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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 管希聖(Hsi-Sheng Goan) | |
dc.contributor.author | Jia-Yang Gao | en |
dc.contributor.author | 高嘉陽 | zh_TW |
dc.date.accessioned | 2021-07-11T14:52:05Z | - |
dc.date.available | 2022-08-04 | |
dc.date.copyright | 2020-08-11 | |
dc.date.issued | 2020 | |
dc.date.submitted | 2020-08-05 | |
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dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/78341 | - |
dc.description.abstract | 近年來,基於變分量子電路(VQC)的機器學習算法已在函數逼近,分類和深度強化學習中獲得成功。 在這項工作中,我們將VQC的功能擴展到了求解常微分方程(ODE)和偏微分方程(PDE)的領域。 在這項工作中,我們使用一種量子資訊編碼方法將古典資料準備成量子態,以供量子電路學習微分方程解。 所提出的框架可以在許多近期有噪聲的中尺度量子(NISQ)設備中實現,因此對於量子計算機在科學計算中的應用具有價值。 | zh_TW |
dc.description.abstract | Recently, machine learning algorithms based on variational quantum circuits (VQC) have been successful in function approximation, classification and deep reinforcement learning. In this work, we extend the capability of VQC to the domain of solving ordinary differential equations (ODE) and partial differential equations (PDE). In this work, we use a quantum information encoding method to prepare classical values into quantum states for a quantum circuit to learn the differential equation solutions. The proposed framework can be implemented in many near-term noisy intermediate scale quantum (NISQ) devices and therefore is invaluable for the application of quantum computers in scientific computing. | en |
dc.description.provenance | Made available in DSpace on 2021-07-11T14:52:05Z (GMT). No. of bitstreams: 1 U0001-0108202018582600.pdf: 2985939 bytes, checksum: 2516e6a96304d7a741a4effcaee93943 (MD5) Previous issue date: 2020 | en |
dc.description.tableofcontents | 誌謝 I 摘要 II Abstract III List of Figures VII List of Tables IX 1 Introduction 1 1.1 overview of thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 Machine learning and Quantum computation 5 2.1 Machine learning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.1 Deep neural network . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.2 Convolutional neural network . . . . . . . . . . . . . . . . . . 9 2.1.3 Unsupervised deep learning . . . . . . . . . . . . . . . . . . . 10 2.1.4 Support vector machine . . . . . . . . . . . . . . . . . . . . . 10 2.2 Neural networks for solving differential equations . . . . . . . . . . . 11 2.2.1 Introduction to surrogate model and its relation to differential equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2.2 Neural network as a surrogate model . . . . . . . . . . . . . . 12 2.3 Introduction and overview of quantum computation . . . . . . . . . . 15 2.3.1 Quantum bits . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3.2 Quantum computation . . . . . . . . . . . . . . . . . . . . . . 20 2.4 Quantum machine learning, Variational quantum circuit and its applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.4.1 Introduction to Quantum machine learning . . . . . . . . . . . 24 2.4.2 Key concepts of quantum machine learning in Pennylane . . . 26 2.5 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3 Methods 36 3.1 Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.2 Optimization method . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.2.1 Some applications on variational quantum circuit . . . . . . . 39 3.3 Quantum circuit architecture and its ability to approximate a function 40 3.4 Quantum circuit expressibility and entangling capability . . . . . . . 43 3.5 Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.6 Optimization Procedure . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.7 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4 Results 52 4.1 Simulation results without noise model . . . . . . . . . . . . . . . . . 52 4.1.1 Ordinary Differential Equations . . . . . . . . . . . . . . . . . 52 4.1.2 Partial Differential Equations . . . . . . . . . . . . . . . . . . 58 4.2 Simulation with noise model . . . . . . . . . . . . . . . . . . . . . . . 63 4.2.1 IBMQ 5-qubit machine rome . . . . . . . . . . . . . . . . . . . 63 4.3 IBMQ real device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.3.1 IBMQ rome . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.3.2 IBMQ 16 melbourne . . . . . . . . . . . . . . . . . . . . . . . 68 4.4 Chapter summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 5 Conclusion 75 5.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 5.1.1 Performance Analysis and possible quantum advantage . . . . 75 5.1.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 5.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 Bibliography 78 | |
dc.language.iso | en | |
dc.title | 量子神經網路求解微分方程 | zh_TW |
dc.title | Quantum Neural Networks for Solving Differential Equations | en |
dc.type | Thesis | |
dc.date.schoolyear | 108-2 | |
dc.description.degree | 碩士 | |
dc.contributor.oralexamcommittee | 林俊達(Guin-Dar Lin),張慶瑞(Ching Ray Chang),陳俊瑋(Jiunn-Wei Chen) | |
dc.subject.keyword | 變分量子電路,機器學習,深度學習,有噪聲的中尺度量子設備, | zh_TW |
dc.subject.keyword | variational quantum circuits,machine learning,deep learning,noise intermediate scale quantum device(NISQ), | en |
dc.relation.page | 83 | |
dc.identifier.doi | 10.6342/NTU202002201 | |
dc.rights.note | 有償授權 | |
dc.date.accepted | 2020-08-06 | |
dc.contributor.author-college | 理學院 | zh_TW |
dc.contributor.author-dept | 應用物理研究所 | zh_TW |
顯示於系所單位: | 應用物理研究所 |
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