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研究生： 劉洪生
Liu, Hung-Sheng
論文名稱： 量子神經網路中Ansatz架構對模型表現之效應
The Effects of Ansatz Architecture on the Performance of Quantum Neural Networks
指導教授： 陳宏斌
Chen, Hong-Bin
學位類別： 碩士
Master
系所名稱： 工學院 - 工程科學系
Department of Engineering Science
論文出版年： 2026
畢業學年度： 114
語文別： 英文
論文頁數： 83
中文關鍵詞： 量子神經網路 、參數化量子電路 、Ansatz 架構 、量子資訊 、量子操縱性
外文關鍵詞： Quantum neural networks, Parameterized quantum circuits, Ansatz architecture, Quantum information, Quantum steering
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    • 隨著量子計算與量子機器學習的發展，如何設計合適的參數化量子電路已成為量子神經網路中的重要問題。量子神經網路的學習能力不只取決於參數數量，也會受到ansatz 架構、電路深度、耦合方式與量子態空間中有效參數方向的影響。因此，如何理解不同ansatz 架構對模型表現的影響，是近程量子機器學習中值得研究的問題。
    本論文以雙量子位元態的量子操縱性問題作為迴歸任務，研究ansatz架構對量子神經網路表現的影響。模型的輸入為與量子操縱性相關的特徵表示，預測目標為透過半正定規劃程序產生的最大可操縱權重。在固定的學習框架下，本研究比較由不同局域旋轉、耦合區塊、連接方式與電路層數所形成的ansatz架構。
    本研究以迴歸表現評估訓練後的模型，並進一步透過expressibility、entangling power、量子費雪資訊矩陣（QFIM）秩與梯度變異數來描述不同電路架構的性質。這些觀察量用來連結模型的預測行為與ansatz的量子態生成能力、有效參數方向及可訓練性。
    結果顯示，增加電路深度可以提升量子神經網路的表現，但提升幅度會受到ansatz 架構明顯影響。即使參數成長方式相近，不同電路仍可能呈現不同的有效參數方向、可訓練性與預測表現。特別是當QFIM秩達到飽和後，額外增加的層數不一定提供新的獨立方向，但超參數化仍可能影響最佳化過程，使模型表現緩慢提升。整體而言，本研究顯示有效的ansatz需要在表達能力、糾纏生成能力、有效參數方向與可訓練性之間取得合適的平衡。

    With the development of quantum computing and quantum machine learning, the design of suitable parameterized quantum circuits has become an important issue in quantum neural networks (QNNs). The learning performance of a QNN is not determined only by the number of rainable parameters, but can also depend on the ansatz architecture, circuit depth, coupling structure, and effective parameter directions in the quantum state space. Understanding how different ansatz architectures affect model performance is therefore an important roblem for near-term quantum machine learning.
    This dissertation uses a quantum steering problem of qubit-pair states as a regression task to study the effect of ansatz architecture on QNN performance. The input data are steering-related feature representations, and the learning target is the ground-truth maximum steerable weight generated by a semidefinite programming-based procedure. Under a fixed learning framework, different ansatz architectures are compared by changing the local rotation blocks, coupling blocks, connectivity patterns, and circuit depths.
    The trained models are evaluated by their regression performance, and the circuit architectures are further characterized using expressibility, entangling power, quantum Fisher information matrix (QFIM) rank, and gradient variance. These quantities are used to connect the observed prediction behavior with the state generation ability, effective parameter directions, and trainability of each ansatz.
    The results show that increasing circuit depth can improve QNN performance, but the improvement is strongly dependent on the ansatz architecture. Circuits with similar parameter growth can exhibit different ffective parameter directions, trainability, and prediction performance. In particular, QFIM-rank saturation in dicates that additional layers do not always introduce new independent directions, while overparameterization may still influence optimization and allow gradual performance improvement. Overall, the results suggest that an effective ansatz should balance expressibility, entangling power, effective parameter directions, and trainability.

    ABSTRACT i ABSTRACT (CHT) iii ACKNOWLEDGEMENT iv Contents v List of Figures vii Chapter I Introduction 1 I. I Quantum Machine Learning 1 I. II Ansatz Architecture in Quantum Neural Networks 3 I. III Quantum Correlations 3 I. IV Research Motivation 7 Chapter II Theoretical Background 9 II. I Quantum Neural Networks 9 II. II Entanglement and Entangling Power 11 II. III Expressibility 14 II. IV Quantum Fisher Information Matrix 16 II. V Trainability and Barren Plateau 19 Chapter III Quantum Steering Regression Task 21 III. I Theoretical Background of Quantum Steering 21 III. II Dataset Construction for the Learning Task 25 Chapter IV Methodology 31 IV. I QNN Regression Model 31 IV. II Training Procedure 36 IV. III Evaluation Metrics 39 IV. IV Ansatz Architectures 39 IV. V Numerical Experiments for Ansatz Architectures 43 Chapter V Effects of Ansatz Architecture on QNN Performance 48 V. I Effect of Circuit Depth on Prediction Performance 48 V. II Entangling Power and Expressibility Analysis 49 V. III QFIM Rank and Overparameterization 53 V. IV Gradient Variance and Trainability 55 V. V Summary of Architecture–Performance Relationship 58 Chapter VI Conclusion 66 VI. I Conclusion 66 VI. II Contributions 67 VI. III Limitations and Future Work 68 Reference 68

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