEE transactions on pattern analysis and machine intelligence, 39(4):640–651, 2016. [28] Francesco Mezzadri. How to generate random matrices from the classical compact groups. Notices of the American Mathematical Society, 54(5):592–604, 2007. [29] Laurens van der Maaten and Geoffrey Hinton. Visualizing data using t-sne. Journal of machine learning research, 9(Nov):2579–2605, 2008. [30] Xiao-Dao Lin. ae-qem: Autoencoder-based quantum error mitigation sdk. https: //github.com/Y-Frieren-Y/ae-qem, 2025. Version v0.1.0, commit 4531147; License: MIT. [31] Qiskit Contributors. Qiskit: Fake lima backend properties (props_lima.json). https://github.com/Qiskit/qiskit/blob/0.45.3/qiskit/providers/fake_provider/backends/lima/props_lima.json, 2024. Accessed: 2025-07-05.zh_TW