发表机构
Yonsei University（延世大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本论文研究量子计算与人工智能的双向交叉，提出神经量子嵌入和Mamba解码器等方法，分别提升量子机器学习性能与量子系统解码效率，并揭示表示学习与统计控制的关键作用。
AI 中文摘要
本论文从两个方向研究量子计算与人工智能的交叉领域：用于机器学习的量子方法和用于量子系统的机器学习方法。在量子机器学习方面，神经量子嵌入学习数据表示，以增加嵌入类别集合之间的迹距离，从而降低依赖于嵌入的经验风险上界，并在有噪声的量子硬件上改善分类性能。基于希尔伯特-施密特内积的训练目标将该方法扩展到单量子比特确定性量子计算（DQC1），并在核磁共振量子处理器上进行了演示。随后，基于间隔的泛化分析将量子神经网络性能与量子态判别联系起来。在所研究的基准测试中，间隔分布比参数计数指标更能可靠地预测泛化性能。对于量子系统，一种基于Mamba的表面码神经解码器在记忆实验中匹配了复现的Transformer基线，同时将推理成本缩放从码距离的四次方降低到二次方。在显式解码器诱导噪声模型下，它实现了更低的逻辑错误率和更高的有效阈值。对于神经量子态，随机重构被解释为切空间岭回归，其对角位移在有限蒙特卡洛采样下控制偏差-方差权衡。与固定位移SR相比，多位移随机重构降低了检查点局部验证残差和更新方差，但增加了额外计算成本。总之，这些贡献展示了学习表示、统计控制和硬件约束如何塑造量子计算与机器学习之间的交流。
英文摘要
This thesis studies the intersection of quantum computing and artificial intelligence in two directions: quantum methods for machine learning and machine learning methods for quantum systems. For quantum machine learning, Neural Quantum Embedding learns data representations that increase the trace distance between embedded class ensembles, lowering an embedding-dependent bound on empirical risk and improving classification on noisy quantum hardware. A training objective based on the Hilbert-Schmidt inner product extends this approach to deterministic quantum computation with one qubit (DQC1) and is demonstrated on an NMR quantum processor. A margin-based generalization analysis then connects quantum neural network performance to quantum state discrimination. In the studied benchmarks, margin distributions predict generalization more reliably than parameter-count metrics. For quantum systems, a Mamba-based neural decoder for surface codes matches a reproduced Transformer baseline in memory experiments while reducing inference-cost scaling from quartic to quadratic in code distance. Under an explicit decoder-induced-noise model, it achieves lower logical error rates and a higher effective threshold. For neural quantum states, stochastic reconfiguration is interpreted as tangent-space ridge regression, with its diagonal shift controlling the bias-variance trade-off under finite Monte Carlo sampling. Multi-shift stochastic reconfiguration reduces checkpoint-local validation residuals and update variance relative to fixed-shift SR, at additional computational cost. Together, these contributions show how learned representations, statistical control, and hardware constraints shape the exchange between quantum computing and machine learning.
Comments171 pages, 28 figures, PhD thesis
