請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/98651完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 黃鐘揚 | zh_TW |
| dc.contributor.advisor | Chung-Yang Huang | en |
| dc.contributor.author | 郭亦翔 | zh_TW |
| dc.contributor.author | Y i-Hsiang Kuo | en |
| dc.date.accessioned | 2025-08-18T01:13:25Z | - |
| dc.date.available | 2025-08-18 | - |
| dc.date.copyright | 2025-08-15 | - |
| dc.date.issued | 2025 | - |
| dc.date.submitted | 2025-08-06 | - |
| dc.identifier.citation | [1] S. Aaronson and D. Gottesman. Improved simulation of stabilizer circuits. Physical Review A—Atomic, Molecular, and Optical Physics, 70(5):052328, 2004.
[2] M. Amy, P. Azimzadeh, and M. Mosca. On the cnot-complexity of cnot-phase circuits. arXiv preprint arXiv:1712.01859, 2017. [3] M. Amy, O. Bennett-Gibbs, and N. J. Ross. Symbolic synthesis of clifford circuits and beyond. arXiv preprint arXiv:2204.14205, 2022. [4] M. Amy, D. Maslov, and M. Mosca. Polynomial-time t-depth optimization of clifford+ t circuits via matroid partitioning. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 33(10):1476–1489, 2014. [5] M. Amy, D. Maslov, M. Mosca, and M. Roetteler. A meet-in-the-middle algorithm for fast synthesis of depth-optimal quantum circuits. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 32(6):818–830, 2013. [6] M. Backens. The zx-calculus is complete for stabilizer quantum mechanics. New Journal of Physics, 16(9):093021, 2014. [7] S. Bravyi, R. Shaydulin, S. Hu, and D. Maslov. Clifford circuit optimization with templates and symbolic pauli gates. Quantum, 5:580, 2021. [8] N. de Beaudrap, X. Bian, and Q. Wang. Fast and effective techniques for t-count reduction via spider nest identities. arXiv preprint arXiv:2004.05164, 2020. [9] T. G. De Brugière, M. Baboulin, B. Valiron, S. Martiel, and C. Allouche. Gaussian elimination versus greedy methods for the synthesis of linear reversible circuits. ACM Transactions on Quantum Computing, 2(3):1–26, 2021. [10] R. Duncan, A. Kissinger, S. Perdrix, and J. Van De Wetering. Graph-theoretic simplification of quantum circuits with the zx-calculus. Quantum, 4:279, 2020. [11] R. Duncan and S. Perdrix. Graph states and the necessity of euler decomposition. In Conference on Computability in Europe, pages 167–177. Springer, 2009. [12] T. Foesel, M. Y. Niu, F. Marquardt, and L. Li. Reinforcement learning for quantum circuit optimization. In APS March Meeting Abstracts, volume 2021, pages F34–010, 2021. [13] Y. Ge, W. Wenjie, C. Yuheng, P. Kaisen, L. Xudong, Z. Zixiang, W. Yuhan, W. Ruocheng, and Y. Junchi. Quantum circuit synthesis and compilation optimization: Overview and prospects. arXiv preprint arXiv:2407.00736, 2024. [14] L. E. Heyfron and E. T. Campbell. An efficient quantum compiler that reduces t count. Quantum Science and Technology, 4(1):015004, 2018. [15] A. Jamiołkowski. Linear transformations which preserve trace and positive semidefiniteness of operators. Reports on mathematical physics, 3(4):275–278, 1972. [16] A. Javadi-Abhari, M. Treinish, K. Krsulich, C. J. Wood, J. Lishman, J. Gacon, S. Martiel, P. D. Nation, L. S. Bishop, A. W. Cross, B. R. Johnson, and J. M. Gambetta. Quantum computing with Qiskit, 2024. [17] A. Kissinger and J. Van De Wetering. Reducing the number of non-clifford gates in quantum circuits. Physical Review A, 102(2):022406, 2020. [18] M.-T. Lau, C.-Y. Cheng, C.-H. Lu, C.-H. Chuang, Y.-H. Kuo, H.-C. Yang, C.-T. Kuo, H.-Y. Chen, C.-Y. Tung, C.-E. Tsai, et al. Qsyn: A developer-friendly quantum circuit synthesis framework for nisq era and beyond. In 2024 IEEE International Conference on Quantum Computing and Engineering (QCE), volume 2, pages 535– 536. IEEE, 2024. [19] M.-T. Lau, H.-C. Yang, H.-Y. Chen, and C.-Y. R. Huang. A lazy resynthesis approach for simultaneous t gate and two-qubit gate optimization of quantum circuits. Manuscript under review, 2025. [20] G. Li, Y. Ding, and Y. Xie. Tackling the qubit mapping problem for nisq-era quantum devices. In Proceedings of the twenty-fourth international conference on architectural support for programming languages and operating systems, pages 1001–1014, 2019. [21] S. Martiel and T. G. De Brugière. Architecture aware compilation of quantum circuits via lazy synthesis. Quantum, 6:729, 2022. [22] D. Maslov, G. W. Dueck, and D. M. Miller. Techniques for the synthesis of reversible toffoli networks. ACM Transactions on Design Automation of Electronic Systems (TODAES), 12(4):42–es, 2007. [23] D. Maslov and M. Roetteler. Shorter stabilizer circuits via bruhat decomposition and quantum circuit transformations. IEEE Transactions on Information Theory, 64(7):4729–4738, 2018. [24] G. Meuli, M. Soeken, M. Roetteler, N. Bjorner, and G. De Micheli. Reversible pebbling game for quantum memory management. In 2019 Design, Automation & Test in Europe Conference & Exhibition (DATE), pages 288–291. IEEE, 2019. [25] G. Meuli, M. Soeken, M. Roetteler, and G. De Micheli. Ros: Resource-constrained oracle synthesis for quantum computers. arXiv preprint arXiv:2005.00211, 2020. [26] Y. Nam, N. J. Ross, Y. Su, A. M. Childs, and D. Maslov. Automated optimization of large quantum circuits with continuous parameters. npj Quantum Information, 4(1):23, 2018. [27] T. Peham, N. Brandl, R. Kueng, R. Wille, and L. Burgholzer. Depth-optimal synthesis of clifford circuits with sat solvers. In 2023 IEEE International Conference on Quantum Computing and Engineering (QCE), volume 1, pages 802–813. IEEE, 2023. [28] F. J. Ruiz, T. Laakkonen, J. Bausch, M. Balog, M. Barekatain, F. J. Heras, A. Novikov, N. Fitzpatrick, B. Romera-Paredes, J. van de Wetering, et al. Quantum circuit optimization with alphatensor. Nature Machine Intelligence, pages 1–12, 2025. [29] S. Schneider, L. Burgholzer, and R. Wille. A sat encoding for optimal clifford circuit synthesis. In Proceedings of the 28th Asia and South Pacific Design Automation Conference, pages 190–195, 2023. [30] W. Simmons. Relating measurement patterns to circuits via pauli flow. arXiv preprint arXiv:2109.05654, 2021. [31] J. van de Wetering, R. Yeung, T. Laakkonen, and A. Kissinger. Optimal compilation of parametrised quantum circuits. arXiv preprint arXiv:2401.12877, 2024. [32] V. Vandaele. Lower t-count with faster algorithms. arXiv preprint arXiv:2407.08695, 2024. [33] V. Vandaele, S. Martiel, and T. G. de Brugière. Phase polynomials synthesis algorithms for nisq architectures and beyond. Quantum Science and Technology, 7(4):045027, 2022. [34] V. Vandaele, S. Martiel, S. Perdrix, and C. Vuillot. Optimal hadamard gate count for clifford+ t synthesis of pauli rotations sequences. ACM Transactions on Quantum Computing, 5(1):1–29, 2024. [35] F. Zhang and J. Chen. Optimizing t gates in clifford+ t circuit as π/4 rotations around paulis. arXiv preprint arXiv:1903.12456, 2019. | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/98651 | - |
| dc.description.abstract | 運算表（Tableau）是一種廣泛應用於量子電路最佳化技術的基礎表示方式，不僅支援相位合併策略，亦可應用於相位多項式最佳化方法，進一步降低小角度旋轉閘的使用量。然而，此類方法在合成階段常將運算表拆解為多個區段處理，導致額外的雙量子位元閘（如 CX）被引入，進而造成顯著的閘數開銷。 為了解決此問題，我們提出一種統一式的包立旋轉運算表合成技術，將分散的運算表區段整合為單一結構，並採用一種全域考量雙量子位元閘成本的合成方法，有效降低額外的 CX 閘使用。實驗結果顯示，相較於現有的技術，我們的方法在不同基準電路上分別可減少 45.93% 與 32.10% 的雙量子位元閘數量。 | zh_TW |
| dc.description.abstract | Tableau representations serve as a widely applicable foundation for various quantum circuit optimization (QCO) techniques, supporting not only phase-merging strategies but also phase-polynomial-like optimization methods that enable further T-count reduction. However, by decomposing the tableau into separate pieces, such methods often introduce redundant double-qubit gates—such as CXs—during synthesis, resulting in substantial CX-count overhead. To address this, we propose a unified Pauli-rotation synthesis technique that merges fragmented tableau pieces into a single structure and employs a CX-efficient holistic synthesis method. This approach significantly mitigates redundant CX gates during synthesis. Experimental results show that our method reduces CX count by 45.93% and 32.10% compared to state-of-the-art techniques across different benchmark sets. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2025-08-18T01:13:25Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2025-08-18T01:13:25Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | Acknowledgements i
摘要 iii Abstract iv Contents v List of Figures viii List of Tables ix List of Algorithms x Denotations xi Chapter 1 Introduction 1 1.1 Quantum Circuit Optimization . . . . . . . . . . . . . . . . . . . . . 1 1.2 Tableau-based QCO . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Motivation and Problem Statement . . . . . . . . . . . . . . . . . . 3 1.4 Thesis Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.5 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Chapter 2 Preliminaries 7 2.1 Basics of Quantum Circuits . . . . . . . . . . . . . . . . . . . . . . 7 2.2 From Quantum Circuit Synthesis to Optimization . . . . . . . . . . . 12 2.3 Tableau Representations . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3.1 Stabilizer States and Stabilizer Tableaux . . . . . . . . . . . . . . . 15 2.3.2 Pauli Rotations and Pauli Rotation Tableaux: . . . . . . . . . . . . 19 2.3.3 Diagonal Rotations and Phase Polynomials: . . . . . . . . . . . . . 22 Chapter 3 Problem Description 24 3.1 Tableau-Based QCO Flow . . . . . . . . . . . . . . . . . . . . . . . 24 3.1.1 Convert Quantum Circuit to Tableau . . . . . . . . . . . . . . . . . 25 3.1.2 Phase Merging Optimization . . . . . . . . . . . . . . . . . . . . . 26 3.1.3 Phase-Polynomial-Like T-count Optimization . . . . . . . . . . . . 29 3.1.4 Tableau Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.2 Limitations of Current Tableau Synthesis Method . . . . . . . . . . . 37 3.2.1 From Scattered Tableau Segments to Global Synthesis . . . . . . . 37 3.2.2 Barriers to Unified Tableau Synthesis . . . . . . . . . . . . . . . . 38 Chapter 4 Proposed Algorithm 41 4.1 Overview of the Proposed Method . . . . . . . . . . . . . . . . . . . 41 4.2 Detailed Description of the pMST Routine . . . . . . . . . . . . . . 43 4.2.1 Constructing the Dependency Graph . . . . . . . . . . . . . . . . . 44 4.2.2 Scheduling Target Rotations . . . . . . . . . . . . . . . . . . . . . 45 4.2.3 Synthesizing Rotations via a Global‐Cost MST Heuristic . . . . . . 46 4.3 Synthesizing the Residual Stabilizer Tableau . . . . . . . . . . . . . 52 Chapter 5 Experiment Results 56 5.1 Setup and Benchmark selection . . . . . . . . . . . . . . . . . . . . 56 5.2 Comparison within the Phase-Polynomial-Like Flow . . . . . . . . . 60 5.3 Comparison within the Phase-merging Optimization Flow . . . . . . 66 5.4 Comparison between Different QCO Schemes . . . . . . . . . . . . 70 Chapter 6 Contribution and Future Work 73 6.1 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 6.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 References 76 Appendix A — Clifford Propagation 81 | - |
| dc.language.iso | en | - |
| dc.subject | 量子計算 | zh_TW |
| dc.subject | 量子電路最佳化 | zh_TW |
| dc.subject | 穩定子運算表 | zh_TW |
| dc.subject | 包立旋轉運算表 | zh_TW |
| dc.subject | MST 啟發式演算法 | zh_TW |
| dc.subject | Stabilizer Tableau | en |
| dc.subject | Quantum Computing | en |
| dc.subject | Quantum Circuit Optimization | en |
| dc.subject | MST-based Heuristic | en |
| dc.subject | Pauli Rotation Tableau | en |
| dc.title | 以一體化包立旋轉合成法降低基於運算表之量子電路最佳化流程中之雙量子邏輯閘增量 | zh_TW |
| dc.title | Unified Pauli-Rotation Synthesis for Relieving CX-Count Overhead in Tableau-Based Quantum Circuit Optimization Flow | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 113-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 江介宏;鄭皓中;洪士涵;邱大維 | zh_TW |
| dc.contributor.oralexamcommittee | Jie-Hong Jiang;Hao-Chung Cheng;Shih-Han Hung;Dah-Wei Chiou | en |
| dc.subject.keyword | 量子計算,量子電路最佳化,穩定子運算表,包立旋轉運算表,MST 啟發式演算法, | zh_TW |
| dc.subject.keyword | Quantum Computing,Quantum Circuit Optimization,Stabilizer Tableau,Pauli Rotation Tableau,MST-based Heuristic, | en |
| dc.relation.page | 82 | - |
| dc.identifier.doi | 10.6342/NTU202503794 | - |
| dc.rights.note | 同意授權(限校園內公開) | - |
| dc.date.accepted | 2025-08-11 | - |
| dc.contributor.author-college | 電機資訊學院 | - |
| dc.contributor.author-dept | 電子工程學研究所 | - |
| dc.date.embargo-lift | 2030-08-04 | - |
| 顯示於系所單位： | 電子工程學研究所 | |
文件中的檔案：
| 檔案 | 大小 | 格式 | |
|---|---|---|---|
| ntu-113-2.pdf 未授權公開取用 | 8.77 MB | Adobe PDF | 檢視/開啟 |
系統中的文件，除了特別指名其著作權條款之外，均受到著作權保護，並且保留所有的權利。